Data Model Conceptual Model – a set of concepts that describe a subject and allow reasoning about it Mathematical Model – a conceptual model expressed in symbols and equations Data Model – a conceptual model expressed in a data structure (e.g. ascii files, Excel tables, …..) Geographic Data Model – a conceptual model for describing and reasoning about the world expressed in a GIS database

Geographic coordinates Tabular attributes A geographic data model is a structure for organizing geospatial data so that it can be easily stored and retrieved.

Raster and Vector Data Point Line Polygon VectorRaster Raster data are described by a cell grid, one value per cell Zone of cells

Themes or Data Layers Vector data: point, line or polygon features How each of these features could be represented using vector or raster?

ArcGIS Geodatabase (what is in a geodatabase) Geodatabase Feature Dataset Feature Class Geometric Network Object Class Relationship Workspace

Geodatabase and Feature Dataset zA geodatabase is a relational database that stores geographic information. zA feature dataset is a collection of feature classes that share the same spatial reference frame.

Feature Class A feature class is a collection of geographic objects in tabular format that have the same behavior and the same attributes. Feature Class = Object class + spatial coordinates

Object Class An object class is a collection of objects in tabular format that have the same behavior and the same attributes (do not have a shape). An object class is a table that has a unique identifier (ObjectID) for each record

Relationship Relationship between spatial and non-spatial objects Water quality data (non-spatial) Measurement station (spatial)

Geodesy, Map Projections and Coordinate Systems Geodesy - the shape of the earth and definition of earth datums Map Projection - the transformation of a curved earth to a flat map Coordinate systems - (x,y) coordinate systems for map data Spatial Reference = Datum + Projection + Coordinate system

Types of Coordinate Systems (1) Global Cartesian coordinates (x,y,z) for the whole earth (2) Geographic coordinates ( , z) (3) Projected coordinates (x, y, z) on a local area of the earth’s surface The z-coordinate in (1) and (3) is defined geometrically; in (2) the z- coordinate is defined gravitationally

Global Cartesian Coordinates (x,y,z) O X Z Y Greenwich Meridian Equator

Geographic Coordinates ( , z) Latitude (  ) and Longitude ( ) defined using an ellipsoid, an ellipse rotated about an axis Elevation (z) defined using geoid, a surface of constant gravitational potential Earth datums define standard values of the ellipsoid and geoid

Latitude and Longitude Longitude line (Meridian) N S WE Range: 180ºW - 0º - 180ºE Latitude line (Parallel) N S WE Range: 90ºS - 0º - 90ºN (0ºN, 0ºE) Equator, Prime Meridian

Latitude and Longitude in North America 90 W 120 W 60 W 30 N 0 N 60 N Austin: (30°N, 98°W) Logan: (42°N, 112°W) Lincoln: (40 ° N, 96 ° W

Length on Meridians and Parallels 0 N 30 N  ReRe ReRe R R A B C  (Lat, Long) = ( , ) Length on a Meridian: AB = R e  (same for all latitudes) Length on a Parallel: CD = R  R e  Cos  (varies with latitude) D

Example 1: What is the length of a 1º increment along on a meridian and on a parallel at 30N, 90W? Radius of the earth = 6370 km. Solution: A 1º angle has first to be converted to radians  radians = 180 º, so 1º =  /180 = /180 = radians For the meridian,  L = R e  km For the parallel,  L = R e  Cos   Cos   km Parallels converge as poles are approached

Example 2: What is the size of a 1 arc-second DEM cell when projected to (x,y) coordinates at 30º N? Radius of the earth = 6370 km = 6,370,000m = 6.37 x 10 6 m Solution: A 1” angle has first to be converted to radians  radians = 180 º, so 1” = 1/3600 º = (1/3600)  /180 radians = x radians For the left and right sides,  L = R e  6.37 x 10 6 * x =  30.88m For the top and bottom sides,  L = R e  Cos  = 6.37 x 10 6 * x * Cos 30º = x = 26.75m Left and right sides of cell converge as poles are approached

Curved Earth Distance (from A to B) Shortest distance is along a “Great Circle” A “Great Circle” is the intersection of a sphere with a plane going through its center. 1. Spherical coordinates converted to Cartesian coordinates. 2. Vector dot product used to calculate angle  from latitude and longitude 3. Great circle distance is R , where R=6370 km 2 X Z Y  A B Longley et al. (2001)

Horizontal Earth Datums An earth datum is defined by an ellipse and an axis of rotation NAD27 (North American Datum of 1927) uses the Clarke (1866) ellipsoid on a non geocentric axis of rotation NAD83 (NAD,1983) uses the GRS80 ellipsoid on a geocentric axis of rotation WGS84 (World Geodetic System of 1984) uses GRS80, almost the same as NAD83

Vertical Earth Datums A vertical datum defines elevation, z NGVD29 (National Geodetic Vertical Datum of 1929) NAVD88 (North American Vertical Datum of 1988) takes into account a map of gravity anomalies between the ellipsoid and the geoid

Types of Projections Conic (Albers Equal Area, Lambert Conformal Conic) - good for East-West land areas Cylindrical (Transverse Mercator) - good for North-South land areas Azimuthal (Lambert Azimuthal Equal Area) - good for global views

Projections Preserve Some Earth Properties Area - correct earth surface area (Albers Equal Area) important for mass balances Shape - local angles are shown correctly (Lambert Conformal Conic) Direction - all directions are shown correctly relative to the center (Lambert Azimuthal Equal Area) Distance - preserved along particular lines Some projections preserve two properties

Universal Transverse Mercator Uses the Transverse Mercator projection Each zone has a Central Meridian ( o ), zones are 6° wide, and go from pole to pole 60 zones cover the earth from East to West Reference Latitude (  o ), is the equator (Xshift, Yshift) = (x o,y o ) = (500000, 0) in the Northern Hemisphere, units are meters

UTM Zone 14 Equator -120° -90 ° -60 ° -102°-96° -99° Origin 6°

ArcGIS Reference Frames Defined for a feature dataset in ArcCatalog Coordinate System –Projected –Geographic X/Y Domain Z Domain M Domain

X/Y Domain (Min X, Min Y) (Max X, Max Y) Maximum resolution of a point = Map Units / Precision e.g. map units = meters, precision = 1000, then maximum resolution = 1 meter/1000 = 1 mm on the ground Long integer max value of 2 31 = 2,147,483,645

National Hydro Data Programs National Elevation Dataset (NED) National Hydrography Dataset (NHD) Watershed Boundary DatasetNED-Hydrology Data Sources for GIS in Water Resources What is it? What does it contain? What is the GIS format? Where would it be obtained

1:250,000 Scale Soil Information

1:24,000 scale soil information SSURGO: County Level Digital Soil Maps

National Land Cover Dataset the data:

National Water Information System Web access to USGS water resources data in real time

Flow Time Time Series HydrographyHydro Network Channel System Drainage System Arc Hydro Components GIS provides for synthesis of geospatial data with different formats

x y f(x,y) Two fundamental ways of representing geography are discrete objects and fields. The discrete object view represents the real world as objects with well defined boundaries in empty space. The field view represents the real world as a finite number of variables, each one defined at each possible position. (x 1,y 1 ) PointsLinesPolygons Continuous surface Spatial Analysis Using Grids

Vector and Raster Representation of Spatial Fields VectorRaster Discrete space view of the world Continuous space view of the world

Numerical representation of a spatial surface (field) Grid TIN Contour and flowline

Six approximate representations of a field used in GIS Regularly spaced sample pointsIrregularly spaced sample pointsRectangular Cells Irregularly shaped polygonsTriangulated Irregular Network (TIN)Polylines/Contours from Longley, P. A., M. F. Goodchild, D. J. Maguire and D. W. Rind, (2001), Geographic Information Systems and Science, Wiley, 454 p.

Grid Datasets Cellular-based data structure composed of square cells of equal size arranged in rows and columns. The grid cell size and extent (number of rows and columns), as well as the value at each cell have to be stored as part of the grid definition. Number of columns Number of rows Cell size

From: Blöschl, G., (1996), Scale and Scaling in Hydrology, Habilitationsschrift, Weiner Mitteilungen Wasser Abwasser Gewasser, Wien, 346 p. Extent Spacing The scale triplet Support Extent: domain which is being made Spacing: distance between measurements Support: footprints for what those measurements are…

Spatial Generalization Central point ruleLargest share rule

Raster Calculator Cell by cell evaluation of mathematical functions

Raster calculation – some subtleties Analysis extent + = Analysis cell size Analysis mask Resampling or interpolation (and reprojection) of inputs to target extent, cell size, and projection within region defined by analysis mask

Nearest Neighbor Resampling with Cellsize Maximum of Inputs m m *4 = *6 = *2 = *4 = 39

Interpolation Estimate values between known values. A set of spatial analyst functions that predict values for a surface from a limited number of sample points creating a continuous raster. Apparent improvement in resolution may not be justified

Topographic Slope Defined or represented by one of the following –Surface derivative  z –Vector with x and y components –Vector with magnitude (slope) and direction (aspect)

Hydrologic processes are different on hillslopes and in channels. It is important to recognize this and account for this in models. Drainage area can be concentrated or dispersed (specific catchment area) representing concentrated or dispersed flow.

Drainage Density D d = L/A EPA Reach Files100 grid cell threshold1000 grid cell threshold

Network Definition A network is a set of edges and junctions that are topologically connected to each other. Hydro Networks in GIS

Edges and Junctions Simple feature classes: points and lines Network feature classes: junctions and edges Edges can be –Simple: one attribute record for a single edge –Complex: one attribute record for several edges in a linear sequence A single edge cannot be branched No!!

Polylines and Edges

Junctions Junctions exist at all points where edges join –If necessary they are added during network building (generic junctions) Junctions can be placed on the interior of an edge e.g. stream gage Any number of point feature classes can be built into junctions on a single network

Connectivity Table J124 J125 J123 J126 E1 E3 E2 J123J124, E1 J124J123, E1 J125, E2 J126, E3 J125J124, E2 J126J124, E3 JunctionAdjacent Junction and Edge This is the “Logical Network” p. 132 of Modeling our World

Flow to a sink

Network Tracing on the Guadalupe Basin

Linear Referencing Where are we on a line?

Addressing

Streams WatershedsWaterbody Hydro Points Arc Hydro Framework Input Data

Arc Hydro Framework Data Model

DEM Based Watershed and Stream Network Delineation Steps DEM Reconditioning/Burning in Streams Fill Sinks Eight direction pour point model to evaluate flow directions Flow accumulation Threshold stream network definition Stream segmentation Watershed delineation Raster to vector conversion of streams and watersheds

+ =  Take a mapped stream network and a DEM  Make a grid of the streams  Raise the off-stream DEM cells by an arbitrary elevation increment  Produces "burned in" DEM streams = mapped streams “Burning In” the Streams Synthesis of Raster and Vector data

AGREE Elevation Grid Modification Methodology

Filling in the Pits DEM creation results in artificial pits in the landscape A pit is a set of one or more cells which has no downstream cells around it Unless these pits are filled they become sinks and isolate portions of the watershed Pit filling is first thing done with a DEM

Slope: Hydrologic Slope - Direction of Steepest Descent

55 a47 b48 c 67 d56 e A 49 f 52 g45 h42 i (i) standard slope function standard slope = atan( /( )) = o = aspect of o Aspect = o Grid cell size 100m

Eight Direction Pour Point Model Water flows in the direction of steepest descent

Flow Direction Grid

Cell to Cell Grid Network Through the Landscape Stream cell

Contributing Area Grid Drainage area threshold > 5 Cells

Delineation of Streams and Watersheds on a DEM

Stream Segments in a Cell Network

ArcHydro Page 74 Stream links grid for the San Marcos subbasin Each link has a unique identifying number

Vectorized Streams Linked Using Grid Code to Cell Equivalents Vector Streams Grid Streams ArcHydro Page 75

DrainageLines are drawn through the centers of cells on the stream links. DrainagePoints are located at the centers of the outlet cells of the catchments ArcHydro Page 75

Same Cell Value Catchments for Stream Links

For every stream segment, there is a corresponding catchment Catchments are a tessellation of the landscape through a set of physical rules Delineated Catchments and Stream Networks

Raster Zones and Vector Polygons Catchment GridID Vector Polygons DEM GridCode Raster Zones One to one connection

Watershed A watershed is the area draining to any point on the stream network A new kind of connectivity: Area flows to a point on a line

Connecting Drainage Areas to the Network Area goes to point on line

HydroID – a unique identifier of all Arc Hydro features HydroIDs of Drainage PointsHydroIDs of Catchments

Catchment, Watershed, Subwatershed. ArcHydro Page 76 Watershed outlet points may lie within the interior of a catchment, e.g. at a USGS stream-gaging site. Catchments Subwatersheds Watershed