Error Quantification of Topographic Index in Relation to Terrain Condition and Grid Spacing

Transcription

1 Error Quantification of Topographic Index in Relation to Terrain Condition and Grid Spacing Samadrita Adhikari January, 2008 i

2 Error Quantification of Topographic Index in Relation to Terrain Condition and Grid Spacing by Samadrita Adhikari Thesis submitted to the International Institute for Geo-information Science and Earth Observation in partial fulfilment of the requirements for the degree of Master of Science in Geoinformation Science and Earth Observation, Specialisation: Geoinformatics Thesis Assessment Board Chairman: Prof. Dr. Ir. Alfred Stein External Expert: Dr. P.K. Garg IIRS Member: Mr. Ashutosh Bharatdwaj Dr. C. Jeganathan Mrs. Shefali Agrawal Thesis Supervisor ITC : Dr. Klaus Tempfli IIRS: Mr. Ashutosh Bharatdwaj INTERNATIONAL INSTITUTE FOR GEO-INFORMATION SCIENCE AND EARTH OBSERVATION ENSCHEDE, THE NETHERLANDS (ITC) & INDIAN INSTITUTE OF REMOTE SENSING, NATIONAL REMOTE SENSING AGENCY (NRSA) DEPARTMENT OF SPACE, GOVT. OF INDIA, DEHRADUN, INDIA ii

3 Disclaimer This document describes work undertaken as part of a programme of study at the International Institute for Geo-information Science and Earth Observation. All views and opinions expressed therein remain the sole responsibility of the author, and do not necessarily represent those of the institute. iii

4 Dedicated To My Parents iv

5 Abstract Digital Terrain Model provides the basic information about the terrain relief. DTM are subjected to different types of errors. The information required to characteristics the terrain relief are derived from DTM in terms of primary and secondary attribute. Topographic Index(x,y) is an important terrain attribute which is required for hydrological modelling. It computed from specific catchment area of a point and down slope. The algorithm of TI is α Ln ( ). Hence TI is very important for hydrological modelling. The variation of TI calculation tan β effect the outcome of the model prediction. Hence, the accuracy assessment of Topographic Index generation is necessary.in order to do this; the current study has attempted to develop a method for prediction of TI accuracy considering the prime influencing factor. The different factors which affect the accuracy of Topographic Index were identified, namely grid spacing of DTM, roughness of the terrain, systematic error of DTM, improper delineation of drainage basin, random errors of elevation values of the DTM, gross error of DTM (including the effect of not filtering a DSM to a DTM), the algorithm used for computing slope from a DEM, and the TI generation algorithm. Within those factors only the first 4 factors were empirically evaluated in this study. The study was carried out over the Western Dehradun terrain using Cartosat-1 stereo data. Five drainage basins with different roughness characteristics were taken into account. We computed for each catchment DEM s of different grid spacing derived the TI for all and validated with respect to reference data (10m resolution TI). Four methods were used for accuracy assessment of TI. It has been found that mean of TI increases with grid spacing and it is become more erroneous in the rough terrain. A behavioral dissimilarity between DEM and TI was found. The mean of TI increases with spacing but the mean elevation remains constant. The systematic error of DEM not only effect the horizontal accuracy but can also have an inclination effect on surface model which influence the accuracy of TI. It was also found that improper catchment delineation makes significant changes on upslope area computation which affects the accuracy of TI. Finally the ruggedness of the terrain has been quantified for different terrain and established a relationship with TI RMSE for predicting the accuracy of TI with respect to roughness of terrain and DEM spacing. Although the R-square value is not very high (0.49), the study suggest that prediction of TI accuracy is feasible and it is more certain for rough terrain. v

6 Acknowledgements I take this opportunity towards my sincere thanks to Dr. V.K. Dadhwal, Dean, IIRS, for all the necessary support during the course work and for all the facilities in IIRS. I am also thankful to Mr. P.L.N. Raju, In charge, Geo-Informatics Division for his moral support, encouragement, and guidance for improvement during the research work. Words are inadequate to convey the gratitude to my ITC supervisor, Dr. Klaus Tempfli, EOS division, ITC. It is my proud privilege to express my deep sense of gratitude to him for his timely advice, support, comments, guidance and encouragement through out my research period. His valuable guidance and critical comments rendered for the improvement, which has contributed to the successful completion of this thesis. My sincere thanks to my IIRS supervisor, Mr.Ashutosh Bharatdwaj, PRS division, for his ever enthusiastic spirit, constant support and suggestion during the research period. I am extremely grateful to Dr. C. Jeganathan, Course coordinator, MSc. Geoinformatics, IIRS for his motivation, support and guidance throughout this period. I am also specially thankful to Mr. Ram Mohan Rao, Mr. Praveen Thakur, Mrs. Shefali Agrawal and Dr. V. Hariprasad for all the help provided by them. I am also grateful to Mr. Bhaskar and Mr. Avdesh for the help and assistance provided by them. I am also thankful to my friends Mr. Anil Rawat, Mr. Subrata Nandi and Mr. Tushar Zanje for their help during the research. I am indebted to my Father and Mother for taking care of me and for giving me constant encouragement and support without which I would not have been able to come this far. vi

7 Table of contents 1. Introduction General introduction Problem definition and Motivation: Objective of the Research: Research Questions: Primary research questions: Secondary research Questions: Structure of the thesis: Theoretical background & literature review Topographic index and TOPMODEL: Algorithm for generation of topographic index: Topographic Index and sensitivity of hydrological computation: Sensitivity of Topographic Index to DEM resolution: DTM uncertainty and accuracy of topographic index: Spatial autocorrelation of Topographic index: Terrain ruggedness and topographic index: Study Area and Material Used Important of the study area in the present study: Geographical Location: Description of the study area: Landcover information of selected catchments: Study area selection: Terrain selection: Basin / Catchment selection: Data used: Satellite data: Ground survey data: Ancillary Data: Experimental Investigation Reference Data Generation: DGPS Survey: Post Processing of the GPS data: Generation of DSM using Cartosat-1 stereo data: Removal of Blunders from DSM Selection of the Study Area: Selection of the Basin: Selection of terrain based on ness: Derivation of Topographic Index: Spatial Autocorrelation of Topographic Index: Accuracy Assessment of Topographic Index: Method 1 (Location wise Comparison): Method 2 (Areal Mean Based Comparison): Method 3 (Detail RMSE Method):...31 vii

8 4.6. Quantification of terrain ruggedness: Moran s I Autocorrelation Index: Mean and Variance of Slope: Terrain ness Index (TRI): Laplace Filter: Normalize Laplace filter: Results and Discussion Effect of DEM Grid Spacing and Terrain Roughness on accuracy of Topographic Index: Effect of grid spacing on the accuracy of topographic index: Method-1 (Location wise comparison): Method-2 (Areal mean basis comparison): Method -3 (Detailed RMSE computation method): Effect of Grid Spacing on the Accuracy of Slope: Relation between DEM accuracy and accuracy of Topographic index: Effect of Systematic Error on the accuracy of Topographic index: Effect of incomplete catchment area on the accuracy of Topographic index: Relevance of DSM filtering for the Topographic index generation: Quantification of Terrain ness: Moran s I Autocorrelation Index: Mean and Variance of Slope: Terrain ness Index (TRI): Laplace Operator: Normalize Laplace : Development of method for predicting the accuracy of topographic index with respect to terrain ruggedness and grid spacing: Conclusion and Recommendation...69 References:...72 Appendix...75 Appendix Appendix Appendix Appendix Appendix Appendix Appindix Appendix Appendix viii

9 List of figures Figure 3-1: Location of the study area...13 Figure 3-2: Schematic representation of study area selection procedure Figure 3-3: % of area under each slope class...16 Figure 3-4: % of area within curvature class...17 Figure 3-5: Cross profile of different catchment showing the variation of terrain relief Figure 4-1: Schematic representation of reference data generation Figure 4-2: Removal of blunders from DSM...24 Figure 4-3: Derivation of flow directions...24 Figure 4-4: Curvature computation...26 Figure 4-5: Implementation of FCN algorithm...27 Figure 4-6: Customize Model of Topographic Index...28 Figure 4-7: Schematic representation of accuracy assessment of TI using location wise comparison..29 Figure 4-8 : (a) TI 10 m, (b) TI 30 m, (c) Mean of 10 m TI block, (d) difference between b & c. Representation of areal mean based comparison method...30 Figure 4-9: Schematic representation of accuracy assessment of TI using detailed RMSE method...31 Figure 4-10: Kernel of TRI...32 Figure 4-11: Kernel of Laplace Filter...32 Figure 5-1: Topographic Index computed from 10 m to 150 m DEM...34 Figure 5-2: shows the drainage network of the Highly Basin...35 Figure 5-3: Moran s I index plotted against grid spacing Figure 5-4: Mean of TI Figure 5-5: Mean of Slope...36 Figure 5-6: Relationship between DEM resolution and Mean of topographic index considering (10 m to 150 m resolution)...37 Figure 5-7: Relationship between DEM resolution and Mean of topographic index considering (10 m to 90 m resolution)...38 Figure 5-8 (a) & (b): Effect of grid spacing on accuracy of TI...41 Figure 5-9: Grid spacing and Relation between RMSE Figure 5-10: RMSE of TI (areal mean method)...44 Figure 5-11: Mean error of TI (areal mean method)...44 Figure 5-12: RMSE (detailed RMSE method)...45 Figure 5-13: Mean error (detailed RMSE method)...45 Figure 5-14: Relation between RMSE and Grid spacing...46 Figure 5-15: Standard Error of TI...47 Figure 5-16: RMSE of slope (Method a)...48 Figure 5-17: RMSE of slope (Method b)...48 Figure 5-18: RMSE of slope (Method c)...49 Figure 5-19: (a) Mean error of Method-1, (b) Mean error of method-2 and (c) Mean error of Method Figure 5-20: effect of grid spacing on RMSE of DEM; (a) method 1, (b) method 2 and (c) method 3.51 Figure 5-21: Mean elevation of DEM at different resolution...52 Figure 5-22: Terrain specific relationship between RMSE of DEM and RMSE of TI Figure 5-23: Relation between DEM RMSE and RMSE of TI...53 Figure 5-24: Inclination due to systematic error...55 ix

10 Figure 5-25 : (a) RMSE of TI and 5.25(b) RMSE of Slope...56 Figure 5-26: (a) RMSE of upslope area, (b) RMSE of TI, (c) ME of upslope area, (d) ME of TI (highly rugged catchment)...57 Figure 5-27: (a) RMSE of upslope area, (b) RMSE of TI, (c) ME of upslope area, (d) ME of TI ( Undulated catchment)...58 Figure 5-28: Moran s I index of different Terrain...60 Figure 5-29: Moran s I autocorrelation plot of five terrain with the function of lag spacing...61 Figure 5-30: Mean of Slope...62 Figure 5-31: Plot of variance of slope...63 Figure 5-32: Plot of Terrain ruggedness Index...63 Figure 5-33 Plot of r.m.s Laplace...65 Figure 5-34: Plot of r.m.s Laplace & mean TRI...65 Figure 5-35: Plot of r.m.s of normalize Laplace...66 Figure 5-36: Relation between terrain ruggedness (r.m.s. normalize Laplace and RMSE of TI)...67 Figure 5-37: Relation between terrain ruggedness (variance of slope and RMSE of TI) x

11 List of tables Table 2-1: Effect of DEM grid spacing on mean of TI and efficiency of TOPMODEL prediction....9 Table 2-2: Effect of DEM grid spacing on mean of topographic index...11 Table 3-1: Slope category...16 Table 3-2 : Classification of curvature Table 3-3: Description of different basin Table 5-1: Moran s I value of Topographic Index...35 Table 5-2 : Mean of Topographic index...36 Table 5-3: RMSE of TI (Location wise comparison)...41 Table 5-4: Mean error of TI (Location wise comparison)...41 Table 5-5: RMSE of TI (areal mean method)...43 Table 5-6: Mean error of TI (areal mean method)...43 Table 5-7: RMSE table (detailed RMSE method)...45 Table 5-8: Mean error table (detailed RMSE method)...45 Table 5-9: Standard Error of topographic index...47 Table 5-10: RMSE table of slope (Method a)...48 Table 5-11: RMSE table of slope (Method b)...48 Table 5-12: RMSE table of slope (Method c)...49 Table 5-13: RMSE of DEM & RMSE of TI...53 Table 5-14: Shift in RPC DEM...54 Table 5-15: Vertical errors in RPC DEM...55 Table 5-16 (a): Effect of systematic error on RMSE of slope and RMSE of TI...55 Table 5-17: Moran s I Index value...59 Table 5-18: Variance of slope...62 Table 5-19: Mean of TRI...63 Table 5-20: Laplace table...64 Table 5-21: Terrain ruggedness quantification using normalize Laplace operator Table 5-22: (a) TI RMSE with respect to the terrain ruggedness (r.m.s. normalize Laplace) and (b) TI RMSE with respect to the terrain ruggedness (variance of slope) xi

12 1. Introduction 1.1. General introduction Data quality assessment is an important issue in the field of geo-informatics. In order to extract information or prediction of any phenomena using geospatial modelling, input data set is always required. The outcomes of predictions depend on the accuracy of input data sets. A digital terrain model provides the basic information regarding the terrain relief. It is a quantitative representation of the Earth s surface and it is typically given in one of the three formats: grid DEM, elevation in a Triangular Irregular Network (TIN) and contour based storage structure. When a Digital Elevation Model (DEM) represents the Earth s surface including object height (tree height, building height etc.) it is often referred to as Digital Surface Model (DSM). A model of the bare Earth s surface is referred to as Digital Terrain Model (DTM). Like other spatial data sets a DTM is subject to different types of error such as gross errors during data collection, deficient orientation of stereo images (systematic error) when photogrammetrically determining elevation values, and some accidental or unknown combinations of mistakes (random error) which can not be avoided. The other issues related to DTM accuracy are grid spacing and interpolation techniques (Tempfli, K. 2000) Terrain relief influences gravity and the movement of water in a catchment and therefore it must be taken into account in hydrological modelling like flow path of the run-off, distribution of soil moisture and depth of the ground water level etc (Wolock et al. 1994). The information required to characterize the terrain relief can be derived from DTM in terms of primary and secondary attributes. The primary attributes, which can be derived from the DTM are slope, aspect, profile curvature and catchment area. The secondary attributes, which can be derived from a DTM are upslope area, topographic index, stream power index, radiation index and temperature index. Parameterizing the terrain relief into a mathematical representation of landscape determination of dominant terrain relief control on the hydrological response of a watershed remains an important research area. The topographic index is a popular means to hydrologists to parameterize terrain relief. It has been applied to different hydrologic studies and applications for water flow path estimation and moisture redistribution (Hjerdt et al. 2004). The topographic index has been introduced by Beven and Kirkby (1979) in their topography based watershed model (TOPMODEL) for characterizing the distribution of moisture status in a basin. The effect of terrain relief on watershed hydrology is represented in TOPMODEL as the spatial distribution of topographic index. The topographic index (TI) at a point is the ratio of 1

13 upslope area and local down slope. TI(x,y) is derived from a DTM. So, the error associated with the DTM affects the accuracy of topographic index (Peifa et al. 2006). We know from previous research that the accuracy of a DTM is most strongly influenced by the grid spacing of the DTM relative to terrain variability. The rougher a terrain the smaller the grid spacing has to be to achieve the same DTM accuracy. How is a derived attribute such as the TI affected by the grid spacing of the DTM and the terrain condition? 1.2. Problem definition and Motivation: TI(x,y) is an important terrain attribute which is required for hydrological modelling. It is a compound terrain attribute which is computed from specific catchment area of a point and the local slope (Schmidt et al. 2003). TI(x,y) reflects the spatial distribution of soil saturation (Beven and Kirkby 1979). It indicates the accumulated water flow at any point in a catchment. A high value of TI indicates the region has higher potential to be saturated (Raaflaub, 2006). A high value of upslope area / drainage area and low slope results in a high TI and hence a high probability of occurrence of soil α saturation. The TI of any location in a catchment is computed as Ln( ) where α (specific tan β catchment area) represents upslope area per unit contour length which means the area above a certain contour that contributes flow across the contour. For grid data, the contour length is equivalent to grid spacing, and tan β is the local down slope (Raaflaub et al. 2006). The specific catchment area (α) indicates the amount of water that can flow through the location. Basically two models of catchment hydrology have significant use of TI. TOPMODEL is based on the concept of variable contributing area for rainfall run-off generation in catchments (Cai et al. 2006) while the steady state model TOPOG examines the pattern of surface saturation (O Loughlin et al. 1986). The topographic index is used in TOPMODEL as surface which represents the estimation of the accumulation of flow at any point (Raaflaub et al. 2006). The spatial distribution of topographic index can be calculated for any cathment and is used for the prediction of source area, saturation excess overland flow, subsurface flow and computation of local water table depth at any point in the catchment (Quinn et al. 1991). The importance of the topographic index is: 1. To simulate surface saturation zone in natural catchment (O Loughlin et al. 1986) and mapping of field surface soil moisture (Tombul et al. 2007). 2. Topography based watershed run-off simulation (Wu et al. 2007). 3. Identifying the location of returning subsurface water using measurement of the topsoil moisture (Chappell et al. 2006). 4. To predict the spatial distribution of soil moisture (Quinn and Beven 1993). 5. Predicting the wetlands distribution along a climatic gradient (Merot et al. 2003). 2

14 Many studies used the topographic index since 1979 when Beven and Kirkby incorporated Topographic Index in the hydrological model (TOPMODEL). Modification has been done by hydrologists dealing with three types of topographic index: α Topographic Index: Ln ( ) which is also called wetness index or TOPMODEL topographic tan β index. α Soil topographic index: Log( ) where α is drainage area per unit contour length and T is the T tan β lateral transmissivity of soil. With the increase of soil transmissivity the topographic index value decreases and the probability of occurrence of soil saturation also decreases. But in compare to the variation of slope and aspect the variation of soil transmissivity is negligible (Merot et al. 2003). Vr Climato-topographic index: Log( ) Where T is the lateral transitivity of soil and Vr is volume tan β of annual precipitation (Merot et al. 2003). Climato-topographic index is useful to compare the topographic index of different climatic region. α Nevertheless, the TOPMODEL Topographic Index Ln( ) is important in the field of hydrology tan β and hydrologists are using it for various applications in recent years (Wu et al. 2007, Kakembo et al and Chappell et al. 2006). The accuracy assessment of topographic index is very important in hydrological modelling because it of the assumption that spatial distribution of topographic index approximates the spatial distribution of the depth to the water table and potentiality of soil saturation in catchments. Hence any variation in topographic index calculation affects the out come of the model prediction (Raaflaub et al. 2006). Hydrologists commonly assume that the topographic index is accurate enough and use it for modelling without much consideration of what the requirements are on the input DTM. The most important influencing factor of topographic index accuracy is expected to be grid spacing of DTM (Zhang et al. 1994) and terrain roughness. Topographic index has been used by different hydrologist considering different grid spacing DTM for their application in local and regional scale (Wu et al. 2007, Kumar et al. 2000). Grid spacing directly affect the calculation of upslope area as well as topographic index (Quinn et al. 1995). With the increase of DTM grid spacing the mean of topographic index is also increases which causes error in hydrologic prediction (Zhang et al. 1994). 3

15 Attempts have been made to examine the effect of DTM accuracy on the distribution of topographic index as well as TOPMODEL prediction using statistical indexes (Peifa et al. 2006), effect of different data capture procedure on topographic index generation (Schmidt et al. 2003), DTM resolution effects on the topographic index (Brasington et al. 1998), effect of uncertainty of various algorithms of slope and aspect computation on the topographic index (Raaflaub et al. 2006), DTM map scale and grid spacing on topography based watershed model (Wolock et al. 1994, Zhang et al. 1994) and comparison of different algorithm for topographic index computation (Pan et al. 2004). Quantification of spatial auto-correlation of topographic index in different catchment using Moran s I index has been demonstrated by Cai and Wang (Cai et al. 2006). Spatial autocorrelation depicts the existence of spatial correlation of TI in reference to its spatial location. The study shows that near the stream lines TI value is higher, which indicates the strong correlation between TI surface and drainage network. But with the increase of grid spacing this correlation is become decline, which influence the statistics of TI surface. But still there is enough scope to deal with the accuracy of topographic index. In this study an attempt will be made to develop a method for estimating the accuracy of topographic index considering various factors, in particular the terrain ruggedness and DTM grid spacing Objective of the Research: Develop a method for predicting the accuracy of Topographic Index considering prime influencing factors Research Questions: Primary research questions: What are the influencing factors on the accuracy of Topographic Index? How grid spacing of the DTM influence the accuracy of Topographic Index? Which terrain characteristics influence the accuracy of Topographic Index? Can the relevant terrain characteristics be quantified using Moran s I (auto)correlation index? If not, could a slope or change of slope parameter serve the purpose? Secondary research Questions: Do systematic errors of the DTM influence the accuracy of the Topographic Index? 4

16 What is the impact of incomplete catchment area in computing the Topographic Index? What is relationship between DTM accuracy and accuracy of the Topographic Index? How relevant is filtering of the DSM for the Topographic index? 1.5. Structure of the thesis: The present thesis is elaborated in six chapters. Chapter 1 deals with the introduction, problem definition and motivation, research objective and research questions. Chapter 2 contains the theoretical background of the research and literature review. Chapter 3 contains the selection and description of the study area as well as data and material used in this research. Chapter 4 deals with the approach to the experimental investigation which has been used in this research, elaborating on DEM generation, computation of topographic index, quantification of terrain ruggedness characteristics, Filtering of DSM and accuracy assessment. Chapter 5 contains the analysis part of the research and discussion. Chapter 6 contains the conclusion of the study and recommendation for further studies. 5

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18 2. Theoretical background & literature review 2.1. Topographic index and TOPMODEL: Terrain relief is considered as a major control on hydrological response to rainfall of a catchment. Hydrological processes are dominated by the terrain relief. Thus attributes of terrain relief are important for simulating the hydrological processes. Topographic index is a combined attribute of specific catchment area and local down slope. It is α defined as Ln ( ) in which α is the upslope area and tan β is local down slope. The specific tan β catchment area α reflects tendency of upslope water flow drain to a pixel and tan β can be considered as an approximation of hydraulic gradient forcing water down slope (Brasington et al. 1998). TOPMODEL is topography based watershed run-off simulation model that makes an explicit link between catchment relief and stream flow (Brasington et al. 1998). TOPMODEL represents three things: Prediction of total catchment stream flow. Surface and subsurface flow contribution using spatial variation of topographic index. Visualization of spatial distribution of soil moisture deficit and contributing areas. Within the TOPMODEL framework topographic index is useful to calculate the local storage deficit. Si = S + m [ λ Ln( α / tan β ) i] α Where λ is the aerial average of Ln ( ) tan β S = Average storage deficit m = rate of decline of hydraulic conductivity with deficit. This equation is to predict the saturated contributing area at each time step (Huang et al. 2002). The variable contributing area is also compute with respect to topographic index (Brasington et al. 1998). 7

19 Successful application of TOPMODEL requires accurate topographic index, which can be computed from a high resolution DTM. A high resolution DTM describes in detail the real ground surface. According to the TI literature, 10 m grid size of a DTM provides a substantial improvement over 30 and 90 m data, but 2 or 4 m data provides only marginal additional improvement for the moderate to steep gradient terrain (Zhang et. al 1994). The previous study has concluded that to simulate the geomorphic and hydrological processes, 10 m grid size datasets makes a rational compromise between increasing grid spacing and data volume. In the current study, topographic index is calculated from 10 m Cartosat DSM, considered as reference or true TI. The DSM instead of the DTM is taken because of the non-availability of efficient filtering software. Moreover, when studying the influence of grid spacing and surface roughness it does not matter what kind of surface is represented by the DEM. It is found from the TI literature (Brasington, 1998) that mean of TI surface increases rapidly from finer to course resolution. This indicates that due to the low resolution of DEM, the representation of terrain becomes smooth and thus mean value of TI increases. This higher value of TI at coarse resolution in comparison with high resolution can be considered as error Algorithm for generation of topographic index: The input needed for topographic index calculation is slope and upslope area. The first derivative of elevation describes the rate of change of elevation, which is the slope. Together the slope in the x direction and slope in the y direction (partial derivatives of z with respect to the x and y directions), define the gradient vector of the surface. The maximum slope can be determined by taking the norm of this vector. Slope = dz dx 2 + dz dy 2 When determining the slope from discrete data (a grid DEM) we have different options for selecting neighbours of a grid node. 8 different algorithms have been used by the previous researchers: three point plane algorithm, four closest neighbour algorithm, four diagonal neighbour algorithm, eight neighbours unweighted, one over distance cover, maximum downhill gradient, multiple downhill neighbours, and maximum adjacent gradient (Raaflaub et al. 2006). In the present study only the four closest neighbour algorithm has been considered. Because the more the neighbours used in the algorithm, the slope will become more erroneous. FCN algorithm uses the four orthogonal neighbours to compute the slope and define the steepness and downhill direction. Steepest neighbour algorithm is most suitable for topographic index generation (Raaflaub et al. 2006). 8

20 Upslope area can be generated using the two main algorithms; Single flow direction algorithm (sfd) and multiple flow direction algorithm (mfd). Single flow direction algorithm considered that drainage will occur only in the steepest downhill direction. Multiple flow direction algorithm assumes that drainage from a cell can occur in all the direction. Wolock et al. (1995) suggested that the choice of these two (sfd and mfd) algorithms does not make a difference in topographic index computation. Hence, in the present study single flow direction algorithm has been considered for TI computation. Topographic index is influenced by the slope and upslope area computation algorithm. Hence, the computation procedure must be considered as one of the factors influencing the TI accuracy Topographic Index and sensitivity of hydrological computation: Hydrologists are likely to be interested in the bare ground surface, which is described by a DTM. But it has been found from the literature that topographic index has also been generated from Digital Surface Model (DSM) and referred as DEM. Mean of topographic index increases progressively with DTM grid spacing which negatively effects the efficiency of model prediction. Brasington and Richards (1998) calibrated the TOPMODEL for a range of grid spacing 20 m to 500 m considering the topographic index and calculated the model efficiency (model error), which shows that the increase of the mean of topographic index with grid spacing leads to decrease the model efficiency (Table:2.1). GRID SIZE (M) MEAN OF TI ( λ ) OVERLAND FLOW (%) MODEL EFFICIENCY (%) Reference: Brasington and Richards 1998 Table 2-1: Effect of DEM grid spacing on mean of TI and efficiency of TOPMODEL prediction. The study concluded that the trend towards higher predictions of surface run-off at low resolution, results from the higher mean of TI value. 9

21 The hydrological model TOPOG estimates the surface saturation within a catchment. The expression of surface saturation condition at any location in a catchment is according to O Loughlin (1986): α / tan β w Where w = average wetness state of a catchment The pixels having value of α / tan β w is considered as saturated pixels. The total saturated area of a catchment is calculated in terms of sum of total saturated pixels. The study of Zhang and Montgomery (1994) shows that as the topographic index increases progressively from 2 m grid spacing to 90 m grid spacing the percentage of predicted saturated area also increases. It is about 13% of the total catchment area for 2 m grid spacing, 32% for 30 m grid spacing and 50% for 90 m grid spacing. So, it is essential to asses the accuracy of topographic index before using it in hydrological modelling Sensitivity of Topographic Index to DEM resolution: Topographic index is most sensitive to the grid spacing of the data set (DTM/DEM). Grid spacing directly effect on the calculation of accumulated contributing area shared out differently over space according to grid size. Significant difference has been found in the spatial pattern of topographic index computed from 5 m grid spacing to 50 m grid spacing (Quinn et al. 1991). Another problem is to delineate accurate catchment boundary and loss of information in near the boundary with the increase of DEM grid spacing. Zhang and Montgomery (1994) also determined grid spacing to be a significant control specific catchment and topographic index. The study shows that mean of topographic index surface increased with grid size. The mean value of specific catchment area (α) increase from 20 m for a 2 m grid spacing to 102 m for a 90 m grid spacing. The mean of topographic index calculated as 4 in the 2 m grid spacing which became 6.2 in 90 m grid spacing. Wolock and Prince (1994) generated the elevation model from 1:24,000 and 1:250,000 scale toposheet using the interpolation technique and compare the effect of both DEM map scale and data resolution on the statistics of topographic index. It has been found from this study that the mean of topographic index increases with increase of grid size (Table 2.2). Brasington and Richards (1998) studied the sensitivity of terrain attribute to DTM resolution. The study shows the increasing trend of topographic index with respect to lower slope angle and increasing contributing areas with larger grid size biases. The mean of topographic index has shifted from 6.12 to 8.87 at the range 20 m to 500 m resolution. DEM Map scale and Data Resolution VARIABLE 1:24,000 SCALE,30-M RESOLUTION 1:24,000 SCALE, 90-M RESOLUTION 1:250,000 SCALE,90-M RESOLUTION 10

22 Mean ln (α ) Mean ln (1/tanβ) Mean ln (α / tanβ) Reference: Wolock and Prince (1994) Table 2-2: Effect of DEM grid spacing on mean of topographic index DTM uncertainty and accuracy of topographic index: Terrain relief controls the movement of water in a landscape. The function of terrain can be represented using digital terrain model (Schmidt et al. 2003). DTM is having its inherent error which cannot be eliminated and causes uncertainty (Peifa et al. 2006). Topographic index is a secondary attribute of DTM, thus the error associated with DTM contributes the error in topographic index. The quality of DTM depends on: Method of data capturing like accuracy of data collection; amount, pattern and significance of sample point. Representation of data format i.e. DEM in raster format, triangulated irregular network (TIN) and contours. Grid spacing of data set. Interpolation method for raster DEM (Schmidt et al. 2003). When generating a DTM from a stereopair of images, a deficient orientation introduces a systematic error in the DTM. A systematic error of DTM possibly influences the TI accuracy too. The major input for topographic index computation is slope and upslope area. Upslope area can be calculated based on flow direction. The accuracy of slope and flow direction both depends upon accuracy of DTM. The effect of DTM error on topographic index has been investigated by using Monte Carlo Simulation and error realization of DTM (Raaflaub et al. 2006), suggested that error of topographic index is more sensitive to the number of neighbours used in the algorithm. The error in topographic index is mainly showing up along the drainage network. Comparison with DTM data capture process and relation with topographic wetness index has been work out by Schmidt, The study reflect how the elevation capturing method like RTK GPS, Stereo data and airborne laser scanning effect the height accuracy of raw data and interpolated DEM as well as effect of flow direction algorithm on topographic index. The error associated with DEM or uncertainty also affects the topographic index. The effect of DTM uncertainty on the spatial pattern of topographic index (Peifa et al. 2006) reflects that mean value of topographic index increases due to DEM uncertainty. 11

23 Generating DTM and derivation of terrain attribute using stereo data is a common practice. Due to the deficient orientation of stereo images systematic error added in the DTM. This causes error in both horizontal and vertical direction. The vertical error effect the computation of topographic index Spatial autocorrelation of Topographic index: Spatial autocorrelation represent the clustering the phenomena with respect its spatial location. It measures the relationship between the difference of spatial attributes of an object with respect to the distance. It also gives an indication of dissimilarity of the values with respect to space. Previous study (Cai et al 2006) shows that spatial autocorrelation of TI surface decline with respect to grid spacing. The value of Moran I varies from +1 to -1. Positive value indicates that the objects are highly correlated or clustered whereas negative value indicates the dissimilarity (Goodchild, 1986) Terrain ruggedness and topographic index: Higher the undulation or variation of slope in terrain relief means higher the terrain ruggedness. In other way more dissected terrain can be defined as rugged terrain. The error associated with DTM is more in the hilly and mountainous terrain and less towards the flat terrain. Zhang and Montgomery (1994) have found that in the Mettman ridge catchment the mean value of specific catchment area (α) (upslope area divided by length of the pixel) increase from 20m for a 2m grid size to 102m for a 90m grid size, but at the same resolution in Tennessee valley catchment the mean value of α merge from 19m to 120m.This study reflect effect of terrain relief on specific catchment area. Hence, it is important to see the effect of terrain variability on TI. From the above discussion it clear that the possible factor of TI accuracy is grid spacing of DTM, roughness of the terrain, systematic error of DTM, improper delineation of drainage basin, random errors of elevation values of the DTM, gross error of DTM, the algorithm used for computing slope and TI generation. Within those factors only the first 4 factors will be empirically evaluated in this study. 12

24 3. Study Area and Material Used 3.1. Important of the study area in the present study: Study area selection is an important task in the present study. The objective of the research is to reveal the impact of grid spacing and terrain roughness on the accuracy of topographic index. As the topographic index is one of the inputs to hydrological modelling, the study area should be a drainage basin. In order to study the impact of terrain relief on topographic index various terrain roughness has to be considered. Because of this reason five drainage basin having different relief characteristics (highly rugged to flat) has been selected for this study Geographical Location: Five small drainage basins have been selected within a Cartosat-1 scene. The area is located near Dehradun (western part) which is geographically situated within N to N and E to E. Figure 3-1: Location of the study area 13

25 3.3. Description of the study area: Geomorphologically the area is characterised by hills and valleys. The lower middle part of the area is highly rugged and mainly dominated by hills. Because of the high slope, the area is disected by number of small rivers. The northern part of this area is the foot of the Mussourie hill and relief of the terrain is less in compare to the lower middle part. Middle part of the terrain has little undulation but southern part is completely flat. In the following a quantitative description is given Landcover information of selected catchments: a) Highly rugged and rugged catchments: Relief of these terrains is highly rugged and variation of slope is very high. Area is covered by the tree and forest which is located in the high slope. Forest type is mainly Sal and density is medium to scattered. In the side of the river valley very small vegetation covers is present. b) Moderately rugged basin: Upper part of the catchment is the foot of the Mussourie hill and almost ¼ of the area is covered by the forest. Type of forest is mixed; within this Sal forest is dominating. Density of the forest is medium to low. Number of buildings is very less. c) Undulated terrain: Upper part of the catchment is covered by the forest (mainly dense forest). Type of the tree is Sal and tree heights are almost equal (8 to 10 m which was found during the field survey). Lower catchment is dominated by agricultural and bare land. Little number of buildings is present. d) Flat: Upper part of the flat terrain is little rugged (very small portion) and some scattered trees are present here. whole terrain is dominated by agricultural (not cultivated during the data was captured) land and open field (without vegetation). Along the river line same patches of tree has been found. Very less number of buildings are located in the middle and lower part of the terrain Study area selection: Study area selection procedure in the present study can be divided into two parts; terrain selection and basin identification. 14

26 Study Area Selection Terrain Selection Basin Selection Slope Profile Study Contour Pattern Profile Curvatur Outlet Algorithm Highly Basin Basin Moderately Basin Undulated Basin Flat Basin Figure 3-2: Schematic representation of study area selection procedure Terrain selection: Five catchments are located at various rugged terrains (highly rugged to flat). Three factors have been considered for selecting the terrain: a) Slope: ness of the terrain can be judged by the slope (change of elevation). In rugged terrain difference in elevation of an area with its neighbourhood is high in compare to flat terrain. Because of that reason rugged terrain is having high slope. Slope has been derived using Four Closest Neighbour (FCN) algorithm and classified into 8 categories. Percentage of area within each slope class to total area of the basin has been calculated and plotted with respect to slope class (Fig: 3.3). It is visible from Fig: 3.3 that more than 80% area of flat and undulated basin, 63% of moderately rugged basin having less than10 degree slopes, while highly rugged and rugged basin more area having greater than 20 degree slope. 15

27 Slope Category Flat Undulate d Moderately Rugge d Highly > Table 3-1: Slope category % of area to total area Slope of Different Terrain >70 Slope categorie Flat Undulated Moderately Highly Figure 3-3: % of area under each slope class b) Profile curvature: In case of a highly inclined terrain, the slope of the area will be high that does not mean that the terrain is rugged. ness implies the variation of slope in a terrain which is indicated by curvature. It determines the rate of change of slope along the direction at that point. A positive curvature indicates that the surface is upwardly convex at that cell. A negative curvature indicates that the surface is upwardly concave at that cell. A value of zero indicates that the surface is flat. Curvature of the study areas has been computed and divided into 8 classes. Percentage of area within each class to total area of the basin has been calculated and plotted with respect to curvature class. Class Flat Undulated Moderate Highly rugged < to to to to to to > Table 3-2 : Classification of curvature. 16

28 Profile Curvature of Different Basin % of area to total area < to to to 0 0 to to to 0.2 >0.2 Basin Flat Undulated Moderate Highly rugged Curvature Class Figure 3-4: % of area within curvature class According to the classification the area having curvature within to 0.02 can be considered as flat terrain. It is visible from the Fig: 3.4 that more than 80% area of flat and undulated basins, are falling under this category. The highly rugged and rugged basins the change of slope is more in compare to flat terrain and thus curvature is high. c) Cross section of the study area: Cross profile of the terrain has been considered in order to identify the ruggedness of the terrain. Three cross section of each basin has been taken (upper, middle and lower part of each catchment) which reflects the variation of relief in the study area. It is visible from the Fig: 3.5 that change of elevation with respect to distance is very high in highly rugged and rugged basin. Most of the area of these two basins is situated above 500 m elevation and the area is highly disected. In comparison to rugged and highly rugged basin the relief of the undulated and flat basin is very low as well as less disected because of the few number of drainage line. d) Contour pattern: Contour pattern is one of the indicators of the terrain roughness. If the spacing of the contours is small then slope is large. If the contour lines are highly curved terrain relief is highly varied. Survey of India toposheet (1:50000 scale) has been considered (contour interval 20 m) in order to visual interpretation of the contour. Highly Basin Basin 17

29 Moderate Basin Undulated Basin Flat Basin Figure 3-5: Cross profile of different catchment showing the variation of terrain relief. 18

30 Basin / Catchment selection: Drainage basin is a region of land where water from rain or snow melts drains downhill into a body of water. The drainage basin includes both the streams and rivers that convey the water as well as the land surfaces from which water drains into those channels. Each drainage basin is separated from adjacent basins by a ridge, hill or mountain, which is known as a water divide. Every drainage basin is having an outlet from which water drain towards downslope. In other way, area which contributes to the flow of the outlet is included within this basin. Five drainage basins have been selected in this study using the automatic catchment selection algorithm implemented on ILWIS software. Five outlets has been specified and based on that catchment extraction was done using 10 m resolution Cartosat DSM. The information regarding the basins is given in the Table: 3.3. Catchment Type Area (Sq m) Stream Order Outlet Elevation (m) Outlet Coordinate Highly '35.23"N, 77 46'28.20"E Perimeter (m) '43.51"N, 77 57'31.68"E Moderately '39.67"N, 77 56'21.48"E Undulated '10.2"N, 77 52'50.70"E Flat '56.6"N, 77 47'00.36"E Table 3-3: Description of different basin Data used: Satellite data: High resolution (2.5 m x 2.5 m) Cartosat- 1 stereo data has been used for generation of DSM. The date of pass of the data is 2 October 2005 and path number is 0526 and row number is The main reason of using this data source is to obtain a 10 m resolution DSM which has been used as a reference data for comparison different resolution TI in the present study. The topographic index which is calculated from the 10 m DEM has been considered as a reference topographic index. According to the TI literature 10 m grid size provides a substantial improvement over 30 and 90 m data, but 2 or 4 m data provides only marginal additional improvement for the moderate to steep gradient terrain (Zhang, W. et. al 1994). The DEM does not represent (in all parts) the ground surface, which however, is not relevant when studying the behaviour of the TI of a surface when the spacing of its model is relaxed. 19

31 Ground survey data: Differential GPS survey was conducted in order to take the GCP's. All the GCP s are well distributed over the scene. 20 GCPs were collected and out of that 15 were used after post processing in order to orient the Cartosat-1 stereo model Ancillary Data: Survey of India toposheet has been considered during the differential GPS survey as well as visual interpretation of the drainage basin to identify the basin outlets and roughness of the terrain. 20

32 4. Experimental Investigation 4.1. Reference Data Generation: In the current study reference data (10m resolution topographic index) generation is most important. Reference data sets have been generated using the following steps: DGPS Data Processing Using Ski-Pro Processed GCP s Cartosat-1 Stereo Data Block Orientation DEM Generation (10m) Blunders Check DEM (Without Blunders) Slope Upslope Area Topographic Index (10 m) Figure 4-1: Schematic representation of reference data generation. 21

33 DGPS Survey: Digital Elevation Model generation using Cartosat-1 stereo data has been done using two ways. Orientations of stereo block using Rational Polynomial Co-efficient (RPC) and using both GCP s and RPC s. The former is the easier but the later is more accurate. In order to derive DEM using second method Global Positioning System (GPS) survey in Differential Mode (using Leica 500 single frequency GPS receiver) was carried out over the Dehradun and its surrounding terrain which was scene by Cartosat-1 sensor on 2nd October, 2005.Position of ground control points were identified and marked on the images during the survey. For the GPS survey we used one pair of instrument, which has one base and other rover station. Co-ordinate system has been set in the base and rover as geographic lat long and WGS 84 datum. The rover was set up over every ground control point location for approximately 45 minutes to 1 hour for taking the reading. The system was setup to read the signal for every 10 seconds. 20 points have been determined during the DGPS survey Post Processing of the GPS data: The ground control survey data has been post processed using ski-pro data processing software. The configuration of GPS processing parameters were used to resolve the ambiguity and the differentially corrected ground control point co-ordinates are shown in the Appendix: 1. In order to resolve the ambiguity of the GCP cut off angle has been changed and some satellite has been excluded by analyzing the ambiguity resolve states of ski-pro software. The ground control coordinate are shown in the Appendix: 2. The quality obtained for each point has been shown in the Appendix: Generation of DSM using Cartosat-1 stereo data: The digital surface model has been generated using the cartosat-1 stereo data. Cartosat-1 stereo data comes with two RPC (Rational Polynomial co-efficient) file. The band-a (Aft image) and Band-F (Fore image) were used to generate surface model, with only RPC and GCP and RPC both Orientation of Stereo Model: Orientation of stereo model was done with the LPS software. Stereo-Pair has been oriented 22

34 internally and externally using RPC s and generated the DSM named as RPC only DSM with cell size of 10 m (LPS Tour Guide) Generation of DSM using RPC and GCP: Systematic error can be introduced in the RPC oriented DSM because of a deficient external orientation. In order to minimize the systematic error, we need to orient the stereo pair using Ground Control Point. After processing 15 Ground Control Points have been used for the orientation of Cartosat stereo block. After putting the GCP s in the stereo pair, 100 tie points have been generated and triangulation was carried out. Overall accuracy of the triangulation has been achieved is pixels. Control and check point accuracy is following: Control point RMSE Check point RMSE X = (8) X = Y = (8) Y = Z = (6) Z = Horizontal accuracy (RMSE of X, Y) is in degree decimal and vertical accuracy (RMSE of Z is in meter. During the orientation, stereo pair has been projected into Geographic (Lat/Long) and Datum was set to WGS-84.From this oriented block 10m resolution DSM has been generated. After that from the same block 30m, 50m, 90m, 110m, 150m DSM has produced in similar way Removal of Blunders from DSM Artifacts/blunders are the topographic depressions or elevations of digital surface model which introduce in DSM due to wrong image matching. Blunders come in the model due to cloud cover, water body, etc. Some pixel value of DSM become very high due to blunders and it is necessary to remove that. During the removal of blunders, first the area having blunders was checked with SOI toposheet, in order to confirm that DSM originally represents the blunders or it is actually a hill or rock. A small IDL program has been written for removal of this artifact. The logic used is that, if a pixel having very high value in comparison with surrounding pixels, this value will be replaced by the 23

35 surrounding pixel value. By observing the surrounding pixels, a threshold has been derived. The threshold has been set to the program and a constant height was added to maintain the continuity. DEM with blunders Corrected Replaced Figure 4-2: Removal of blunders from DSM 4.2. Selection of the Study Area: In the present study, selection of the study area was carried out using two ways: Selection of the Basin: Computation of Topographic Index should be done with respect to a particular drainage basin. In order to delineate the drainage basin Automatic Basin Delineation Algorithm was applied (ILWIS User Guide). This algorithm is derived in the following steps: Flow Direction: Flow direction is calculated for every central pixel of input blocks of 3 x 3 pixels. The calculation is based on the Steepest Slope Algorithm. Slope of the central pixel and its 8 neighbours are compared to assign the flow direction of a pixel. The algorithm is derived diagrammatically as below: CP = CP S DEM 3x3 block Z-difference Distance Slope Flow direction Figure 4-3: Derivation of flow directions 24

36 Flow Accumulation: Based on the flow direction, flow accumulation calculates the cumulative count of the number of pixels that naturally drain into outlets Drainage Network Extraction: Based on flow accumulation raster, drainage network has been extracted. Drainage lines having length greater than 500 meters were taken into consideration Drainage Network Ordering: Drainage network ordering has been done based on the method given by Strahler Catchment merging: The relevant catchment has been extracted and merged. A point map is created containing the locations of the outlets of the desired catchments, by which five catchments was delineated Selection of terrain based on ness: In order to select the terrain based on variation of relief, 3 factors were considered; slope, cross profile and curvature. Within this three factors curvature is the most suitable to express the terrain roughness. a) Curvature: Profile curvature represents the rate of change in slope in the gradient direction at each grid node. Curvature is the second directional derivative. We need to determine the downhill direction at each point on the surface and then determine the rate of change of slope along the direction at that point. Overall curvature represents the slope of slope of a surface. The Positive curvature indicates that the surface is upwardly convex, the Negative curvature indicates that the surface is upwardly concave and the Zero value indicates that the surface is flat. Curvature of a surface is calculated on a cell by cell basis. For each cell, a second order polynomial is fit to the elevation values of a 3 x 3 window (Arc/Info help). The equation of curvature computation used is as follows: Z = Ax2y2 + Bx2y + Cxy2 + Dx2 + Ey2 + Fxy + Gx + Hy + I A = [(Z1 + Z3 + Z7 + Z9) /4 - (Z2 + Z4 + Z6 + Z8) /2 + Z5] /L4 B = [(Z1 + Z3 - Z7 - Z9) /4 - (Z2 - Z8) /2] /L3 C = [(-Z1 + Z3 - Z7 + Z9) /4 + (Z4 - Z6)] /2] /L3 25

37 D = [(Z4 + Z6) /2 - Z5] /L2 E = [(Z2 + Z8) /2 - Z5] /L2 F = (-Z1 + Z3 + Z7 - Z9) /4L2 G = (-Z4 +Z6) /2L H = (Z2 - Z8) /2L I = Z5 Where L = distance between cells Figure 4-4: Curvature computation 4.3. Derivation of Topographic Index: α According to the algorithm ( Ln ( ) ), two parameters are needed to derive the Topographic Index; tan β a) Specific Catchment Area ( α) b) Slope ( tan β ) a) Calculation of Specific Catchmenta Area The calculation of specific catchment area requires the total area draining into each cell (upslope area) and the contour length. For a DEM contour length is considered to be the grid spacing. Single flow direction algorithm (Jenson & Domingue, 1988) is used in this study to calculate the upslope area, assuming that drainage from a cell can only occur in the steepest down slope direction (Wolock et al. 1995). The elevation of each grid cell is compared with the elevation of its octagonal neighbour and the steepest down slope direction assigned to the each cell in the grid. The number of upslope cells draining into a particular cell is calculated using this single flow algorithm (Sfd), and this upslope area of a grid cell is calculated as: Upslope Area (A) = (No. of upslope cells +1) * (grid cell area) Specific Catchment Area ( α ) is computed as α = A/L Where L = Grid spacing b) Calculation of Slope ( tan β ): Four closest neighbours algorithm has been used for computing the slope. By this algorithm the calculation of slope of a cell is done by taking the elevation difference between two orthogonal neighbours. In other words the algorithm used the four cardinal neighbours i.e. North, South, East and West representing a second order finite difference relationship. It takes into account of two orthogonal components of slope, slope in x direction and slope in y direction. This defines the steepness and downhill direction. 26

38 We have implemented the algorithm in ERDAS Modeler. Kernel definition and slope computation procedure is shown below: Figure 4-5: Implementation of FCN algorithm Topographic Index is generated by combining slope and specific catchment area. In order to automate the process, the algorithm is customized in ArcGIS model builder, which is shown below: 27

39 Figure 4-6: Customize Model of Topographic Index Topographic Index has been generated from different resolution DEM (10m, 30m, 50m, 90m, 110m, and 150m) for various study area.10 m resolution Topographic Index considered as a reference TI surface (Appendix-5) Spatial Autocorrelation of Topographic Index: The algorithms used to compute the Moran s I autocorrelation relation index is as follows: N - the total number of cells in a grid : NROWS * NCOLS I,J - any two adjacent cells Z i - the value of TI of cell i C i,j - the similitaries of i s and j s TI value: (Z i - Z m ) + (Z j - Zm ) W i,j - the similarity of the i s and j s locations, W i,j = 1 if cells I and j are directly adjacent (4- Adjacent) and O otherwise, σ 2 - the sample variance : (Z i Z m ) 2 / n, where Z m is the mean TI value for the grid. In the terms of the above notation, spatial autocorrelation is simply a measure of the TI value similarities in the set of C i,j with the locational similarities of the set of W i, j and then summing the results into a single index (Goodchild, 1986). The formula for calculating the Moran Index is: C = W i j C i j / ( W i ) ( (Z i - Z m ) 2 / n) Where W i = 4 * n 28

40 4.5. Accuracy Assessment of Topographic Index: We compute the accuracy of the topographic index in terms of the RMSE and mean error. The error is the difference between the value of the computed topographic index and the value, which is perceived as true value. The RMSE is a single quantity characterizing the error surface, and the mean error reflects the bias of the error surface. RMSE n 1 = n i= 1 n 1 ME = n i= 1 ( TI TI ) ref 10 ( TI TI ) Re f We have used 3 different approaches for the accuracy assessment of the topographic index. The approaches are described below: Method 1 (Location wise Comparison): In this method the RMSE is calculated by comparing the value of the higher grid spacing pixels of TI surface and corresponding central pixel of reference TI (10m resolution TI surface) TI of 10 m cell size TI of 30 m cell size TI 30 M RMSE Table TI 10 M Sq. Diff RMSE = Difference Image Figure 4-7: Schematic representation of accuracy assessment of TI using location wise comparison. 29

41 Method 2 (Areal Mean Based Comparison): To avoid the discripency of above method, the Areal Mean Based Comparison method was applied. In this method, RMSE of the TI is computed by taking the difference between higher grid spacing TI value with the mean of corresponding 10 m TI block. This method was adopted based on the assumption that TI of 30 m pixel is the function of 9 pixels of 10 m resolution. If the mean of the 10 m pixel is equal to the TI value of corresponding coarse resolution pixel, no error will be encountered. The difference between these two values will be the error (A) (B) (C) (D) TI 30 M TI 10 M RMSE: 1.82 Sq. Diff Figure 4-8 : (a) TI 10 m, (b) TI 30 m, (c) Mean of 10 m TI block, (d) difference between b & c. Representation of areal mean based comparison method. 30

42 Method 3 (Detail RMSE Method): RMSE of topographic index has been computed by up sampling the low resolution TI surface into 10m TI surface and compared with reference (10m resolution) TI surface. The advantage of this approach is that it gives the more detailed error surface of with respect to the reference TI (a) TI 10 m TI 30m (B) (C) TI 30 convert to TI 10 (d) Difference image RMSE = Figure 4-9: Schematic representation of accuracy assessment of TI using detailed RMSE method Quantification of terrain ruggedness: ness is a relevant terrain characteristic. In order to quantify the ruggedness of the terrain, the different procedures were investigated in the present study. The conceptual algorithm for each method is explained in this following section Moran s I Autocorrelation Index: In order to quantify the terrain ruggedness Moran s I index has been applied. It was found that single value of spatial autocorrelation index is not able to depict the ruggedness characteristics of the terrain. In order to avoid this, the Moran s I index computed with respect to the function of lag distance. 8 pixel distances were taken as lag distance to calculate Moran s I index. 31

43 Mean and Variance of Slope: An investigation has been made to quantify the terrain ruggedness using mean and variance of slope. Slope is considered as a distribution and first two moments (i.e., mean and variance) were taken. Variance of the slope is calculated in terms of standard deviation. The equation used for calculation of variance is following: n n 1 i= 1 ( Z Z ) mean But it found that mean of slope is not suitable sufficient classifier of terrain ruggedness. An inclined plane can have a large slope but it would not be an example of rugged terrain Terrain ness Index (TRI): Another approach is investigated in this study is Terrain ness Index (TRI). TRI represents the amount of elevation difference among the adjacent cells of a Digital Elevation Model. The process computes the differences in elevation value from central cell to its 8 neighbours. TRI is derived by taking the root-mean square of the elevation differences. TRI reflects average elevation change between any point on a grid and its surrounding area. The algorithm has been implemented in the ERDAS Modeler (Appindix-6) Figure 4-10: Kernel of TRI Laplace Filter: Another attempt has made to quantify the terrain ruggedness using Laplace filter. The Laplace filter is defined as below: Figure 4-11: Kernel of Laplace Filter. But at the time of computing the Laplace filter, the distance has not taken into consideration. Although it is necessary to prove that representation of the surface is very rough in high resolution and smooth in the low resolution. Hence, to compare the terrain ruggedness from different resolution data sets, it is important to normalize the Laplace value by spacing. 32

44 Normalize Laplace filter: In order to quantify the terrain ruggedness Laplace filter has been normalized by dividing the cell size of the DEM. Root mean Square of the normalized Laplace has taken to achieve a single value of terrain ruggedness. All these methods of terrain ruggedness quantification were applied on 10 m, 30 m, 50 m, 90 m, 110 m and 150 m DEM of five selected catchments in order to get a single value of terrain roughness. The result of this different approach is shown in the Chapter 5. 33

45 5. Results and Discussion 5.1. Effect of DEM Grid Spacing and Terrain Roughness on accuracy of Topographic Index: Topographic index is a secondary attribute of a DEM. Hydrologist are basically interested in the ground surface, so it is important to compute the topographic index from a DTM (bare surface model). In the present study five drainage basins have been taken into consideration, having different relief characteristics (highly rugged to flat).topographic index has been computed for all the five drainage basin from low to high (10 m to 150 m) grid spacing of Cartosat DSM. It has been found that the computation of topographic index is effected by grid spacing of DEM. If we move towards low resolution, topographic index of the catchment reflects only higher order stream and will trend to ignore the existence of low order channels (Fig: 5.1). Due to the high smoothing effect at low resolution small channels are hidden within the large grid cells. In high resolution the spatial pattern of topographic index matches with the stream network (Fig: 5.2), near the stream network TI values are high and TI declines away from stream lines. This reflects the spatial correlation of TI with respect to its spatial location, which is referred as spatial autocorrelation (Cai et al. 2006). But towards the low resolution spatial autocorrelation of TI becomes violated. Spatial autocorrelation of TI has been investigated in terms of Moran s I index for different resolution TI surface. Fig: 5.3 shows that Moran s I of TI surface decreases (Table: 5.1) with decreasing the resolution. The decrease of spatial autocorrelation of TI suggests that pattern of TI surface is changing (becoming more random) with the increase of grid spacing. Figure 5-1: Topographic Index computed from 10 m to 150 m DEM 34

46 Figure 5-2: shows the drainage network of the Highly Basin Basin / Resolution 10 m 30 m 50 m 90 m 110 m 150 m Highly Moderately Undulated Flat Table 5-1: Moran s I value of Topographic Index Spatial Autocorrelation of Topographic Index With Respect to Grid Spacing 0.50 Moran's I of TI Highly Moderately Undulated Flat m 30m 50m 90m 110m 150m Grid spacing Figure 5-3: Moran s I index plotted against grid spacing. Mean of topographic index is continuously increasing with increasing grid spacing (Table: 5.2). It has been found that mean of the topographic index is more in the flat basin in compare to rugged basin, because the flat area is having more potential to be saturated due to lower ground slope (Fig: 5.5). Due to the higher slope in rugged areas the water will flow in down slope direction. So, the potentiality of soil saturation and topographic index both will be less. When lowering the resolution of the DEM, the 35

47 representation of surface is becoming smoother. A smooth surface is having high value of TI. The empirical results match with the expectation. Basin / Grid Spacing Highly Moderately Undulated Flat Table 5-2 : Mean of Topographic index Mean of Topographic In d ex Mean of Topographic Index with respect to Grid Spacing Basin Grid Spacing Highly M oderately Undulated Flat Mean of slope Mean of Slope in different grid spacing Grid spacing Basin Highly Moderately Undulated Flat Figure 5-4: Mean of TI Figure 5-5: Mean of Slope Mean of TI is plotted with respect to grid spacing (Fig: 5.4). The Fig: 5.4 shows that the overall relation between mean of the TI and grid spacing is parabolic in nature, but up to 90 m resolution this relationship is found to be close to linear. In order to find out the influence of terrain relief on the mean of topographic index (related to grid spacing), linear regression has been generated considering grid spacing of 10 m to 150 m (independent) and mean of TI (dependent) for five terrain (Fig: 5.6). The slope of the regression line for rugged and moderately rugged basins are more inclined than flat basins, which suggests that in the higher grid spacing TI of rugged terrain is more effected than flat terrain. Basically if we increase the grid spacing the terrain model become smoother. A smoother surface implies a larger mean TI. The smoothing effect of increasing the DEM spacing is stronger for the most rugged terrain. But a flat terrain is less influenced by grid spacing in terms of smoothing effect. 36

48 In order to study the effect of grid spacing on topographic index up to 90 m resolution (where the relationship appears more linear), we also find that the rugged terrain has more effect on mean of TI than moderate, undulated and flat terrain (Fig: 5.7). From the above discussion it can be said that the influence of grid spacing on TI deterioration depends on terrain variability. The effect is larger in the more rugged terrain in comparison with moderate and undulated terrain. As noticed already in the Moran s I results, our flat terrain does not fit well the trend observed in the other basins. Highly Basin Basin y = x R 2 = y = x R 2 = Moderately Basin Undulated Basin Mean of TI y = 0.025x R 2 = y = x R 2 = Flat Basin y = x R 2 = Slope of the relationship between Mean of TI & Grid Spacing Highly Moderately 7 Undulated Flat Grid spacing Figure 5-6: Relationship between DEM resolution and Mean of topographic index considering (10 m to 150 m resolution) 37

49 Highly Basin Basin y = x R 2 = y = x R 2 = Mean of TI Moderately Basin y = x R 2 = Undulated Basin y = 0.036x R 2 = Flat Basin y = 0.039x R 2 = Grid spacing slope of the relationship between Mean of TI & Grid Spacing Highly Moder ately Undulated Flat Figure 5-7: Relationship between DEM resolution and Mean of topographic index considering (10 m to 90 m resolution) The mean is more sensitive to outliers. If the few pixels value of topographic index surface increases due to the increase of grid spacing, the mean of the whole TI surface will be high. In order to verify this scale effect it is necessary to check whether the TI value of the whole surface is increasing progressively or not. Topographic index computed from the each grid spacing has been classified into 6 classes and percentage of area to total area within each class is plotted against the TI class (Fig: 5.7a). The shift of the curves towards higher range of topographic index with increasing grid spacing suggests that the value of topographic index is directly related with grid spacing of DEM. 38

50 % of Area Highly >15 TI Class Index 10m 30m 50m 90m 110m 150m % of Area Terrain TI class 15 >15 Index 10m 30m 50m 90m 110m 150m % of Area Moderately >15 TI class Index 10m 30m 50m 90m 110m 150m % of Area Undulated Almost Flat >15 TI class Index 10m 30m 50m 90m 110m 150m % of Area Flat Terrain >15 TI class Index 10m 30m 50m 90m 110m 150m Figure: 5-7 (a): Distribution % of basin area each TI class with respects grid spacing. 39

51 5.2. Effect of grid spacing on the accuracy of topographic index: From the above discussion it is clear that mean of the topographic index increases with increasing of DEM grid spacing. DTM represents the surface of the Earth. Higher the resolution, the representation of the Earth surface is much more detailed. Because of this reason RMSE (Root Mean Square Error) and ME (Mean Error) is computed by finding the difference between the topographic index computed from 10 m resolution DEM (reference TI) and coarser resolution topographic index (30 m, 50 m, 90 m, 110 m and 150 m). The RMSE gives us a measure of accuracy. It tells us how far, on average, the observed values are from the assumed true value. The ME tells us whether a set of measurements consistently underestimate (negative ME) or overestimate (positive ME) the true value. The topographic index which is calculated from 10 m DEM has been considered as a reference topographic index, because the high resolution DTM describes the real ground surface and thus the TI computed from it can be considered as reference or true TI. It is also found in the literature that 10 m grid size provides a substantial improvement over 30 and 90 m data, but 2 or 4 m data provides only marginal additional improvement for the moderate to steep gradient terrain (Zhang, W. et. al 1994). The previous study has concluded that to simulate the geomorphic and hydrological processes, 10 m grid size datasets makes a rational compromise between increasing grid spacing and data volume. Brasington, et. al (1998) investigated that efficiency of TOPMODEL prediction decreases with respect to grid size of DEM and topographic index. As we move further from high resolution to low resolution, mean of topographic index and predicted overland flow both increases and the efficiency of model reduces. Four different approaches have been considered for accuracy assessment of topographic index Method-1 (Location wise comparison): RMSE has been calculated by comparing the value of higher grid spacing pixel of TI and central pixel of corresponding 10 m TI. In rugged drainage basins the range of RMSE (Table: 5.3) of Topographic index is more (2.14) than the flat drainage basin (1.36). Overall the RMSE of Topographic index is low in the 30 m grid spacing and it increases towards higher grid spacing (Fig: 5.8a). TI value of the surface increases with grid spacing because slope of the terrain is become low due to the smoothing of DSM (Fig: 5.5). According to the topographic index algorithm Ln ( α / tan β ), TI value will be high if the slope of the area decreases. The result depicts in high resolution (30 m) the topographic index surface of flat terrain is more erroneous than rugged terrain, but in the low resolution (150 m) the error is more in the rugged terrain. The curve of the Mean Error (Fig: 5.8b) shows that with the increase of spacing, overestimation of TI 40

52 value increases. Upto 30 m grid spacing overestimation of TI value is stronger in undulated / flat basins in compare to highly rugged / rugged basins, but from 90 m to 150 m vice versa. Basin / Resolution (m) Highly Moderately Undulated Flat Table 5-3: RMSE of TI (Location wise comparison) Basin / Resolution Highly Moderately Undulated Flat Table 5-4: Mean error of TI (Location wise comparison) RMSE of TI RMSE of Topographic Index with respect to Grid Spacing Highly Moderately Undulated Flat ME of TI ME of Topographic Index with respect to Grid Spacing Highly Moderately Undulated Flat Grid spacing Grid Spacing (a) (b) Figure 5-8 (a) & (b): Effect of grid spacing on accuracy of TI The tread of the RMSE curve is linear in nature. So, linear regression has been generated considering grid spacing of 10 m to 150 m (independent) and RMSE of TI (dependent) for five terrain (Fig: 5.9) to find out the influence of terrain relief on the accuracy of topographic index (related to grid spacing). The slope of the regression line for rugged and moderately rugged basins are more inclined than flat basins, which suggests that in the higher grid spacing TI of rugged terrain is more effected than flat terrain, at low resolution. Hence, it can be said that deterioration of TI is higher in rugged terrain when the spacing increases. 41

53 Highly Basin y = x R 2 = Basin y = 0.015x R 2 = Moderate Basin Undulated Basin y = x R 2 = y = x R 2 = RMSE Flat Basin y = 0.013x R 2 = slope of the relationship Hig hly Moderately Undulated Flat Grid Spacing Figure 5-9: Grid spacing and Relation between RMSE. In this approach of RMSE computation only the location basis comparison is taken into account. For example this approach computes the difference between 30 m grid spacing TI and central pixel of corresponding pixels of 10m TI. But the TI of higher grid spacing is the function of areal average of corresponding 10 m TI surface. 42

54 Method-2 (Areal mean basis comparison): In this approach RMSE of TI has been computed by comparing higher grid spacing TI with the mean of corresponding 10 m TI block. In this approach also RMSE and ME (Table: 5.5 and 5.6) of topographic index increases with resolution. But the RMSE and ME range (2.65 and 2.05) of highly rugged basin is reduces from previous approach (2.14 and 2.87). In flat basin RMSE and ME range was 1.36 and 2.12 in previous approach which has been increased to 1.58 and 2.15 respectively. The progressing trend of RMSE of topographic index (Fig: 5.10) is almost same for all five basins. In this approach areal mean of reference TI (10m TI) has been considered as true / reference TI. But within the low resolution TI pixel, all the 10 m TI pixels are having different value. So, difference between low resolution TI pixels and corresponding all 10 m TI pixels (reference TI) is necessary to compute the detailed RMSE of topographic index. Basin / Resolution Highly Moderately Undulated Flat Table 5-5: RMSE of TI (areal mean method) Basin / Resolution Highly Moderately Undulated Flat Table 5-6: Mean error of TI (areal mean method) 43

55 RMSE of Topographic inde RMSE of Topographic Index with respect to grid spacing using areal mean base approach Grid spacing Basin Highly Moderately Undulated Flat Figure 5-10: RMSE of TI (areal mean method) ME of Topographic Index With Respect To Grid Spacing 5.00 ME of TI Grid Spacing Highly Moderately Undulated Flat Figure 5-11: Mean error of TI (areal mean method) Method -3 (Detailed RMSE computation method): RMSE of topographic index has been computed by upsampling the low resolution TI surface into 10m TI surface and compared with reference (10m resolution) TI surface. The advantage of this approach is that it gives the more detailed error surface of with respect to reference TI. The RMSE and ME range (Table: 5.7 and 5.8) of highly rugged basin (2 and 2.66) is higher than undulated flat basin (1.38, 2.07 and 1.65, 2.19). Error in topographic index increasing more rapidly upto 90 m resolutions (Fig: 5.12) and from 90 m to 150 m rate of change is lower. Over prediction of 44

56 TI surface is initially high (Fig: 5.13) in the flat and undulated basins, but after 50 m resolution highly rugged and rugged basins are more influenced by over prediction. Basin / Resolution 30m 50m 90m 110m 150m Highly Moderately Undulated Flat Table 5-7: RMSE table (detailed RMSE method) Basin / Resolution 30m 50m 90m 110m 150m Highly Moderately Undulated Flat Table 5-8: Mean error table (detailed RMSE method) RMSE of Topographic index Effect of grid spacing on the accuracy of topographic index Grid Spacing Basin Highly Moderate ly Undulated Flat Figure 5-12: RMSE (detailed RMSE method) 4.50 Mean Error of TI With Respect to Grid Spacing ME of TI Highly Moderately Undulated Flat Grid Spacing Figure 5-13: Mean error (detailed RMSE method) 45

57 6.00 Highly Basin 6.00 Basin y = x R 2 = y = x R 2 = Moderate Basin Undulated Basin RMSE y = x R 2 = y = x R 2 = Flat Basin Slope of the Relationship y = x R 2 = Highly Moderately Undulated Flat Grid Spacing Figure 5-14: Relation between RMSE and Grid spacing It is also visible from the regression analysis (grid spacing and RMSE of TI) that TI accuracy in rugged terrain is more influenced in compare to flat terrain(slope of the regression line (Fig: 5.14) is more steep in highly rugged / rugged terrain in compare to flat terrain). The RMSE and ME also depict the same conclusion. Among the three approach of RMSE computation the 3 rd approach is more scientific and using this method error can be represents in more detailed way. We found that the RMSE increases with increasing spacing whether we compute it using the method a, b and c. Now the point is that the mean TI increases with grid spacing, thus the RMSE of TI also increases. So, it is necessary to asses whether the dispersion of the TI increases too with spacing or not. In order to do this RMSE has been computed by subtracting the mean TI from every TI surface 46

58 considering method c (Table: 5.6). The curve of the standard error shows that the dispersion RMSE of TI increases very slowly upto 90 m and after 90 m resolution it decreases (Fig: 5.12). This observation again supports the finding that terrain ruggedness is a relevant terrain characteristic for TI accuracy. Only in the flat terrain the standard error of TI surface increases after 110m resolution as well as there is sudden break in the curve of flat and undulated terrain. From this observation it can be suggest that increasing mean is the prime deterioration effect on topographic index. Basin / Resolution 30m 50m 90m 110m 150m Highly Moderately Undulated Flat Table 5-9: Standard Error of topographic index Standard Error of Topographic Index RMSE of TI m 50m 90m 110m 150m Grid Spacing Basin Highly Moderately Undulated Flat Figure 5-15: Standard Error of TI 5.3. Effect of Grid Spacing on the Accuracy of Slope: One of the important input parameter for topographic index computation is ground slope. Topographic index is inversely related with the slope. So, it is important to visualize the effect of grid spacing on slope calculation. RMSE of the slope has been calculated using the above mentioned three approaches for comparing different resolutions (Table: 5.10, 5.11 and 5.12).The results are almost same in approach-2 & approach-3 which is little bit differs from approach-1. The accuracy of the slope is found to be decreases from high resolution to low resolution. 47

59 Basin / Resolution 30m 50m 90m 110m 150m Highly Moderately Undulated Flat Table 5-10: RMSE table of slope (Method a) RMSE of Slope RMSE of Slope With Respect to Grid Spacing & Terrain Condition Highly Moderately Undulated Flat Grid Spacing Figure 5-16: RMSE of slope (Method a) Basin / Resolution Highly Moderately Undulated Flat Table 5-11: RMSE table of slope (Method b) RMSE of Slope with respect to Grid Spacing and terrain Condition 25 RMSE of Slope Highly Moderately Undulated Flat Grid Spacing Figure 5-17: RMSE of slope (Method b) 48

60 Basin / Resolution 30m 50m 90m 110m 150m Highly Moderately Undulated flat Table 5-12: RMSE table of slope (Method c) RMSE of Slope RMSE of Slope With Respect to Grid Spacing & Terrain Condition Highly Moderately Undulated Flat Grid Spacing Figure 5-18: RMSE of slope (Method c) The accuracy curves of the slope suggest that the accuracy decrease is influenced by the terrain roughness. In the flat, undulated and moderately rugged terrain the accuracy of the slope decreases slowly with increasing grid spacing but in highly rugged and rugged basin the slope accuracy decreases more rapidly. It is happening mainly because of the smoothing of the DSM when increasing spacing. As we increase the grid spacing the relative relief of an area with its neighbourhood decreases. Slope and topographic index are become more erroneous when resolution decreases. As it has been mentioned earlier that the over estimation of TI (ME) is high in the low resolution, so we may observe the reverse for slope. The curve of mean error (Fig: 5.19 a,b,c) shows that under estimation (negative mean error) of the slope increase more rapidly with decreasing the resolution (Appendix-7). This negatively increasing rate is much faster in the rugged terrain than flat terrain. After the 50 m resolution ME of flat terrain become stabilize but the in the rugged terrain still ME is negatively increasing. Due to this reason it seems to be the RMSE of TI is high in the rugged terrain in compare to flat terrain after 50 m resolution. The Fig: 5.19 a,b,c also illustrates the smoothing effect of increasing the grid spacing. 49

61 Mean Error of slope with respect to Grid Spacing of DSM MEof Slope With Respect To Grid Spacing m 50m 90m 110m 150m Mean error of slope Grid Spacing Highly Moderately Undulated Flat ME of Slope Grid Spacing Highly Moderately Undulated Flat (a) (b) Mean Error of slope With Respect to Grid Spacing ME of slope Grid Spacing (c) Highly Moderately Undulated Flat Figure 5-19: (a) Mean error of Method-1, (b) Mean error of method-2 and (c) Mean error of Method Relation between DEM accuracy and accuracy of Topographic index: Topographic index is deriving by combine the slope and specific catchment area. Both the input parameters are computed from DEM. So, it is important to assess the impact of DEM error on topographic index. The DEM error has been calculated in terms of RMSE using the above mentioned three approaches. As we move from the high to low resolution the accuracy curve of DEM is found to be progressive in nature. Moreover, the trend of the accuracy curve is near linear (Fig: 5.20) in moderately rugged, undulated and flat basin. In highly rugged and rugged terrain upto 110 m resolution the trend is increasing and near linear and after that it is become flat (Tables: Appendix 9). This is mainly because of the terrain roughness. In rugged terrain the variation of relief is very high and it is represented well in the high resolution DEM. If we increase the grid spacing the mean elevation does not change (Fig 5.21). The mean elevation not changing with increasing spacing makes the RMSE a good accuracy measure for digital terrain models. The behaviour of slope and TI is different; because of the changing mean with increasing grid spacing the RMSE alone as accuracy 50

62 measure is less expressive. Slope and relief variation decreases vary rapidly with increasing spacing in rough terrain rapidly and due to this reason DEM error is more in the rugged terrain than flat terrain. Accuracy of Terrain Model in Different Grid Spacing (Approach-1) RMSE of Terrain Model Grid Spacing Basin Highly M oderately Undulated Flat (a) RMSE of Terrain Model Effect of Grid Spacing on the Accuracy on Terrain Model (Apprach-2) 40 Basin Grid Spacing Hig hly rugged Moderately rugged Undulated Flat (b) RMSE of Terrain Model Effect of Grid Spacing on the Accuracy of Terrain Model (Approach - 3) Grid spacing Basin Hig hly Moderately Undulated Flat (c) Figure 5-20: effect of grid spacing on RMSE of DEM; (a) method 1, (b) method 2 and (c) method 3. 51

63 Elevation Mean Elevation of DEM in different Resolution Basin Highly Moderately Undulate m 30m 50m 90m 110m 150m Resolution Flat Figure 5-21: Mean elevation of DEM at different resolution. The relationship between DEM accuracy and accuracy of topographic index is positive (Fig: 5.22). At first the variation has been established within each specific basin. The relation is found to be linear and positive. The degree of correlation (R 2 ) between DEM accuracy (RMSE) and TI RMSE reduced from rugged to flat basin. The slope of the regression line does not seem to depend on terrain ruggedness. RMSE of TI Highly 6 5y = x R 2 = RMSE of Terrain Model RMSE of TI Terrain y = x R 2 = RMSE of Terrain Model RMSE of TI Moderately y = x R 2 = RMSE of terrain Model Rmse of TI Undulated y = x R 2 = RMSE of Terrain Model RMSE of TI Flat y = x R 2 = RMSE of Terrain Model Figure 5-22: Terrain specific relationship between RMSE of DEM and RMSE of TI. 52

64 If we build up the relationship between the accuracy of DEM (RMSE) and RMSE of TI of the five basins altogether (Fig: 5.23), the slope, intercept and correlation (R 2 ) of regression are (0.0236, and ) become low. It can be said that terrain variability has a much stronger influence on the DEM accuracy than on the TI. Here it should be remarked that the accuracy of DEM does not only depend on spacing, but also on the accuracy of the elevation values. This, however, is not subject of the current investigation. RMSE of DSM (X) RMSE of TI (Y) RMSE of Topographic Index Relationship Between DEM accuracy and accuracy of Topographic Index y = x R 2 = RMSE of DEM Figure 5-23: Relation between DEM RMSE and RMSE of TI Table 5-13: RMSE of DEM & RMSE of TI In order to reveal the uncertainty of the slope and intercept the confidence interval (CI) has been computed. The level of confidence has been taken 95% and the confidence limit of the slope and intercept is to and to respectively. That means in 95 % cases the slope and intercept can be vary within this limit. The range of the CI of slope is By observing the regression analysis it has been found that the regression is very week. Hence, the prediction of TI accuracy based on RMSE of DEM is not suitable. 53

65 5.5. Effect of Systematic Error on the accuracy of Topographic index: Generation of DEM from satellite stereo data is a common practice. To generate the DEM using this method we need to do the interior and exterior orientation. Interior orientation defines the internal geometry of a camera or sensor as it existed at the time of data capture. Exterior orientation defines the position and angular orientation of associated with an image and builds the relationship between sensor and ground coordinate system for each line of the data. Due to the deficient orientation of the stereo model an error is introduced in the DEM, referred as systematic error. Cartosat-1 stereo data comes with Rational Polynomial Coefficients (RPC s) by which stereo model can be oriented. But in order to improve the orientation as defined by the RPCs, Ground Control Points (GCP s) are needed. The present study has focused on the effect of systematic error on topographic index. Derivation of topographic index needed the slope and specific catchment area as input. Accuracy of both the attribute depends on the accurate height value of the surface. So, it is necessary to asses whether the systematic error, which is left when orienting a Cartosat stereo pair with RPCs only, significantly influences the TI. In order to visualize this stereo model has been oriented using (1) only RPC s and derived DEM and (2) using RPCs and GCPs in which systematic error has been minimised Table 5.14 shows that RPC oriented stereo model suffers from a large positional shift with respect to Ground Control Point (GCP s). POINT_ID X Y X (RPC DEM) Y (RPC DEM) Shift in X Shift in Y Point Point Point Point Point Point Point Point Point Point Point Table 5-14: Shift in RPC DEM A positional shift only, however, has no impact on slope derived from the DEM and thus not on the TI. It is important to calculate whether the systematic error causes the DEM to be inclined. We tested the vertical accuracy of both DEMs, the one from the RPC oriented stereo model and the one from the RPC and GCP oriented stereo model, with respect to GCP s. The results are shown in Table:

66 POINT_ID X Y Z Z GCP DEM Error in DEM GCP Table 5-15: Vertical errors in RPC DEM Z RPC DEM Error in RPC DEM Point Point Point Point Point Point Point Point Point Point Point It has been found to be the error in height value is much high in the RPC oriented DEM. But the distribution of systematic error is not equal to every where, so the effect of systematic error on the inclination has been studied. Computed the mean shift of X and Y in RPC oriented DEM with respect to GCP s and applied the shift on DEM, calculated the difference DEM ( RPC oriented DEM and RPC and GCP oriented DEM) and check the inclination trend. Figure 5-24: Inclination due to systematic error We found that the surface is inclined South East direction (Fig: 5.24) due to the systematic error. In order to visualize the effect of the systematic error on the TI surface, the computation of TI and slope was done from RPC oriented DEM (10 m resolution) and compared with the reference DEM. From the difference surfaces the RMSE was computed (Table: 5.16a). Basin RMSError in slope RMSError in TI Highly Moderate Undulated Flat Table 5-16 (a): Effect of systematic error on RMSE of slope and RMSE of TI 55

67 Effect of systematic error on the accuracy of Topographic index Effect of systematic error on the accuracy of slope RMSE of TI Highly Moderate Undulated Flat RMSE of Slope Highly Moderate Undulated Flat Basin Basin (a) (b) Figure 5-25 : (a) RMSE of TI and 5.25(b) RMSE of Slope We found that the TI of the undulated and flat basins is more affected by the systematic error (Fig: 5.25 a & b). The effect of systematic error is less in the central part of the DEM than along the edges. Both the basins (undulated and flat) are located in the northern and south eastern edge of the DEM. Because of that the influence of systematic error on TI surface is high in these two basins. Basin Mean Error in slope Mean Error in TI Highly Moderate Undulated Table 5.16 (b): Effect of systematic error on ME of slope and ME of TI Mean error of slope Mean Error of Slope due to systematic error of DEM Highly Moderate Undulated Flat Basin Mean error of TI Mean Error of Slope due to systematic error of DEM Highly Moderate Undulated Flat Basin Figure: 5.25 (c) & (d): ME of slope and ME of TI. The plot of mean error shows that due to the systematic error the slope is over predicted in the highly rugged basin and under predicted in the flat basin. Because of this reason TI is under estimated in the highly rugged basin and over estimated in the flat basin. The mean error of slope and TI in rugged, undulated and moderate very low in comparison with other basin. 56

68 5.6. Effect of incomplete catchment area on the accuracy of Topographic index: In order to find out the importance of catchment delineation for derivation of topographic index, an investigation is carried out in the present study. Two incomplete catchments were selected from the upper catchment of highly rugged and undulated basin. Upslope area and topographic index is derived in different resolution (10 m, 50 m and 90 m) with respect to this incomplete catchment and compare with the upslope area and TI of complete catchment. It is found that slope of the catchment does not change with respect basin area but the upslope area is highly changing with respect to complete basin. The major difficulties of upslope area and TI are found along the drainage line. RMSE RMSE of Upslope area due to Incomplete catchment delineation (Higly rugged catchment) RMSE of TI RMSE of TI due to Incomplete catchment delineation (Higly rugged catchment) 0 10m 30m 50m 90m 110m 150m Re solution 0 10m 30m 50m 90m Re solution (a) (b) Mean error Mean Error of upslope area due to Incomplete catchment delineation (Higly rugged catchment) Mean error Mean error of TI due to Incomplete catchment delineation (Higly rugged catchment) m 30m 50m 90m Resolution m 30m 50m 90m Resolution (c) (d) Figure 5-26: (a) RMSE of upslope area, (b) RMSE of TI, (c) ME of upslope area, (d) ME of TI (highly rugged catchment) Fig.5.26 shows the RMSE and Mean error calculated for incomplete (Highly Terrain) basin. RMSE and Mean error calculated by taking the difference between upslope area and TI of incomplete basin and upslope area and TI of complete basin. Mean error plot shows that the upslope area is under estimated, and due to this reason the RMSE of TI and upslope area is increasing. If we move towards the low resolution the RMSE and TI is increasing because of under estimation of upslope area. 57

69 RMSE RMSE of upslope area due to Incomplete catchment delineation (undulated catchment) RMSE of TI RMSE of TI due to Incomplete catchment delineation (undulated catchment) 0 10m 30m 50m 90m 110m 150m Resolution 0 10m 30m 50m 90m Re solution (a) (b) Mean Error of upslope area due to Incomplete catchment delineation (Undulated catchment) Mean Error of TI due to Incomplete catchment delineation (Undulated catchment) Mean error Mean error m 30m 50m 90m Re solution m 30m 50m 90m Res olution (c) (d) Figure 5-27: (a) RMSE of upslope area, (b) RMSE of TI, (c) ME of upslope area, (d) ME of TI ( Undulated catchment) Fig: 5.27 shows that RMSE and Mean error curve of another incomplete basin taken from the upper part of undulated basin. The RMSE curve, upslope area and TI show that the RMSE is highly increasing after 30 m gird spacing. From the above investigation, it can be concluded that proper catchment delineation is needed for deriving Topographic Index and larger the spacing the more important proper delineation becomes Relevance of DSM filtering for the Topographic index generation: Topographic index computation should be done based on bare earth surface model (DTM). Hydrologists are interested on Digital Terrain Model for computation of flow direction, flow accumulation, upslope area and topographic index, because the water flows according to the slope of the ground surface. If we calculate the slope from the DSM, an additional error could be introduced in the slope map. This error is depend upon the forest density and homogeneity. DSM also provides the higher apparent terrain ruggedness. The accuracy of TI depend upon the computation of slope as well 58

70 as terrain ruggedness (discuss in the previous section). Hence, the filtering of DSM is necessary for TI computation. But in the current study filtering of DSM has not been done because of the unavailability of the tools Quantification of Terrain ness: An investigation has been made in this study to quantify the terrain ruggedness Moran s I Autocorrelation Index: Moran s I autocorrelation index has been used to quantify the terrain roughness. In case of highly rugged terrain the elevation of the surface changes within very short distance due to the high variation of the slope. But in flat terrain variation of the slope is very low and elevation values are similar over a large area. Hence rough terrain should have low spatial autocorrelation in comparison with inclined and flat terrain. Fig: 5.28 shows the Moran I value for different terrains as calculated from different resolution DEM. The curve shows that rugged terrain have less spatial autocorrelation in comparison to flat and moderate terrain. But in the flat terrain Moran s-i value is much lower as well as for moderate terrain having very high spatial autocorrelation. Hence, the single value Moran s- I spatial autocorrelation index is not able to depict the ruggedness characteristics of the terrain. Basin/Resolution 10m 30m 50m 90m 110m 150m Highly Moderate Undulated Flat Table 5-17: Moran s I Index value Moran's I index computed from different resolution DEM 1.00 Moran's I Ex_hilly Hilly Moderate Almost_flat Flat m 30m 50m 90m 110m 150m Resolution 59

71 Figure 5-28: Moran s I index of different Terrain In order to avoid this, the Moran s I index computed with respect to the function of lag distance. 8 pixel distances were taken as lag distance to calculate Moran s I index (all table are in the Appendix- 8). DEM with different resolution, the lag spacing is not constant. So, the comparison of the resultant value is difficult. Moran's I index with the function of lag distance (Highly T errain) 1 DEM 10 m Moran's I m 50m 90m 110 m 150m d 2d 3d 4d 5d 6d 7d 8d Lag spacing (a) 1 Moran's I index with the function of lag distance ( Terrain) Moran's I m 30m 50m 90m 110m 150m d 2d 3d 4d 5d 6d 7d 8d Lag distance (b) 60

72 Moran's I Moran's I index with the function of lag distance (M oderate Terrain) DEM 10m 30m 50m 90m 110m 150m d 2d 3d 4d 5d 6d 7d 8d Lag distance (c) 1 Moran's I index with the function of lag distance (undulated Terrain) Moran's I d 2d 3d 4d 5d 6d 7d 8d Lag distance (d) 10m 30m 50m 90m 110m 150m 1 Moran's I index with the function of lag distance (Flat Terrain) Moran's I m 30m 50m 90m 110m 150m d 2d 3d 4d 5d 6d 7d 8d Lag distance Figure 5-29: Moran s I autocorrelation plot of five terrain with the function of lag spacing (a) Highly terrain, (b) terrain, (c) Moderate terrain, (d) Undulated terrain,(e) Flat terrain. (e) 61

73 The plots of Moran s I value with respect to lag spacing suggest that the variation of spatial autocorrelation in a particular terrain with respect to grid spacing is very low. More over in the undulated and flat terrain the index value of 30 m and 50 m resolution DEM is higher in compare to the 10 m resolution DEM. The plots also indicate that the slope of the curve in undulated and flat terrain is less in comparison with highly rugged and rugged terrain. Hence, this method cannot be considered as good terrain classifier Mean and Variance of Slope: Mean and Variance of slope has been taken into consideration to classify the terrain according to ruggedness. Fig: 5.30 shows the mean and Fig: 5.31 shows the variance of slope computed for five terrains. Mean of slope gives an indication of terrain roughness. But mean of slope cannot be a good classifier of terrain roughness, because of an inclined terrain can have high mean of slope but it would not be rugged. Mean of slope Mean of slope Highly Moderately Undulated Flat m 30m 50m 90m 110m 150m resolution Figure 5-30: Mean of Slope ness of terrain can be expressed as variation of slope. Fig: 5.31 shows that from rough to flat terrain, variance of slope is decreasing. But flat terrain shows high variance in comparison with undulated terrain as well as moderate terrain (90 m to 150 m resolution). Hence it appears that, if the terrain is rough, variance of slope can be used as an indicator of roughness. But for flat terrain, it is not suitable terrain classifier. Terrain / Resolution 10m 30m 50m 90m 110m 150m Highly Moderately Undulated Flat Table 5-18: Variance of slope 62

74 16.00 Variance of slope Variance of slope Highly Moderately Undulated Flat m 30m 50m 90m 110m 150m Resolution Figure 5-31: Plot of variance of slope Terrain ness Index (TRI): Terrain ruggedness index has been applied to quantify the roughness of terrain. Mean of TRI surface has been taken as an indication of terrain ruggedness. Fig: 5.32 shows that mean of TRI value plotted against resolution. It is visible from the curves that within the same resolution terrain could possibly be classified using mean of TRI. But the TRI curves depict that ruggedness increases with decreasing the resolution, which is misleading. When increasing the grid spacing terrain does not get rougher but neighbouring elevation values in the DEM become more disjoint thus slope calculations which do not take the spacing into account will lead to larger values. Terrain / resolution 10 30m 50m 90m 110m 150m m Highly Moderately Undulated Table 5-19: Mean of TRI Mean of TRI Terrain ness Index (Using TRI) 10m 30m 50m 90m 110m 150m Resolution Highly Moderatel y Undulated Flat Figure 5-32: Plot of Terrain ruggedness Index 63

75 TRI represents the root-mean-square slope of the 8 neighbours. The RMS slope is not suitable roughness indicator, because a perfectly flat but inclined plane also gives the high TRI value. As mentioned above roughness is the change of slope, which is also referred to as curvature. We can apply Laplace operation to calculate a second difference. In order to demonstrate the difference between TRI and Laplace, two examples are shown in the following: Example-1 represents an inclined plane elevation matrix-1. elevation matrix squared slope matrix TRI = 17 Laplace Apply on elevation matrix 1 Laplace = 0 elevation matrix squared slope matrix TRI = 10 Laplace =40 The TRI value for the inclined plane is 17, while the Laplace filter yields 0 Example-2 (elevation matrix 2) represents an element of rough terrain with slope values not larger than in example 1. The rougher surface 2 produces a TRI value of 10 but a Laplace value of 40. This simple example shows that TRI is unlikely to consistently provide a suitable terrain ruggedness measure Laplace Operator: Based on above mentioned conclusion Laplace Operator has been applied and root mean square of the Laplace surface has been taken to quantify terrain ruggedness. In Fig: r.m.s. Laplace is plotted against grid spacing. The plot shows that the terrain can be differentiated according to ruggedness, but it is not independent with respect to grid spacing. The same applies as outlined above for the TRI. Basin/Resolution 10m 30m 50m 90m 110 m Table 5-20: Laplace table 150 m Highly Moderately Undulated Flat

76 22.00 Quantification of terrain ruggedness (Using Laplace Filter) r.m.s Laplace Highly Moderately Undulated Flat m 50m 90m 110m 150m Grid s pacing Figure 5-33 Plot of r.m.s Laplace Sum of mean TRI and r.m.s. Laplace also taken into consideration in order to prepare a combined index. (Fig: 5.34). The combined index does not seem to offer a better differentiation of the terrain types than the component indicates. Sum of TRI & Laplace Terrain ness (sum of r.m.s. Laplace and Mean of TRI) m 30m 50m 90m 110m 150m Grid Spacing Highly Moderatel y Undulated Flat Figure 5-34: Plot of r.m.s Laplace & mean TRI Normalize Laplace : In Laplace operator calculation, grid spacing of DEM over which elevation variation happens, is not considered. Laplace operator has been normalized using the grid spacing (Table 5.21). In Fig: 5.35 r.m.s of normalize Laplace value of five terrain is plotted with respect to grid spacing. Terrain / Resolution 10m 30m 50m 90m 110m 150m Highly Moderately Undulated Flat Table 5-21: Terrain ruggedness quantification using normalize Laplace operator. 65

77 The plot shows that rougher the terrain higher the value of r.m.s.laplace. The ruggedness indicator decreases from high to low resolution. Based on these limited experiments we may conclude that the normalized Laplace is a simple but good candidate for a terrain roughness classifier, worth further investigations Quantification of terrain ruggedness (Using Normalize Laplace Filter) Normalize Laplace Highly Moderately Undulated Flat m 30m 50m 90m 110m 150m Grid spacing Figure 5-35: Plot of r.m.s of normalize Laplace 5.9. Development of method for predicting the accuracy of topographic index with respect to terrain ruggedness and grid spacing: The main objective of the study has been to develop method for prediction of TI accuracy. During the analysis it has been found that grid spacing and terrain ruggedness are prime factors which affect of Topographic index (among the various factor considered in the present study). In order to achieve it, terrain ruggedness is quantified using several candidates (mentioned in previous section). Among those r.m.s. of normalized Laplace and variance of slope (with the function of grid spacing) was found to be good terrain classifier. The RMSE of TI is computed by Detailed RMSE Method. It would be convenient if a simple linear regression could serve as a means of predicting the accuracy of TI, the RMSE of TI as function of the terrain ruggedness value, which can be derived from the DTM at hand. In order to do this linear regression has been established with respect to terrain ruggedness (variance of slope and r.m.s.normalized Laplace operator value) value and RMSE of TI (computed using detailed RMSE method). The slope and intercept of the regression derived using the following table: 5.7 and 5.21 (RMSE of TI and normalize Laplace value), Table: 5.7 and 5.18 (RMSE of TI and variance of slope). The combined table of five terrains is given below: 66

78 r.m.s.normalize Laplace RMSE of TI (a) Variance of slope RMSE of TI (b) Table 5-22: (a) TI RMSE with respect to the terrain ruggedness (r.m.s. normalize Laplace) and (b) TI RMSE with respect to the terrain ruggedness (variance of slope). RMSE of TI Relation between Terrain ness and Accuracy of Topog raphic Index y = x R 2 = ness Value (rms normalize Laplace) Figure 5-36: Relation between terrain ruggedness (r.m.s. normalize Laplace and RMSE of TI) 67

79 The slope and intercept of the regression derived from the Table: 5.22 (a) is and respectively R-square of the relationship is RMSE of the TI can be predict using this equation RMSE of TI = * Terrain ruggedness Equation 1 RMSE of TI Relation between Terrain ness and Accuracy of Topog raphic Index 6.00 y = x R 2 = ness Value (variance of slope) Figure 5-37: Relation between terrain ruggedness (variance of slope and RMSE of TI). The slope and intercept of the regression derived from the Table: 5.22 (b) is and respectively R-square of the relationship is RMSE of the TI can be predict using this equation RMSE of TI = * Terrain ruggedness Equation 2 The R-square of (Equation 1 and 2) 0.33 and 0.49 are not very high, although variance of slope is better correlated with RMSE of TI than normalized Laplace. However, if we quantify the ruggedness of the terrain applying the normalized Lapace or variance of slope, we can get an idea how accurate topographic index will be, when using the above equations. Figure 5.36 and 5.38 suggests that the accuracy prediction becomes more certain for DEMs with larger roughness values. The above mentioned equation (equation 1 and 2) could be use to solve the following practical problem: If we want to compute the TI of a particular basin and the RMSE of the TI should not be larger than 4, the largest spacing which will still be good enough for TI generation can be determine from the above equation by calculating the terrain roughness value from a small sample DEM. 68

80 6. Conclusion and Recommendation The main aim of the study is to develop a method for predicting the accuracy of topographic index considering the prime influencing factors. The different factors which affect the accuracy of Topographic Index were identified, namely grid spacing of DTM, roughness of the terrain, systematic error of DTM, improper delineation of drainage basin, random errors of elevation values of the DTM, gross error of DTM (including the effect of not filtering a DSM to a DTM), the algorithm used for computing slope from a DEM, and the TI generation algorithm. Within those factors only the first 4 factors were empirically evaluated in this study. Among the influencing factors Grid Spacing and Terrain ness were identified as prime factor of topographic index accuracy. The empirical study was carried out over Western Dehradun terrain using Cartosat-1 stereo data. The accuracy of the topographic index was defined in relative terms: how much does the TI deviate from a reference TI when changing prime influencing factors. We took as reference the TI calculated from the 10 m DEM, which we generated from the Cartosat-1 images. We did not filter the elevation data because of lacking resources. Five catchments having different ruggedness characteristics were selected. We computed for each catchment DEMs of different grid spacing, derived the TI for all, and then assessed how much they deviate from the reference. In order to do so, four different methods were used for accuracy assessment. a) Location wise Comparison Method b) Areal Mean based Comparison Method c) Detailed RMSE Method d) Standard Error Assessment Method Within these four methods, the Detailed RMSE method was found to most suitable for accuracy assessment. The study showed that mean of the topographic index increases with the grid spacing. Up to a grid spacing of the DEM of 90 m the relation between the mean of topographic index and grid spacing turned out to be near linear in nature. 69

81 We also found that topographic index surface becomes more erroneous with decreasing the grid spacing the rougher the terrain. The lower the resolution of a DEM the smaller the calculated slope will be, hence the topographic index will be over estimated when reducing the grid spacing. We found that there is a behavioral dissimilarity between DEM and TI when decreasing the DEM resolution. The mean of TI increases with spacing but the mean of elevation remains constant. The sensitivity to terrain roughness of the accuracy decrease with increasing grid spacing is likely to be larger for the DEM than for the TI. Investigation was made to asses the systematic error of DEM and its effect on topographic index. It has been found that systematic error of DEM not only affects the horizontal accuracy but can also have an inclination effect on surface model. Due to this reason topographic index accuracy is affected by the systematic error. In order to find out the importance of catchment delineation for generation of topographic index an investigation was carried out considering two incomplete catchment. It has been found that upslope area of incomplete basin is highly changing with respect to complete basin. The TI surface also erroneous due to the improper catchment delineation. The major difficulties of upslope area and TI are found along the drainage line. An investigation was carried out to establish the relationship between DEM accuracy and accuracy of topographic index. By analyzing the linear regression it has been found that the relationship is very week. Hence, the study concludes that prediction of TI accuracy based on RMSE of DEM is not feasible. An attempt has been made to quantify the terrain ruggedness using Moran s I autocorrelation index. It has been found that Moran s I is not a suitable terrain roughness classifier. The change of slope parameter (variance of slope and normalize Laplace operator) has been found to suitable terrain roughness classification. In order to identify the effect of terrain variability on TI accuracy, we have tested various parameters for their suitability to quantify roughness of the terrain. Several methods were used (Moran s I autocorrelation index, mean and variance of slope, terrain ruggedness index, Laplace operator, normalized Laplace operator) and found that normalized Laplace and variance of slope are good 70

82 candidates for classifier of terrain ruggedness. More investigations, however, are necessary to find the best suited one. Analyzing the influencing factors of TI, the study concludes that for the given setting beyond 90 m TI s become unreliable with respect to a TI calculated from a 10 m DEM. Because after 90 m resolution accuracy of TI is highly deteriorates which is more pronounced in rugged terrain. Finally an attempt is made to develop a simple method for prediction of TI accuracy with respect to grid spacing and terrain roughness. Linear regression has been established between ruggedness value and RMSE of TI. It is found that, though the R-square is not very exciting, the prediction of TI accuracy with respect to terrain ruggedness value and grid spacing is feasible. The study also suggests that the accuracy prediction of TI is more certain for rough terrain. Recommendations Further investigation should be made to assess the TI accuracy considering the different slope algorithm. How the accuracy of TI can be vary with respect to various slope algorithms and finding out the most suitable algorithm for derivation of TI is important to further study in specific terrain. Topography index can derived using single flow direction algorithm and multiple flow direction algorithms. The further study can be carried out to select the optimum algorithm for TI generation in different rugged terrain. Further study can be carried out to asses the accuracy of topographic index with respect to gross error and random error of DTMs. It is also need to investigate the effect of TI accuracy on prediction of Hydrological model. In the present study validation 30 m to 150 m resolution TI was done with respect to 10 m data sets. Instead of taking this any other high resolution and accurate DEM (like LiDAR DEM) could be used for validation purpose. Due to the limited resource availability filtering of DSM to a DTM was not possible in this study. But it is important to investigate the effect of DSM filtering on derivation of topographic index. 71

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86 Appendix Appendix-1 SL. NO Point ID Date & Time Latitude (Y) Longitude (X) Elevation (Z) in m 2 Pnt-1 7/31/07 12: ' " 77 48' " Pnt-2 7/31/07 14: ' " 77 49' " Pnt-3 7/31/07 15: ' " 77 53' " Pnt-4 1/8/07 14: ' " 77 53' " Pnt-5 1/8/07 16: ' " 77 50' " Pnt-6 1/8/07 17: ' " 77 49' " Pnt-7 7/8/07 11: ' " 77 56' " Pnt 8 7/8/07 13: ' " 77 47' " Pnt_9 7/8/07 14: ' " 77 45' " Pnt 10 7/8/07 16: ' " 77 44' " Differentially corrected ground control point co-ordinates Appendix-2 SL. NO Point ID Time of operation Satelites Viewed (Satelite ID) Excluded Satelite for processing Cut-off angle in degrees 2 Pnt-1 0h 53m 20s 1,3,13,16,19,20,23,25,27,31 1,19,27, Pnt-2 0h 58m 00s 3,8,13,16,19,20,23,25,27,28 None 15 4 Pnt-3 0h 58m 00s 3,8,11,13,17,19,23,25,27,28 None 18 5 Pnt-4 1h 06m oos 1,3,13,16,20,23,25,31 None 10 6 Pnt-5 0h 55m 00s 3,8,13,16,19,20,23,25, Pnt-6 1h 00m 40s 3,8,11,13,19,23,25,27, Pnt-7 0h 58m 00s 3,8,11,17,19,23,25,26,27,28,29 3, Pnt-8 0h 55m 00s 8,11,17,19,25,26,27,28,29 None Pnt-9 0h 42m 20s 3,,8,13,16,19,20,23,25,27,28 None Pnt-10 0h 59m 20s 3,8,11,13,19,23,25,27,28 None 10 Post processing of GPS data 75

87 Appendix-3 SL. NO Point ID Position quality (Degree decimal) Height quality (m) GPS points quality report position & height quality 2 Pnt Pnt Pnt Pnt Pnt Pnt Pnt Pnt Pnt Pnt Appendix-4 Orientation of the Cartosat stereo block 76