Wet May 29/30 Avg. June 26/28 Dry August 22 R 2 =0.79 R 2 =0.24

Transcription

1 GEOG 090 Quantitative Methods in Geography Wet May 29/30 Avg. June 26/28 Dry August Pond Branch - PG 11.25m DEM Theta R 2 = TMI Theta R 2 = TMI Theta R 2 = TMI Glyndon LIDAR 0.5m DEM 11x11 Theta R 2 = TMI Theta 0.5 R 2 = TMI Theta R 2 = TMI

2 GEOG 090 Quantitative Methods in Geography Course Description: Geography is a diverse discipline, that seeks to understand our world in terms of space and place. A significant proportion of geographers approach these issues quantitatively they make use of numerical and computational approaches to describe, understand, and assess the significance of geographic phenomena This course will provide you with an introduction to quantitative approaches in geography

3 GEOG 090 Quantitative Methods in Geography Quantitative methods refers primarily, but not exclusively, to statistics We are going to cover a range of descriptive and inferential (univariate and multi-variate to a lesser extent) statistical methods in this course, BUT We are also going to spend some time talking about some of the background and theory that you need to make use of statistics properly in the context of geography

4 GEOG 090 Quantitative Methods in Geography Statistics and the scientific method, data types, data portrayal and frequency distributions (Review of notation), descriptive statistics including measures of central tendency and dispersion, plus skewness and kurtosis Probability distributions, data sources and sampling and the central limit theorem Hypothesis testing and inferential statistics Correlation and regression approaches

5 GEOG 090 Quantitative Methods in Geography Goals for the Course: For students to gain some familiarity with quantitative methods in geography, such that you can be effective consumers of statistical information and results (in geographic contexts and in general) become producers of meaningful statistical results (i.e. if you choose to pursue research etc.) although this may require further coursework

6 Reading - Required Textbook Statistical Methods for Geography by Peter Rogerson Softcover - $36.95 at Student Stores This text is very readable and rather concise (unlike many stats texts that are rather verbose)

7 Lectures - Where, When, and Who Where: Phillips Hall Room 328 When: Tuesday and Thursday at 2:00 PM Who: Students enrolled in the course Who else: The instructor teaching the course Name David Tenenbaum Degrees Hon. B.Sc. & M.Sc. (Univ. of Toronto), Ph.D. (UNC-Chapel Hill) Research Multi-scale Analysis of Moisture Patterns in Urbanizing Landscapes

8 Goal and Key Questions The overall goal of my dissertation is to investigate how soil moisture patterns and dynamics are functions of the characteristics of urbanizing landscapes. Key questions to be addressed are: 1. What is the relationship between near surface soil moisture and topographic moisture index in urbanizing catchments? 2. In the same catchments, what relationships can be established between LULC configuration and landscape terrain statistics? 3. What relationships can be established between surface moisture conditions and patterns of natural and anthropogenic moisture forcings?

9 Fine Scale Topographic Effects on Near Surface Soil Moisture Patterns The urbanizing landscape s greater heterogeneity impacts land cover and modifies flowpaths: Soil moisture is a key, observable hydrologic store that can be used to characterize the spatial distribution of changes in patterns and processes

10 Study Catchments in Suburban Maryland

11 Pond Branch Catchment Control Color Infrared Digital Orthophotography

12 Glyndon Catchment Urbanizing Color Infrared Digital Orthophotography

13 Soil Moisture Sampling Method 25 samples taken using a random walk within a 5 meter circle ThetaProbe Soil Moisture Sensor - measures the impedance of the sensing rod array, a f(x) of the soil s moisture content 5 meter diameter

14 Topographic Moisture Index TMI = ln(a/tanβ) Hornsberger, G.M., Raffensberger, J.P., Wiberg, P.L. and K.N. Eshleman Elements of Physical Hydrology, Johns Hopkins Press, U.S.A., p. 210 & p. 216.

15 Pond Branch Catchment Control Topographic Index Example

16 Comparing Soil Moisture and TMI Sites Theta TMI Compare Vol. Soil Moisture (V/V) Pond Branch - 6/26/02 - Average TMI

17 Pond Branch - PG 11.25m DEM Wet May 29/30 Avg. June 26/28 Dry August 22 Theta R 2 = TMI Theta R 2 = TMI Theta R 2 = TMI Glyndon LIDAR 0.5m DEM 11x11 Theta R 2 = TMI Theta R 2 = TMI Theta R 2 = TMI

18 Glyndon Average Theta vs. Theta-TMI Correlation (derived from Theta vs. TMI from 0.5m LIDAR, 11x11 Kernel) Correlation R 2 = Average Theta

19 Pond Branch Average Theta vs Theta-TMI Correlation (derived from Theta vs. TMI from 11.25m Photogram.) Correlation R 2 = Average Theta

20 Transect Sampling for Land-Use/Land Cover Characterization Development in the urbanizing landscape clearly modifies the flow of water through the presence of infrastructure that affects drainage patterns Where do specific types of land covers and materials at the fine scale tend to be located in urbanizing catchments? Land use / land cover characterization can be obtained by transect sampling of digital orthophotography in conjunction with highresolution DEMs

21 Land Use/Land Cover Characterization to Support Hydroecological Models Landscape Representations Method: Transect sampling by visual interpretation Identify LULC segments in transects to characterize the urban landscape Why transect sampling? More efficient than complete census Provides information on proportion, adjacency and arrangement, and can be used to collect band statistics or statistics from co-registered raster layers Remotely sensed transects do not require property owner permission to sample sites of interest (thus avoiding the need to dodge vicious dogs!)

22 Transects & Segments

23 BES Segment Classes Primary Class Secondary Class Primary Class Secondary Class Deciduous Soil Coniferous Ground Rock Woody Small tree/shrub Debris Hort. Shrub Parking lot (# of cars?) Mixed Driveway (# of cars?) Pavement Orchard Walkway Lawn - Home Other Lawn - Institutional Interstate/Highway Recreational Field > 2 Lanes Road Golf course <= 2 Lanes Herbaceous Cemetary Alley Unmanaged field Res. - Detached Row crop Res. - Attached Pasture Res. - Apartment/Condo. Wetland Structure Res. - Garage Pond/Lake/Reservoir Non-residential Water Stream Barn Bay Outbuilding Swimming pool

24 Transect Placement Software selects a random starting position for each transect, applying criteria Software assigns a random to each direction transect

25 Segment Identification User selects a transect in which to identify segments Segment s spatial extent and attributes are specified using custom-designed GUIs

26 Upper Baismans Run

27 Glyndon Sampling Kilometers N Glyndon Sample 1 Glyndon Sample 2 Glyndon Sample 3 W E S 3 Samples, 100 meters/ha, 100 meter long transects

28 Upper Baismans Run Sampling Kilometers W N E Upper Baismans Run Sample 1 Upper Baismans Run Sample 2 Upper Baismans Run Sample 3 S 3 Samples, 100 meters/ha, 100 meter long transects

29 Primary Class Proportions Class Glyndon Percentage of Total Length Upper Baismans Run Primary Class Sample 1 Sample 2 Sample 3 Total Sample 1 Sample 2 Sample 3 Total Woody Herbaceous Water Ground Pavement Road Structure

30 Glyndon Segment Length Distributions Upper Baismans Run Percent of all segments in class Percent of all segments in class Segment length (meters) Woody Herbaceous Pavement Roads Structures Segment length (meters) Woody Herbaceous Pavement Roads Structures

31 Glyndon Primary Class Slope Distributions Upper Baismans Run Percent of all cells in class Percent of all cells in class D-infinity Slope (Degrees) Woody Herbaceous Pavement and Road Structures Ground D-infinity Slope (Degrees) Woody Herbaceous Pavement and Road Structures Ground

32 Glyndon Primary Class TMI 11x11 Distributions Upper Baismans Run Percent of all cells in class Percent of all cells in class x11 Kernel Average of D-infinity Topographic Moisture Index Woody Herbaceous Pavement and Road Structures Ground x11 Kernel Average of D-infinity Topographic Moisture Index Woody Herbaceous Pavement and Road Structures Ground

33 100 Glyndon Primary Class Distance from Stream Distributions Upper Baismans Run Percent of all cells in class Percent of all cells in class Distance to stream along D8 flow paths (m eters) Woody Herbaceous Pavement and Road Structures Ground Distance to stream along D8 flow paths (m eters) Woody Herbaceous Pavement and Road Structures Ground

34 Segment Relative Elevation Statistics by Primary Class Primary Class Mean Elevation of Segment - Mean Elevation of Transect (meters) Glyndon Upper Baismans Run Structure Pavement Herbaceous Road Woody

35 Segment Adjacency Contingency Tables Indicating Higher Segments Rows - Adjacent Segment with Lower Elevation Primary Class Columns - Adjacent Segment with Higher Elevation Woody Herbaceous Pavement Road Structure Woody Herbaceous Pavement Road Structure Glyndon Rows - Adjacent Segment with Lower Elevation Primary Class Columns - Adjacent Segment with Higher Elevation Woody Herbaceous Pavement Road Structure Woody Herbaceous Pavement Road Structure Upper Baismans Run Higher of Pair Lower of Pair

36 Scaling Up the Land Cover-Surface Moisture Relationship TMI in Glyndon Surface moisture in Maryland CD6 While developing these relationships at the small catchment scale is important, ultimately we want to know something about them at the scale of regional metropolitan areas How do we assess the surface moisture condition at this scale? Remote sensing!

37 Generating TVDI Values VI-T s T s VI TVDI

38 Modeling TVDI TVDI API LULC REG

39 Study Climate Divisions

40 MODIS LULC In Climate Divisions Maryland CD6 North Carolina CD3

41 Stepwise Linear Regression TVDI = α + β 1 API + β 2 Wat + β 3 Dbf + β 4 Mf + β 5 Cr + β 6 Ur + β 7 Cnv + β 8 Oth + ε API - Antecedent precipitation index value for the pixel Wat - Percentage of the pixel belonging to the water class Dbf - Percentage of the pixel belonging to the deciduous broadleaf forest class Mf - Percentage of the pixel belonging to the mixed forest class Cr - Percentage of the pixel belonging to the cropland class Ur - Percentage of the pixel belonging to the urban class Cnv - Percentage of the pixel belonging to the cropland-natural vegetation mosaic Oth - Percentage of the pixel belonging to other land use classes. Stepwise procedure selects the best model for each image

42 Maryland CD6 Regression Results Yearday totalr2 dr2lulc dr2api R2

43 North Carolina CD3 Regression Results R Yearday totalr2 dr2lulc dr2api

44 Correlation Tables Cloud totalr2 dr2lulc dr2api Cloud totalr2 dr2lulc dr2api Cloud 1 Cloud 1 totalr totalr dr2lulc dr2lulc dr2api dr2api Maryland CD6 Models relatively insensitive to cloud cover Models rely heavily on LULC North Carolina CD3 Models very sensitive to cloud Models rely on API to a greater extent, and LULC as well

45 Grading 7 exercises, together worth 40% of your grade 10% of the value of an exercise is deducted for each day late that an exercise write-up is submitted 2 tests during the term, each worth 15%, together worth 30% of your grade Tests may not be missed without a legitimate, documented reason, in which case, the value of remaining tests and exams will be adjusted accordingly; otherwise, a grade of 0 will be recorded An open book final exam, worth 30% of your grade The usual Honor Code provisions apply (i.e. if you cheat, plagiarize, etc. you will be subject to sanctions)

46 Exercises The exercises will be due roughly every two weeks They will draw upon the material we cover in lecture They will primarily (but not exclusively) be drawn from the exercises provided at the ends of chapters in the Rogerson text You will make use of digital datasets which will be provided online through the class webpage The software of choice for performing calculations will be Microsoft Excel

47 Open Book Final The final exam is open book because the goal of the course is for you to understand the material and how to apply the concepts, not for you to memorize all the formulae (and by the time we are done, there will be quite a few of them). It will include identifying the appropriate statistical test to use given a scenario, performing statistical tests with simple calculations, and critiquing the use of statistics in a refereed journal article.

48 Instructor Contact Information David Tenenbaum Room 325 Saunders Hall Office Hours: Monday 1:00 3:00 PM Tuesday 3:30 5:00 PM