Graphical Summary of Data Distribution Statistical View Point Histograms Skewness Kurtosis Other Descriptive Summary Measures Source:

Graphical Summary of Data DistributionStatistical View PointHistogramsSkewnessKurtosisOther Descriptive Summary MeasuresSource: www.unc.edu/courses/2006spring/geog/090/001/www/Lectures/ 2006- Geog090-Week03-Lecture02-SkewsnessKurtosis.ppt

Measures of Dispersion Coefficient of VariationCoefficient of variation (CV) measures the spread of a set of data as a proportion of its mean. It is the ratio of the sample standard deviation to the sample mean

It is sometimes expressed as a percentageThere is an equivalent definition for the coefficient of variation of a population

Coefficient of Variation (CV)It is a dimensionless number that can be used to compare the amount of variance between populations with different means

Histogram: Frequency & DistributionA histogram is one way to depict a frequency distributionFrequency is the number of times a variable takes on a particular value Note that any variable has a frequency distributione.g. roll a pair of dice several times and record the resulting values (constrained to being between and 2 and 12), counting the number of times any given value occurs (the frequency of that value occurring), and take these all together to form a frequency distribution

Frequency & DistributionFrequencies can be absolute (when the frequency provided is the actual count of the occurrences) or relative (when they are normalized by dividing the absolute frequency by the total number of observations [0, 1])Relative frequencies are particularly useful if you want to compare distributions drawn from two different sources (i.e. while the numbers of observations of each source may be different)

HistogramsWe may summarize our data by constructing histograms, which are vertical bar graphsA histogram is used to graphically summarize the distribution of a data setA histogram divides the range of values in a data set into intervalsOver each interval is placed a bar whose height represents the frequency of data values in the interval.

Building a HistogramTo construct a histogram, the data are first grouped into categoriesThe histogram contains one vertical bar for each categoryThe height of the bar represents the number of observations in the category (i.e., frequency)It is common to note the midpoint of the category on the horizontal axis

Building a Histogram Example1. Develop an ungrouped frequency tableThat is, we build a table that counts the number of occurrences of each variable value from lowest to highest:TMI ValueUngrouped Freq. 4.162 4.174 4.180 13.711We could attempt to construct a bar chart from this table, but it would have too many bars to really be useful

Building a Histogram Example2. Construct a grouped frequency table Select an appropriate number of classes Percentage

tmi histograms

&L&"Times New Roman,Regular"&12D.E. TenenbaumFigure 4

tmi histograms

0.4686767693

14.6070926418

33.6197469145

25.4647711295

11.6388064365

5.8897047336

3.171379472

1.9528198719

1.2029370411

1.0935791283

0.624902359

0.2343383846

0.031245118

GLYNDON

Topographic Moisture Index

Percent of cells in catchment

Glyndon TMI Histogram

tmi data

4.0458530007

27.2083614295

47.5724881996

13.7221847606

2.9332434255

1.1126095752

0.5731625084

0.7417397168

1.4497639919

0.6405933918

0

0

0

POND BRANCH



Pond Branch TMI Histogram

GLYNDONPOND BRANCH4GLYNDONPOND BRANCHTMI

43012050.46867676934.04585300074Sums from 5-8

5935807614.607092641827.2083614295585.330417122391.4362778152

621521411733.619746914547.57248819966

71630407825.464771129513.72218476067

874587911.63880643652.93324342558

937733Labels ->105.88970473361.11260957529

Building a Histogram Example3. Plot the frequencies of each classAll that remains is to create the bar graphA proxy for Soil Moisture

Chart2

4.0458530007

27.2083614295

47.5724881996

13.7221847606

2.9332434255

1.1126095752

0.5731625084

0.7417397168

1.4497639919

0.6405933918

0

0

0

POND BRANCH




Figure 4


Figure 4

13.0322102925

31.4821670986

27.878563495

15.9570529434

6.1458718993

2.8878193262

1.3945452302

0.6540787363

0.320868814

0.2097988399

0.0370233247

0

0

0

0

0

0

0

0

0

0

0

GLYNDON

Slope in degrees


Glyndon Slope Histogram

Figure 5

0.9313464609

5.3485896754

8.9941458222

13.7307078233

12.666311868

11.2293773284

8.6216072379

7.4507716871

6.2001064396

5.5082490687

4.7099521022

2.6343799894

2.6343799894

1.9425226184

1.4635444385

1.7030335285

1.3038850452

1.0111761575

0.9845662586

0.3991484832

0.2927088877

0.2394890899

POND BRANCH

Slope in degrees


Pond Branch Slope Histogram

Figure 7

A

B


Figure 7

0.4686767693

14.6070926418

33.6197469145

25.4647711295

11.6388064365

5.8897047336

3.171379472

1.9528198719

1.2029370411

1.0935791283

0.624902359

0.2343383846

0.031245118

GLYNDON



Glyndon TMI Histogram

Figure 10

4.0458530007

27.2083614295

47.5724881996

13.7221847606

2.9332434255

1.1126095752

0.5731625084

0.7417397168

1.4497639919

0.6405933918

0

0

0

POND BRANCH




Figure 11

A

B


Figure 11

0.453581529137288-0.508

37289372890

37290372900

3729137291-0.254

37292372920

37293372930

3729437294-2.54

0.4296432442372950

37296372960

3729737297-0.762

3729837298-1.016

372990.32514472290

37300373000

37301373010

0.4048605132373020

37303373030

37304373040

37305373050

37306373060

3730737307-0.254

373080.3168748414-0.254

0.3905513808373090

37310373100

37311373110

37312373120

3731337313-2.032

37314373140

373150.31012270060

0.3720305873373160

3731737317-18.288

3731837318-7.874

37319373190

37320373200

37321373210

373220.33385069610

0.4141677978373230

3732437324-2.286

3732537325-3.556

37326373260

3732737327-1.524

3732837328-9.652

37329373290

373300.32719585970

3733137331-0.508

3733237332-3.81

3733337333-9.906

3733437334-1.016

3733537335-23.622

37336373360

37337373370

37338373380

37339373390

37340373400

3734137341-13.97

37342373420

37343373430

0.45003085010.3330019860

37345373450

3734637346-5.08

37347373470

37348373480

3734937349-1.016

0.4391274660.32229244490

37351373510

37352373520

37353373530

37354373540

3735537355-3.556

3735637356-0.254

0.40961860170.3269122820

37358373580

37359373590

3736037360-4.064

3736137361-3.81

37362373620

0.4101304315373630

373640.294772987-13.208

3736537365-7.112

37366373660

3736737367-5.08

3736837368-3.048

37369373690

373700.32653323770

0.436022790437371-3.048

37372373720

3737337373-3.556

3737437374-33.274

37375373750

37376373760

37377373770

3737837378-31.75

373790.354065625-0.254

37380373800

37381373810

37382373820

3738337383-2.032

373840.3130474222-0.254

0.413932493237385-2.794

37386373860

37387373870

3738837388-4.064

3738937389-2.286

373900.30799418540

37391373910

0.3575455722373920

3739337393-5.334

3739437394-22.352

37395373950

373960.3332398710

0.3956857077373970

37398373980

37399373990

37400374000

37401374010

3740237402-9.652

3740337403-9.144

3740437404-0.762

0.4589895962374050

374060.33308279790

3740737407-1.016

37408374080

37409374090

37410374100

3741137411-0.762

3741237412-0.762

0.348986752537413-14.224

374140.3081213146-0.508

3741537415-0.254

37416374160

37417374170

37418374180

0.31435491510.23536620750

3742037420-24.384

3742137421-7.874

3742237422-2.032

37423374230

37424374240

37425374250

0.35493156380.2751649934-0.254

37427374270

37428374280

37429374290

37430374300

37431374310

37432374320

374330.21558350180

3743437434-0.508

0.248990273237435-4.064

37436374360

37437374370

37438374380

37439374390

3744037440-1.016

37441374410

37442374420

37443374430

37444374440

37445374450

3744637446-18.796

3744737447-1.016

0.25236035120.19509432320

3744937449-0.762

3745037450-1.27

3745137451-5.588

3745237452-0.254

37453374530

37454374540

37455374550

0.1852237878374560

37457374570

37458374580

37459374590

37460374600

374610.16475377110

37462374620

3746337463-0.254

3746437464-0.762

3746537465-0.254

37466374660

3746737467-0.254

37468374680

0.1674229225374690

37470374700

3747137471-0.508

37472374720

3747337473-0.254

3747437474-0.254

37475374750

37476374760

37477374770

37478374780

37479374790

37480374800

37481374810

37482374820

0.11757869620.11437196540

37484374840

37485374850

37486374860

37487374870

3748837488-2.794

37489374890

0.09348823280.10325055660

Glyndon

Pond Branch

Precipitation

Date

Vol. Soil Moisture (V/V)

Daily Precipitation (mm)

Precipitation and Soil Moisture for Glyndon and Pond Branch

Figure 11 B&W


Figure 11 B&W

0.1700648773

0.2682576671

0.2354975246

0.255470977

0.1994583674

0.1808739293

0.1651498143

0.266659151

0.3140898906

0.2604796819

0.4212195635

0.1970835764

0.1791690566

0.1830981635

0.3267551206

0.2383627445

0.1091661714

0.2963985361

0.3298895679

0.2414922416

0.2014687732

0.2850605853

0.2732474044

0.4582524657

TI_5M11X11

TMI


Glyndon - 6/28/02 - Average

Figure 12

0.2613054641

0.2283643391

0.3568147719

0.3413809061

0.4911210224

0.3508575037

0.3353383832

0.3476247683

0.3254518523

0.4124278769

0.412856096

0.2674577568

0.3268586919

0.3249692209

0.4835668549

0.2805328459

0.2755795367

0.2555248052

0.2505404644

TI11_25MBC

TMI


Pond Branch - 5/30/02 - Wet

Figure 12 B&W

0.4789539248

0.5032712206

0.4271053612

0.5225900397

0.3918205813

0.4424781695

0.4058920562

0.4924496114

0.4792959279

0.4273171097

0.5444826573

0.4413049519

4.5178

0.4438069925

0.4712376267

0.443393971

0.3787522018

0.4624769136

0.4265989423

0.3951214084

0.4310236514

0.4728094161

0.4879961759

0.5541911483

TI_5M11X11

TMI


Glyndon - 5/29/02 - Wet

Figure 13

0.0843882855

0.1238871448

0.139086052

0.0996634813

0.0399461064

0.0344541099

0.0519015339

0.0988067488

0.0977560295

0.1182629887

0.1221882518

0.0985545889

0.1122413933

0.1005489536

0.1612017266

0.113050399

0.0338656924

0.0724866561

0.1139788757

0.0942433896

0.0825330896

0.0966592389

0.1031153381

0.0713881564

TI_5M11X11

TMI


Glyndon - 8/22/02 - Dry

Figure 14

0.0848772375

0.0560429396

0.0961976767

0.1092117647

0.2587091647

0.0822539918

0.0765071308

0.0799957765

0.0931815188

0.1219747975

0.1175129656

0.0656942884

0.0943358051

0.1310419414

0.2499156371

0.0606326485

0.0658768939

0.0622260727

0.0555723249

TI11_25MBC

TMI


Pond Branch - 8/22/02 - Dry

Table 3

0.1696285535

0.1333770912

0.208378388

0.2304897197

0.4113935702

0.2151356079

0.1853029955

0.1984734654

0.2083240472

0.2765943892

0.2715640701

0.1409898361

0.1917807318

0.2400992386

0.447427664

0.1757179469

0.148657329

0.124966085

0.1177858058

TI11_25MBC

TMI


Pond Branch - 6/26/02 - Average

Table 4

A

C

E

B

D

F

R2=0.80

R2=0.56

R2=0.70

R2=0.32

R2=0.79

R2=0.10


Table 4

-0.1024379375-0.2160221966-0.0543228069

0.07757012890.04510843970.0093962149

0.23705226620.15886373960.2620404908

0.1439040319-0.05216531650.2472369546

0.1653479620.0439585708-0.1410250658

0.38682689510.41728994960.0531833091

0.44621406140.22555739770.1514155609

0.55786788990.39819764630.2553783694

0.43850450870.26330716520.1824126146

0.31031106550.3813532960.0342729953

0.32738201240.30970766540.0580947426

0.50150666560.40798590490.1204325705

0.28342419440.42356992250.0862434481

0.34654676160.45597859320.0364918205

0.29719810220.43129818710.0949391458

0.46905476560.47521430.231579944

0.36823733030.28516044330.1862537582

0.16426753560.32943434820.2900077292

0.30078930060.35813457260.0046558987

0.37681428660.34267163480.322884948

0.45893398410.33133983720.0836073498

0.22650841830.40300337050.360267807

0.19935926340.13186101610.1542420728

0.36898720470.50391095110.2887440151

0.24588870340.28511296150.3282030343

0.19444556670.33854944730.1421956515

0.17500634010.25021598220.107905892

0.35457808540.4047687480.3652163721

0.34025162090.38750483620.3454964118

0.31067542240.35797731080.3475213247

05/29/02

06/28/02

08/22/02

Cell Size (metres)

Correlation (r)

Glyndon LIDAR Soil Moisture Correlation vs. Cell Size

Glyndon

0.15303328190.01863639890.0040534288

0.02936735950.02450190450.0111707009

0.0700499192-0.0722304896-0.159977168

0.1577176719-0.0019021137-0.1107502887

-0.00923399-0.1707202837-0.2589824219

0.1496041486-0.0550307926-0.1591352969

0.39577301820.37454388750.2744496813

0.60482613520.58014757480.4667000035

0.77554603640.80777917430.7459113002

0.72795970350.77718074090.7747496436

0.76167999410.81495486090.8048385805

0.67741549870.73681428120.760322476

0.79101395470.82870810560.8015121537

0.81676636880.87042780690.8480400679

0.70642659520.76466115840.7763336438

0.69521223290.75039321410.7651085917

0.6312730310.72136162170.7647748595

0.77463922040.78439426010.7661207592

0.74988233510.82412654110.8340093499

0.67741549870.73681428120.760322476

0.78439264710.80585185240.7679393973

0.62919699310.67509597340.6336546609

0.74827868310.78803396330.7577743198

0.67759704650.67919483830.5986783319

0.61872057410.6213870960.6382774024

0.56661935980.61647139720.5748149557

0.68668931940.78099884030.814016656

0.2996667210.43013088660.4090231883

0.66047200570.70747689860.7430788469

0.64891631930.70513374520.6936879796

05/30/02

06/26/02

08/22/02

Cell Size (metres)

Correlation (r)

Pond Branch LIDAR Soil Moisture Correlation vs. Cell Size

Pond Branch

0.12280286650.0256000639-0.0421502605

0.15030492970.0385098044-0.0421844281

0.26759273650.16558009150.070838412

0.40528195020.31265674480.1859216782

0.30148217430.17842179360.0382759582

0.3208649910.19526288160.0401724184

0.4381688260.32331500170.1823647696

0.35529308990.18764694580.0263208671

0.69498112110.64468434490.5748129837

0.64641101610.53722508260.3910439305

0.76210732510.67085638390.6320354855

0.69414128520.70798319080.7066984773

0.77048254810.80057395350.7942315597

0.81166740670.83728193080.8314499049

0.83611328090.88863545760.8914110115

0.79688065210.83880933440.8083249116

0.71355623240.81210847740.8291896077

0.78747038560.83246069670.8166077293

0.69214188890.74441260150.7464967385

0.78705453470.83613259380.8150567969

0.78260794420.8315567480.8190939562

0.67178524920.72882495230.6720341625

0.72651497880.79746446820.7987558448

0.49183739510.53561235510.4732244469

0.46082400750.5218250920.4801683834

0.67009553620.72621276610.7473345536

0.52749599180.59034937570.5791999178

0.80258702620.82422503110.8040278669

0.70125018510.73176065610.7346651911

0.51078538760.55433076020.5009682741

05/30/02

06/26/02

08/22/02

Cell Size (metres)

Correlation (r)

Pond Branch PG Soil Moisture Correlation vs. Cell Size

stddev data

0.39709082190.34407665250.1012227343

0.4535889540.17106740330.0254288542

0.36278942490.26003908620.3687878906

0.26184728230.21396220340.1861053717

0.49401025830.35175827890.1009992125

0.48694983660.33176792950.070354804

0.48322810090.46183196440.1675110938

0.25059933370.42008464510.4630456879

0.19718367570.32672893990.3713272076

0.12615175010.22642445110.1717379243

0.29202232030.43244102770.28340716

0.23329188440.40113229610.28618954

0.28755382010.28529639280.2814087832

0.15585399650.39483273830.2507498503

0.34385150060.31945401160.2100610532

0.29171104620.47401370480.5650532243

0.50697987760.19847848830.2496879062

0.21188933380.35588300240.1542779164

0.41550438560.37216130920.5002139878

0.31084601450.47088663310.3883234783

0.28881809790.35665409630.5311163703

0.30853415280.3494515050.3316548049

0.2900754370.3706484090.5636261014

0.31221043460.4447498670.3456178454

0.35998832990.35032336810.5740371023

0.23530758460.14827266070.4187977223

0.32160108230.42366426760.4524246872

0.07128553790.35878081850.3046309103

0.29288231440.25770634540.4737547215

0.26386987360.21522489490.4565309965

05/29/02

06/28/02

08/22/02

Cell Size (metres)

Correlation (r)

Glyndon PG Soil Moisture Correlation vs. Cell Size

plot data

A

B

C

D


plot data

-0.1024379375-0.2160221966-0.0543228069

0.07757012890.04510843970.0093962149

0.23705226620.15886373960.2620404908

0.1439040319-0.05216531650.2472369546

0.1653479620.0439585708-0.1410250658

0.38682689510.41728994960.0531833091

0.44621406140.22555739770.1514155609

0.55786788990.39819764630.2553783694

0.43850450870.26330716520.1824126146

0.31031106550.3813532960.0342729953

0.32738201240.30970766540.0580947426

0.50150666560.40798590490.1204325705

0.28342419440.42356992250.0862434481

0.34654676160.45597859320.0364918205

0.29719810220.43129818710.0949391458

0.46905476560.47521430.231579944

0.36823733030.28516044330.1862537582

0.16426753560.32943434820.2900077292

0.30078930060.35813457260.0046558987

0.37681428660.34267163480.322884948

0.45893398410.33133983720.0836073498

0.22650841830.40300337050.360267807

0.19935926340.13186101610.1542420728

0.36898720470.50391095110.2887440151

0.24588870340.28511296150.3282030343

0.19444556670.33854944730.1421956515

0.17500634010.25021598220.107905892

0.35457808540.4047687480.3652163721

0.34025162090.38750483620.3454964118

0.31067542240.35797731080.3475213247

05/29/02

06/28/02

08/22/02

Cell Size (metres)

Correlation (r)

Glyndon LIDAR Soil Moisture Correlation vs. Cell Size

gl 0.5x11 LI

0.15303328190.01863639890.0040534288

0.02936735950.02450190450.0111707009

0.0700499192-0.0722304896-0.159977168

0.1577176719-0.0019021137-0.1107502887

-0.00923399-0.1707202837-0.2589824219

0.1496041486-0.0550307926-0.1591352969

0.39577301820.37454388750.2744496813

0.60482613520.58014757480.4667000035

0.77554603640.80777917430.7459113002

0.72795970350.77718074090.7747496436

0.76167999410.81495486090.8048385805

0.67741549870.73681428120.760322476

0.79101395470.82870810560.8015121537

0.81676636880.87042780690.8480400679

0.70642659520.76466115840.7763336438

0.69521223290.75039321410.7651085917

0.6312730310.72136162170.7647748595

0.77463922040.78439426010.7661207592

0.74988233510.82412654110.8340093499

0.67741549870.73681428120.760322476

0.78439264710.80585185240.7679393973

0.62919699310.67509597340.6336546609

0.74827868310.78803396330.7577743198

0.67759704650.67919483830.5986783319

0.61872057410.6213870960.6382774024

0.56661935980.61647139720.5748149557

0.68668931940.78099884030.814016656

0.2996667210.43013088660.4090231883

0.66047200570.70747689860.7430788469

0.64891631930.70513374520.6936879796

05/30/02

06/26/02

08/22/02

Cell Size (metres)

Correlation (r)

Pond Branch LIDAR Soil Moisture Correlation vs. Cell Size

pb 11.25 PG

0.12280286650.0256000639-0.0421502605

0.15030492970.0385098044-0.0421844281

0.26759273650.16558009150.070838412

0.40528195020.31265674480.1859216782

0.30148217430.17842179360.0382759582

0.3208649910.19526288160.0401724184

0.4381688260.32331500170.1823647696

0.35529308990.18764694580.0263208671

0.69498112110.64468434490.5748129837

0.64641101610.53722508260.3910439305

0.76210732510.67085638390.6320354855

0.69414128520.70798319080.7066984773

0.77048254810.80057395350.7942315597

0.81166740670.83728193080.8314499049

0.83611328090.88863545760.8914110115

0.79688065210.83880933440.8083249116

0.71355623240.81210847740.8291896077

0.78747038560.83246069670.8166077293

0.69214188890.74441260150.7464967385

0.78705453470.83613259380.8150567969

0.78260794420.8315567480.8190939562

0.67178524920.72882495230.6720341625

0.72651497880.79746446820.7987558448

0.49183739510.53561235510.4732244469

0.46082400750.5218250920.4801683834

0.67009553620.72621276610.7473345536

0.52749599180.59034937570.5791999178

0.80258702620.82422503110.8040278669

0.70125018510.73176065610.7346651911

0.51078538760.55433076020.5009682741

05/30/02

06/26/02

08/22/02

Cell Size (metres)

Correlation (r)

Pond Branch PG Soil Moisture Correlation vs. Cell Size

wet

0.39709082190.34407665250.1012227343

0.4535889540.17106740330.0254288542

0.36278942490.26003908620.3687878906

0.26184728230.21396220340.1861053717

0.49401025830.35175827890.1009992125

0.48694983660.33176792950.070354804

0.48322810090.46183196440.1675110938

0.25059933370.42008464510.4630456879

0.19718367570.32672893990.3713272076

0.12615175010.22642445110.1717379243

0.29202232030.43244102770.28340716

0.23329188440.40113229610.28618954

0.28755382010.28529639280.2814087832

0.15585399650.39483273830.2507498503

0.34385150060.31945401160.2100610532

0.29171104620.47401370480.5650532243

0.50697987760.19847848830.2496879062

0.21188933380.35588300240.1542779164

0.41550438560.37216130920.5002139878

0.31084601450.47088663310.3883234783

0.28881809790.35665409630.5311163703

0.30853415280.3494515050.3316548049

0.2900754370.3706484090.5636261014

0.31221043460.4447498670.3456178454

0.35998832990.35032336810.5740371023

0.23530758460.14827266070.4187977223

0.32160108230.42366426760.4524246872

0.07128553790.35878081850.3046309103

0.29288231440.25770634540.4737547215

0.26386987360.21522489490.4565309965

05/29/02

06/28/02

08/22/02

Cell Size (metres)

Correlation (r)

Glyndon PG TMI-Soil Moisture Correlation vs. Cell Size

avg

A

B

C

D


avg

-0.1024379375-0.2160221966-0.0543228069

0.0338397515-0.05850078080.319923907

0.43692196290.29548054320.4154837123

0.52596215680.34068674580.2737285493

0.5983532740.374628190.2551553211

0.74670017720.56968389330.3238456809

0.75060121880.52906665430.281300497

0.73015777190.47085631230.1772287592

0.68540820030.40524442870.1062366012

0.65923356890.37109198010.0841178066

0.62565186310.33542334650.0859838822

0.61981229020.31555316470.0967391499

0.64075350530.33375191490.1073207311

0.68425264010.38868034110.1589812855

0.70016253010.41141729020.1831203203

0.69550347990.3982364340.1932290598

0.68116656260.39721228720.2076995394

0.64454318970.37069825280.1932199563

0.65014487760.36892722290.2205284349

0.630511180.36731969390.2137869094

0.61107472030.36018290460.2007474377

05/29/02

06/28/02

08/22/02

Kernel Size (Cells)

Correlation (r)

Glyndon 0.5m LIDAR TMI-Soil Moisture Correlation vs. Kernel Size

dry

0.15303328190.01863639890.0040534288

-0.0965837793-0.2050147854-0.2182026987

-0.1532202509-0.2321189388-0.2153695699

-0.1815675472-0.2322967953-0.2078278531

-0.2665210579-0.326869259-0.316524123

-0.2823789106-0.3691327028-0.3711084241

-0.2708117901-0.3733514484-0.3882179648

-0.2453946662-0.3520972494-0.3829730683

-0.2269786135-0.3382085716-0.3838637478

-0.2133463045-0.3300768347-0.3891987144

-0.2101504093-0.3279808647-0.3909324714

-0.1944041063-0.3034338274-0.3606472212

-0.1914021328-0.3027103713-0.3567281456

-0.1951607647-0.3051783585-0.3552818813

-0.2138851495-0.3286063632-0.3787489433

-0.2153365257-0.3312964789-0.3810092781

-0.2043957306-0.3259897295-0.3734538384

-0.195480557-0.3212342677-0.3623079767

-0.1814397097-0.3085447109-0.3450053207

-0.1632199963-0.2908219336-0.3246253028

-0.1609507981-0.2880864537-0.3197856783

05/30/02

06/26/02

08/22/02

Kernel Size (Cells)

Correlation (r)

Pond Branch 0.5m LIDAR TMI-Soil Moisture Correlation vs. Kernel Size

cell data

0.45538263050.29940646540.0775390196

0.46908013240.32513847160.0910106979

0.47211684940.34845700150.0514353184

0.48845918780.36955391730.0495688035

0.47256826130.36440043350.0219560432

0.47341585130.36498885510.0179630401

0.4667123690.35191048940.0076011949

0.46777219310.34669451040.0050178962

0.46878080760.33950483610.013069383

0.46646240990.32887582330.0061908858

0.46799826170.326856663-0.0038254923

0.48488334010.3416513036-0.0071789082

0.4950741140.3440935549-0.0096191056

0.5038462740.3456192671-0.0135616413

0.50932844730.3473335119-0.022181752

0.51184668820.3468934012-0.0324663067

0.51281692710.3459100843-0.0421904349

0.5143664420.3487428925-0.048350148

0.51660427460.3525015936-0.0557416852

0.51474810220.3565538181-0.0599981061

0.51844394090.3596777103-0.0578695131

05/29/02

06/28/02

08/22/02

Kernel Size (Cells)

Correlation (r)

Glyndon 0.5m PG TMI-Soil Moisture Correlation vs. Kernel Size

kernel data

0.12280286650.0256000639-0.0421502605

0.1351085680.0319896557-0.0419767203

0.15842509140.0464872485-0.0361184013

0.18722893640.0667423795-0.0255512852

0.21648363540.0898850721-0.0123252387

0.27030068510.13753744870.0280686388

0.33205697120.19601926910.0839381493

0.38343185020.24793782030.1356344582

0.42810255020.29378210020.1807041203

0.45910931250.32647293610.2107002761

0.46213584620.33064605030.2071411506

0.46926279250.33940953820.2103217556

0.47930129930.35093581010.2178636308

0.49832109880.37138241920.2361727583

0.51594718820.39047815480.2535398048

0.53277576250.40887324930.2708362119

0.55083417230.42916653970.2906202614

0.57110895010.45461268170.316711861

0.58836310710.47991430070.3437822993

0.60808882520.50418318750.3676406201

0.62594004710.52399154840.3864090095

05/30/02

06/26/02

08/22/02

Kernel Size (Cells)

Correlation (r)

Pond Branch 0.5m PG TMI-Soil Moisture Correlation vs. Kernel Size

avgtheta data

A

B

C

D


avgtheta data

-0.1024379375-0.2160221966-0.0543228069

0.0338397515-0.05850078080.319923907

0.43692196290.29548054320.4154837123

0.52596215680.34068674580.2737285493

0.5983532740.374628190.2551553211

0.74670017720.56968389330.3238456809

0.75060121880.52906665430.281300497

0.73015777190.47085631230.1772287592

0.68540820030.40524442870.1062366012

0.65923356890.37109198010.0841178066

0.62565186310.33542334650.0859838822

0.61981229020.31555316470.0967391499

0.64075350530.33375191490.1073207311

0.68425264010.38868034110.1589812855

0.70016253010.41141729020.1831203203

0.69550347990.3982364340.1932290598

0.68116656260.39721228720.2076995394

0.64454318970.37069825280.1932199563

0.65014487760.36892722290.2205284349

0.630511180.36731969390.2137869094

0.61107472030.36018290460.2007474377

05/29/02

06/28/02

08/22/02

Kernel Size (Cells)

Correlation (r)

Glyndon 0.5m LIDAR TMI-Soil Moisture Correlation vs. Kernel Size

slope data

0.15303328190.01863639890.0040534288

-0.0965837793-0.2050147854-0.2182026987

-0.1532202509-0.2321189388-0.2153695699

-0.1815675472-0.2322967953-0.2078278531

-0.2665210579-0.326869259-0.316524123

-0.2823789106-0.3691327028-0.3711084241

-0.2708117901-0.3733514484-0.3882179648

-0.2453946662-0.3520972494-0.3829730683

-0.2269786135-0.3382085716-0.3838637478

-0.2133463045-0.3300768347-0.3891987144

-0.2101504093-0.3279808647-0.3909324714

-0.1944041063-0.3034338274-0.3606472212

-0.1914021328-0.3027103713-0.3567281456

-0.1951607647-0.3051783585-0.3552818813

-0.2138851495-0.3286063632-0.3787489433

-0.2153365257-0.3312964789-0.3810092781

-0.2043957306-0.3259897295-0.3734538384

-0.195480557-0.3212342677-0.3623079767

-0.1814397097-0.3085447109-0.3450053207

-0.1632199963-0.2908219336-0.3246253028

-0.1609507981-0.2880864537-0.3197856783

05/30/02

06/26/02

08/22/02

Kernel Size (Cells)

Correlation (r)

Pond Branch 0.5m LIDAR TMI-Soil Moisture Correlation vs. Kernel Size

tmi data

0.45538263050.29940646540.0775390196

0.46908013240.32513847160.0910106979

0.47211684940.34845700150.0514353184

0.48845918780.36955391730.0495688035

0.47256826130.36440043350.0219560432

0.47341585130.36498885510.0179630401

0.4667123690.35191048940.0076011949

0.46777219310.34669451040.0050178962

0.46878080760.33950483610.013069383

0.46646240990.32887582330.0061908858

0.46799826170.326856663-0.0038254923

0.48488334010.3416513036-0.0071789082

0.4950741140.3440935549-0.0096191056

0.5038462740.3456192671-0.0135616413

0.50932844730.3473335119-0.022181752

0.51184668820.3468934012-0.0324663067

0.51281692710.3459100843-0.0421904349

0.5143664420.3487428925-0.048350148

0.51660427460.3525015936-0.0557416852

0.51474810220.3565538181-0.0599981061

0.51844394090.3596777103-0.0578695131

05/29/02

06/28/02

08/22/02

Kernel Size (Cells)

Correlation (r)

Glyndon 0.5m PG TMI-Soil Moisture Correlation vs. Kernel Size

0.12280286650.0256000639-0.0421502605

0.1351085680.0319896557-0.0419767203

0.15842509140.0464872485-0.0361184013

0.18722893640.0667423795-0.0255512852

0.21648363540.0898850721-0.0123252387

0.27030068510.13753744870.0280686388

0.33205697120.19601926910.0839381493

0.38343185020.24793782030.1356344582

0.42810255020.29378210020.1807041203

0.45910931250.32647293610.2107002761

0.46213584620.33064605030.2071411506

0.46926279250.33940953820.2103217556

0.47930129930.35093581010.2178636308

0.49832109880.37138241920.2361727583

0.51594718820.39047815480.2535398048

0.53277576250.40887324930.2708362119

0.55083417230.42916653970.2906202614

0.57110895010.45461268170.316711861

0.58836310710.47991430070.3437822993

0.60808882520.50418318750.3676406201

0.62594004710.52399154840.3864090095

05/30/02

06/26/02

08/22/02

Kernel Size (Cells)

Correlation (r)

Pond Branch 0.5m PG TMI-Soil Moisture Correlation vs. Kernel Size

A

B

C

D


1

1.9322521739

2.1180173913

2.0543086957

2.0322782609

2.1807826087

2.2163565217

2.1955652174

2.1744565217

2.1543608696

2.1440086957

2.1320652174

2.1377391304

2.1195173913

2.1011913043

2.0944217391

2.0898217391

2.0875913043

2.0844391304

2.0828043478

2.0803130435

Kernel Size (Cells)

Standard Deviation

Glyndon 0.5m LIDAR TMI Standard Deviation vs. Kernel Size

1

1.3228684211

1.5641631579

1.7131052632

1.8493473684

1.9248210526

1.9403789474

1.9437421053

1.9456

1.9498894737

1.9486157895

1.9710368421

1.9757421053

1.9829105263

1.9906473684

2.0032947368

2.0136368421

2.0313473684

2.0400736842

2.0605947368

2.0637578947

Kernel Size (Cells)

Standard Deviation

Pond Branch 0.5m LIDAR TMI Standard Deviation vs. Kernel Size

1

0.3719291667

0.7546458333

1.0493833333

1.1689375

1.2235375

1.3186583333

1.3491333333

1.4271791667

1.4426208333

1.4424916667

1.485575

1.4920291667

1.5097125

1.533375

1.548275

1.55745

1.5737583333

1.5906541667

1.6123208333

1.6187333333

Kernel Size (Cells)

Standard Deviation

Glyndon 0.5m PG TMI Standard Deviation vs. Kernel Size

1

0.1313052632

0.2036263158

0.2656473684

0.3632

0.5132368421

0.6201210526

0.6898315789

0.7465684211

0.7907210526

0.8258263158

0.8633421053

0.8918105263

0.9094578947

0.9230315789

0.9354842105

0.9505

0.9790526316

1.0258210526

1.0489526316

1.0664263158

Kernel Size (Cells)

Standard Deviation

Pond Branch 0.5m PG TMI Standard Deviation vs. Kernel Size

A

B

C

D


0.60339546

0.7021852693

0.7285011829

0.6481694061

0.5550706732

0.6571506574

0.7499584573

0.7106245095

0.6802068873

0.6905600069

0.6753971465

0.687752858

0.5755608767

0.5701249137

0.7467001772

0.5621786709

0.5242210489

0.4409197429

0.5696838933

0.3499347867

0.3270030327

0.3903975193

0.2723545608

0.3238456809

TMI-Theta Corr.

Average Volumetric Soil Moisture (V/V)

Correlation (r)

Glyndon Average Soil Moisture vs. Soil Moisture-TMI Correlation (derived from Soil Moisture vs. TMI from 0.5m LIDAR, 11x11 Kernel)

Date

2/1/020.36

2/8/020.49

2/15/020.53

2/22/020.42

3/1/020.31

3/8/020.43

3/29/020.56

4/4/020.50

4/11/020.46

4/17/020.48

4/25/020.46

5/9/020.47

5/16/020.33

5/21/020.33

5/29/020.56

6/6/020.32

6/12/020.27

6/19/020.19

6/28/020.32

7/11/020.12

7/19/020.11

8/1/020.15

8/15/020.07

8/22/020.10

R2=0.83

TMI-Theta Corr.

Average Volumetric Soil Moisture (V/V)

Correlation (r)

Pond Branch Average Soil Moisture vs Soil Moisture-TMI Correlation (derived from Soil Moisture vs. TMI from 11.25m Photogrammetric)

0.3251447229

0.3168748414

0.3101227006

0.3338506961

0.3271958597

0.333001986

0.3222924449

0.326912282

0.294772987

0.3265332377

0.354065625

0.3130474222

0.3079941854

0.333239871

0.3330827979

0.3081213146

0.2353662075

0.2751649934

0.2155835018

0.1950943232

0.1647537711

0.1143719654

0.1032505566

0.8662238591

0.8437180938

0.8514558261

0.9327887143

0.7712995775

0.8626652593

0.8703667662

0.8854485582

0.8728218142

0.8479346718

0.6522067235

0.8801345494

0.7811441848

0.8417075744

0.8361132809

0.8164506496

0.8407099111

0.8612792532

0.8886354576

0.8644705299

0.8935161775

0.9105822734

0.8914110115

R2=0.18

A

B

&L&"Times New Roman,Regular"&12D.E. TenenbaumTable 2

Date

2/12/020.75

2/21/020.71

2/28/020.72

3/7/020.87

3/15/020.59

3/29/020.74

4/4/020.76

4/11/020.78

4/18/020.76

4/24/020.72

5/3/020.43

5/8/020.77

5/14/020.61

5/20/020.71

5/30/020.70

6/7/020.67

6/12/020.71

6/19/020.74

6/26/020.79

7/11/020.75

7/24/020.80

8/15/020.83

8/22/020.79

&L&"Times New Roman,Regular"&12D.E. TenenbaumTable 3

13.0322102925

31.4821670986

27.878563495

15.9570529434

6.1458718993

2.8878193262

1.3945452302

0.6540787363

0.320868814

0.2097988399

0.0370233247

0

0

0

0

0

0

0

0

0

0

0

GLYNDON

Slope in degrees

Percentage of all grid cells in catchment

Glyndon Slope Histogram

0.9313464609

5.3485896754

8.9941458222

13.7307078233

12.666311868

11.2293773284

8.6216072379

7.4507716871

6.2001064396

5.5082490687

4.7099521022

2.6343799894

2.6343799894

1.9425226184

1.4635444385

1.7030335285

1.3038850452

1.0111761575

0.9845662586

0.3991484832

0.2927088877

0.2394890899

POND BRANCH

Slope in degrees

Percentage of all grid cells in catchment

Pond Branch Slope Histogram

GLLIPBLIGLPGPBPG

Kernel Size (cells)

1

31.93225217391.32286842110.37192916670.1313052632

52.11801739131.56416315790.75464583330.2036263158

72.05430869571.71310526321.04938333330.2656473684

92.03227826091.84934736841.16893750.3632

112.18078260871.92482105261.22353750.5132368421

132.21635652171.94037894741.31865833330.6201210526

152.19556521741.94374210531.34913333330.6898315789

172.17445652171.94561.42717916670.7465684211

192.15436086961.94988947371.44262083330.7907210526

212.14400869571.94861578951.44249166670.8258263158

232.13206521741.97103684211.4855750.8633421053

252.13773913041.97574210531.49202916670.8918105263

272.11951739131.98291052631.50971250.9094578947

292.10119130431.99064736841.5333750.9230315789

312.09442173912.00329473681.5482750.9354842105

332.08982173912.01363684211.557450.9505

352.08759130432.03134736841.57375833330.9790526316

372.08443913042.04007368421.59065416671.0258210526

392.08280434782.06059473681.61232083331.0489526316

412.08031304352.06375789471.61873333331.0664263158

DateGlThetaPbThetaPrecip (mm)Precip (mm)Precip (inches)GlThetaPbTheta

2/1/020.4535815291-0.508-0.508-0.020.453582

2/2/020000.450162

2/3/020000.446742

2/4/02-0.254-0.254-0.010.443322

2/5/020000.439902

2/6/020000.436482

2/7/02-2.54-2.54-0.10.433063

2/8/020.42964324420000.429643

2/9/020000.426103

2/10/02-0.762-0.762-0.030.422563

2/11/02-1.016-1.016-0.040.419023

2/12/020.32514472290000.4154820.325145

2/13/020000.4119420.324226

2/14/020000.4084010.323307

2/15/020.40486051320000.4048610.322388

2/16/020000.4028170.321469

2/17/020000.4007730.32055

2/18/020000.3987290.319631

2/19/020000.3966850.318712

2/20/02-0.254-0.254-0.010.394640.317794

2/21/020.3168748414-0.254-0.254-0.010.3925950.316875

2/22/020.39055138080000.3905510.31591

2/23/020000.3879050.314945

2/24/020000.3852590.313981

2/25/020000.3826130.313017

2/26/02-2.032-2.032-0.080.3799680.312052

2/27/020000.3773220.311087

2/28/020.31012270060000.3746760.310123

3/1/020.37203058730000.3720310.313513

3/2/02-18.288-18.288-0.720.3780510.316903

3/3/02-7.874-7.874-0.310.3840710.320293

3/4/020000.390090.323682

3/5/020000.396110.327072

3/6/020000.4021290.330461

3/7/020.33385069610000.4081490.333851

3/8/020.41416779780000.4141680.333019

3/9/02-2.286-2.286-0.090.4158760.332187

3/10/02-3.556-3.556-0.140.4175840.331355

3/11/020000.4192920.330523

3/12/02-1.524-1.524-0.060.4210.329691

3/13/02-9.652-9.652-0.380.4227080.328859

3/14/020000.4244160.328028

3/15/020.32719585970000.4261240.327196

3/16/02-0.508-0.508-0.020.4278320.327611

3/17/02-3.81-3.81-0.150.429540.328026

3/18/02-9.906-9.906-0.390.4312480.328441

3/19/02-1.016-1.016-0.040.4329560.328856

3/20/02-23.622-23.622-0.930.4346630.329271

3/21/020000.4363710.329686

3/22/020000.4380790.3301

3/23/020000.4397860.330515

3/24/020000.4414930.330929

3/25/020000.4432010.331344

3/26/02-13.97-13.97-0.550.4449090.331759

3/27/020000.4466160.332173

3/28/020000.4483230.332588

3/29/020.45003085010.3330019860000.4500310.333002

3/30/020000.4482140.331217

3/31/02-5.08-5.08-0.20.4463970.329432

4/1/020000.444580.327647

4/2/020000.4427620.325862

4/3/02-1.016-1.016-0.040.4409440.324077

4/4/020.4391274660.32229244490000.4391270.322292

4/5/020000.4349120.322952

4/6/020000.4306970.323612

4/7/020000.4264810.324272

4/8/020000.4222660.324932

4/9/02-3.556-3.556-0.140.418050.325592

4/10/02-0.254-0.254-0.010.4138340.326252

4/11/020.40961860170.3269122820000.4096190.326912

4/12/020000.4097040.322321

4/13/020000.4097890.31773

4/14/02-4.064-4.064-0.160.4098740.313139

4/15/02-3.81-3.81-0.150.4099590.308547

4/16/020000.4100450.303956

4/17/020.41013043150000.410130.299365

4/18/020.294772987-13.208-13.208-0.520.4133670.294773

4/19/02-7.112-7.112-0.280.4166040.300066

4/20/020000.419840.305359

4/21/02-5.08-5.08-0.20.4230770.310653

4/22/02-3.048-3.048-0.120.4263140.315946

4/23/020000.429550.32124

4/24/020.32653323770000.4327860.326533

4/25/020.4360227904-3.048-3.048-0.120.4360230.329592

4/26/020000.4344450.332651

4/27/02-3.556-3.556-0.140.4328670.33571

4/28/02-33.274-33.274-1.310.4312890.338769

4/29/020000.4297110.341828

4/30/020000.4281330.344888

5/1/020000.4265550.347947

5/2/02-31.75-31.75-1.250.4249770.351007

5/3/020.354065625-0.254-0.254-0.010.4233990.354066

5/4/020000.4218210.345862

5/5/020000.4202430.337658

5/6/020000.4186650.329454

5/7/02-2.032-2.032-0.080.4170870.32125

5/8/020.3130474222-0.254-0.254-0.010.4155090.313047

5/9/020.4139324932-2.794-2.794-0.110.4139320.312205

5/10/020000.4058770.311363

5/11/020000.3978220.310521

5/12/02-4.064-4.064-0.160.3897670.309679

5/13/02-2.286-2.286-0.090.3817120.308836

5/14/020.30799418540000.3736570.307994

5/15/020000.3656020.312202

5/16/020.35754557220000.3575460.31641

5/17/02-5.334-5.334-0.210.3651740.320618

5/18/02-22.352-22.352-0.880.3728020.324825

5/19/020000.380430.329032

5/20/020.3332398710000.3880580.33324

5/21/020.39568570770000.3956860.333224

5/22/020000.4035990.333208

5/23/020000.4115120.333192

5/24/020000.4194250.333176

5/25/020000.4273380.333161

5/26/02-9.652-9.652-0.380.4352510.333145

5/27/02-9.144-9.144-0.360.4431640.33313

5/28/02-0.762-0.762-0.030.4510770.333114

5/29/020.45898959620000.458990.333099

5/30/020.33308279790000.445240.333083

5/31/02-1.016-1.016-0.040.431490.329963

6/1/020000.4177390.326843

6/2/020000.4039890.323723

6/3/020000.3902380.320603

6/4/02-0.762-0.762-0.030.3764880.317483

6/5/02-0.762-0.762-0.030.3627370.314362

6/6/020.3489867525-14.224-14.224-0.560.3489870.311241

6/7/020.3081213146-0.508-0.508-0.020.3432150.308121

6/8/02-0.254-0.254-0.010.3374430.29357

6/9/020000.3316710.279019

6/10/020000.3258990.264468

6/11/020000.3201270.249917

6/12/020.31435491510.23536620750000.3143550.235366

6/13/02-24.384-24.384-0.960.3201520.241052

6/14/02-7.874-7.874-0.310.3259490.246738

6/15/02-2.032-2.032-0.080.3317460.252423

6/16/020000.3375420.258109

6/17/020000.3433390.263794

6/18/020000.3491360.269479

6/19/020.35493156380.2751649934-0.254-0.254-0.010.3549320.275165

6/20/020000.3431610.266653

6/21/020000.331390.258141

6/22/020000.3196190.24963

6/23/020000.3078480.241118

6/24/020000.2960760.232607

6/25/020000.2843050.224096

6/26/020.21558350180000.2725330.215584

6/27/02-0.508-0.508-0.020.2607610.214218

6/28/020.2489902732-4.064-4.064-0.160.248990.212852

6/29/020000.2492490.211486

6/30/020000.2495080.21012

7/1/020000.2497670.208754

7/2/020000.2500260.207388

7/3/02-1.016-1.016-0.040.2502850.206022

7/4/020000.2505440.204656

7/5/020000.2508030.20329

7/6/020000.2510620.201924

7/7/020000.2513220.200558

7/8/020000.2515820.199192

7/9/02-18.796-18.796-0.740.2518410.197826

7/10/02-1.016-1.016-0.040.25210.19646

7/11/020.25236035120.19509432320000.252360.195094

7/12/02-0.762-0.762-0.030.2439680.19276

7/13/02-1.27-1.27-0.050.2355760.190426

7/14/02-5.588-5.588-0.220.2271840.188092

7/15/02-0.254-0.254-0.010.2187920.185758

7/16/020000.21040.183424

7/17/020000.2020080.18109

7/18/020000.1936160.178756

7/19/020.18522378780000.1852240.176422

7/20/020000.1838550.174088

7/21/020000.1824860.171755

7/22/020000.1811170.169421

7/23/020000.1797480.167088

7/24/020.16475377110000.1783790.164754

7/25/020000.177010.162464

7/26/02-0.254-0.254-0.010.175640.160174

7/27/02-0.762-0.762-0.030.174270.157884

7/28/02-0.254-0.254-0.010.1729010.155594

7/29/020000.1715320.153304

7/30/02-0.254-0.254-0.010.1701620.151014

7/31/020000.1687930.148724

8/1/020.16742292250000.1674230.146434

8/2/020000.1638630.144144

8/3/02-0.508-0.508-0.020.1603030.141854

8/4/020000.1567430.139564

8/5/02-0.254-0.254-0.010.1531830.137274

8/6/02-0.254-0.254-0.010.1496230.134984

8/7/020000.1460630.132694

8/8/020000.1425030.130404

8/9/020000.1389420.128114

8/10/020000.1353820.125824

8/11/020000.1318210.123534

8/12/020000.1282610.121244

8/13/020000.12470.118953

8/14/020000.121140.116663

8/15/020.11757869620.11437196540000.1175790.114372

8/16/020000.1141370.112783

8/17/020000.1106960.111194

8/18/020000.1072540.109605

8/19/020000.1038130.108016

8/20/02-2.794-2.794-0.110.1003710.106428

8/21/020000.096930.10484

8/22/020.09348823280.10325055660000.0934880.103251

ID3/1/023/29/024/17/025/21/025/29/026/28/028/15/028/22/02TI_5M11X11

GG10.34689707760.48409167680.44104720060.31676950010.47895392480.17006487730.09259817450.08438828553.9067

GG20.39410912990.51504385170.45496432330.43374121040.50327122060.26825766710.16267356460.12388714483.8481

GG30.29128392340.35848792490.32911257150.49370266940.42710536120.23549752460.19437860770.1390860523.5198

GG40.42546416820.53493342550.43622336830.34552505610.52259003970.2554709770.13038094680.09966348134.0261

NW10.36605455130.40031552310.39265268450.36032252160.39182058130.19945836740.05873256790.03994610643.2731

NW20.34337961830.42335755080.35017535240.35449630020.44247816950.18087392930.04975737860.03445410994.0838

NW30.34379665850.38618393090.32949605730.32150172370.40589205620.16514981430.06109171270.05190153393.1037

NW40.41329714950.49072657230.4433977410.4325234070.49244961140.2666591510.11332521330.09880674883.4311

NW50.36133473660.47825503950.42140113560.40863462980.47929592790.31408989060.10200107690.09775602953.8990

NW60.38934373260.46349093910.42335593850.39016383440.42731710970.26047968190.10379052010.11826298874.4938

NW70.46919455530.57990131530.55427510140.56850710510.54448265730.42121956350.1390943840.12218825184.9584

SF10.29631584810.44987951220.33953484450.36768425410.44130495190.19708357640.08744369760.09855458893.4674

SF20.31638655510.43597423880.37777913660.34864933340.17916905660.09322543420.11224139334.5178

SH10.35667334650.48515341880.45880955760.37089480090.44380699250.18309816350.11454617310.10054895363.5992

SH20.41549423780.46932332660.4359602290.42259566930.47123762670.32675512060.18231523710.16120172663.9363

SH30.36733421980.40528032630.35725152490.3527352840.4433939710.23836274450.13671900220.1130503993.1557

SH40.31696817730.3786635980.310840030.31305653150.37875220180.10916617140.03336603280.03386569243.0045

SH50.345644030.41130246070.42366602720.43970087170.46247691360.29639853610.09305959330.07248665613.6470

SH60.39862423540.4262894630.40143169460.41003566830.42659894230.32988956790.14321437660.11397887575.3968

SH70.29145292490.34444015920.29300249590.31034527720.39512140840.24149224160.08838938890.09424338962.8013

WW10.38476399630.3787373140.40335077050.36388864220.43102365140.20146877320.15505319770.08253308963.0697

WW20.40308903010.44509851930.45648309440.4137798980.47280941610.28506058530.17739663680.09665923893.4947

WW30.39540817590.46495636550.45084360240.41492140590.48799617590.27324740440.17306659520.10311533814.3454

WW40.52301766430.56711256210.54937713740.55663135050.55419114830.45825246570.16190487670.07138815644.5633

TI_5M11X11

3/1/020.5235793939AVG

3/29/020.5994606813WET

4/17/020.5769030349AVG

5/21/020.5093752948AVG

5/29/020.5424530654WET

6/28/020.5831598129AVG

8/15/020.2919076052DRY

8/22/020.3428597019DRY

ID2/28/023/29/024/18/025/20/025/30/026/26/028/15/028/22/02TI11_25MBC

LP10.2347822130.23137611450.22294357790.26837906760.26130546410.16962855350.07858541920.08487723755.9118

LP20.2177531660.23842750150.21407065990.26260925380.22836433910.13337709120.06953043640.05604293965.2601

S10.31582127140.32237354220.31915329770.35408081860.35681477190.2083783880.10120302030.09619767676.3204

S20.3267729610.34669102440.2755656920.36169248220.34138090610.23048971970.09370066670.10921176475.6571

S30.4891056210.52706876990.43771131780.46171629730.49112102240.41139357020.30133131890.258709164712.3070

U10.31590856690.31833227870.30535286440.30688476340.35085750370.21513560790.0842500040.08225399186.5774

U20.29047725650.33503619280.26350902920.31350215520.33533838320.18530299550.08726369810.07650713086.9281

U30.31694184910.33632339980.27754685510.31527430420.34762476830.19847346540.09455433490.07999577656.6413

U40.31945617720.31466057150.28885666880.31686313080.32545185230.20832404720.10171768480.09318151888.4846

U50.37564064410.40475796460.32363439050.36659451720.41242787690.27659438920.14187448510.12197479759.6434

U60.37029919920.40008640140.32203469720.37678444680.4128560960.27156407010.12793117390.11751296567.9888

UP10.2611313850.27876047490.23412838580.28103902710.26745775680.14098983610.07078592820.06569428846.1589

UP20.32445485520.33792641090.2904521480.30618173480.32685869190.19178073180.0987077590.09433580516.6176

UP30.29933222090.33901175480.31376008020.33876412210.32496922090.24009923860.14190191550.13104194149.4935

UP40.51284800770.51639865340.46461419610.50653767730.48356685490.4474276640.28010451460.249915637111.6750

PE10.25345181820.26524311230.28821240370.33076158760.28053284590.17571794690.08060726080.06063264855.7995

PE20.2314879820.26801042780.2665791720.32069643590.27557953670.1486573290.08019341580.06587689397.8622

PE30.22124480310.27171595770.25111220330.2660683990.25552480520.1249660850.07016093680.06222607275.3588

PE40.21542131380.27483718060.24144911240.27712732850.25054046440.11778580580.06866337020.05557232494.8671

TI11_25MBCTI_5M11X11

5/30/020.8361132809WET5/29/020.5424530654

6/26/020.8886354576AVG6/28/020.5831598129

8/22/020.8914110115DRY8/22/020.3428597019

3.9067

3.8481

3.5198

4.0261

3.2731

4.0838

3.1037

3.4311

3.899

4.4938

4.9584

3.4674

4.5178

3.5992

3.9363

3.1557

3.0045

3.647

5.3968

2.8013

3.0697

3.4947

4.3454

4.5633

TI_5M11X11

Theta

TMI

Glyndon 3/29/02 Wet

5.9118

5.2601

6.3204

5.6571

12.307

6.5774

6.9281

6.6413

8.4846

9.6434

7.9888

6.1589

6.6176

9.4935

11.675

5.7995

7.8622

5.3588

4.8671

TI11_25MBC

Theta

TMI

Pond Branch 3/29/02 Wet

3.9067

3.8481

3.5198

4.0261

3.2731

4.0838

3.1037

3.4311

3.899

4.4938

4.9584

3.4674

4.5178

3.5992

3.9363

3.1557

3.0045

3.647

5.3968

2.8013

3.0697

3.4947

4.3454

4.5633

TI_5M11X11

Theta

TMI

Glyndon 5/29/02 Wet

5.9118

5.2601

6.3204

5.6571

12.307

6.5774

6.9281

6.6413

8.4846

9.6434

7.9888

6.1589

6.6176

9.4935

11.675

5.7995

7.8622

5.3588

4.8671

TI11_25MBC

Theta

TMI

Pond Branch 5/30/02 Wet

3.9067

3.8481

3.5198

4.0261

3.2731

4.0838

3.1037

3.4311

3.899

4.4938

4.9584

3.4674

4.5178

3.5992

3.9363

3.1557

3.0045

3.647

5.3968

2.8013

3.0697

3.4947

4.3454

4.5633

TI_5M11X11

Theta

TMI

Glyndon 3/1/02 Average

5.9118

5.2601

6.3204

5.6571

12.307

6.5774

6.9281

6.6413

8.4846

9.6434

7.9888

6.1589

6.6176

9.4935

11.675

5.7995

7.8622

5.3588

4.8671

TI11_25MBC

Theta

TMI

Pond Branch 2/28/02 Average

3.9067

3.8481

3.5198

4.0261

3.2731

4.0838

3.1037

3.4311

3.899

4.4938

4.9584

3.4674

4.5178

3.5992

3.9363

3.1557

3.0045

3.647

5.3968

2.8013

3.0697

3.4947

4.3454

4.5633

TI_5M11X11

Theta

TMI


5.9118

5.2601

6.3204

5.6571

12.307

6.5774

6.9281

6.6413

8.4846

9.6434

7.9888

6.1589

6.6176

9.4935

11.675

5.7995

7.8622

5.3588

4.8671

TI11_25MBC

Theta

TMI


3.9067

3.8481

3.5198

4.0261

3.2731

4.0838

3.1037

3.4311

3.899

4.4938

4.9584

3.4674

4.5178

3.5992

3.9363

3.1557

3.0045

3.647

5.3968

2.8013

3.0697

3.4947

4.3454

4.5633

TI_5M11X11

Theta

TMI


5.9118

5.2601

6.3204

5.6571

12.307

6.5774

6.9281

6.6413

8.4846

9.6434

7.9888

6.1589

6.6176

9.4935

11.675

5.7995

7.8622

5.3588

4.8671

TI11_25MBC

Theta

TMI


3.9067

3.8481

3.5198

4.0261

3.2731

4.0838

3.1037

3.4311

3.899

4.4938

4.9584

3.4674

4.5178

3.5992

3.9363

3.1557

3.0045

3.647

5.3968

2.8013

3.0697

3.4947

4.3454

4.5633

TI_5M11X11

Theta

TMI


5.9118

5.2601

6.3204

5.6571

12.307

6.5774

6.9281

6.6413

8.4846

9.6434

7.9888

6.1589

6.6176

9.4935

11.675

5.7995

7.8622

5.3588

4.8671

TI11_25MBC

Theta

TMI


3.9067

3.8481

3.5198

4.0261

3.2731

4.0838

3.1037

3.4311

3.899

4.4938

4.9584

3.4674

4.5178

3.5992

3.9363

3.1557

3.0045

3.647

5.3968

2.8013

3.0697

3.4947

4.3454

4.5633

TI_5M11X11

Theta

TMI

Glyndon 8/15/02 Dry

5.9118

5.2601

6.3204

5.6571

12.307

6.5774

6.9281

6.6413

8.4846

9.6434

7.9888

6.1589

6.6176

9.4935

11.675

5.7995

7.8622

5.3588

4.8671

TI11_25MBC

Theta

TMI

Pond Branch 8/15/02

3.9067

3.8481

3.5198

4.0261

3.2731

4.0838

3.1037

3.4311

3.899

4.4938

4.9584

3.4674

4.5178

3.5992

3.9363

3.1557

3.0045

3.647

5.3968

2.8013

3.0697

3.4947

4.3454

4.5633

TI_5M11X11

Theta

TMI

Glyndon 8/22/02 Dry

5.9118

5.2601

6.3204

5.6571

12.307

6.5774

6.9281

6.6413

8.4846

9.6434

7.9888

6.1589

6.6176

9.4935

11.675

5.7995

7.8622

5.3588

4.8671

TI11_25MBC

Theta

TMI

Pond Branch 8/22/02 Dry

Glyndon LIDARPond Branch LIDARGlyndon PhotogrammetricPond Branch Photogrammetric

Cell Size (metres)05/29/0206/28/0208/22/0205/30/0206/26/0208/22/0205/29/0206/28/0208/22/0205/30/0206/26/0208/22/02

0.5-0.10-0.22-0.050.150.020.000.400.340.100.120.03-0.04

1.00.080.050.010.030.020.010.450.170.030.150.04-0.04

1.50.240.160.260.07-0.07-0.160.360.260.370.270.170.07

2.00.14-0.050.250.16-0.00-0.110.260.210.190.410.310.19

2.50.170.04-0.14-0.01-0.17-0.260.490.350.100.300.180.04

3.00.390.420.050.15-0.06-0.160.490.330.070.320.200.04

3.50.450.230.150.400.370.270.480.460.170.440.320.18

4.00.560.400.260.600.580.470.250.420.460.360.190.03

4.50.440.260.180.780.810.750.200.330.370.690.640.57

5.00.310.380.030.730.780.770.130.230.170.650.540.39

6.30.330.310.060.760.810.800.290.430.280.760.670.63

7.50.500.410.120.680.740.760.230.400.290.690.710.71

8.80.280.420.090.790.830.800.290.290.280.770.800.79

10.00.350.460.040.820.870.850.160.390.250.810.840.83

11.30.300.430.090.710.760.780.340.320.210.840.890.89

12.50.470.480.230.700.750.770.290.470.570.800.840.81

13.80.370.290.190.630.720.760.510.200.250.710.810.83

15.00.160.330.290.770.780.770.210.360.150.790.830.82

16.30.300.360.000.750.820.830.420.370.500.690.740.75

17.50.380.340.320.680.740.760.310.470.390.790.840.82

18.80.460.330.080.780.810.770.290.360.530.780.830.82

20.00.230.400.360.630.680.630.310.350.330.670.730.67

21.30.200.130.150.750.790.760.290.370.560.730.800.80

22.50.370.500.290.680.680.600.310.440.350.490.540.47

23.80.250.290.330.620.620.640.360.350.570.460.520.48

25.00.190.340.140.570.620.570.240.150.420.670.730.75

26.30.180.250.110.690.780.810.320.420.450.530.590.58

27.50.350.400.370.300.430.410.070.360.300.800.820.80

28.80.340.390.350.660.710.740.290.260.470.700.730.73

30.00.310.360.350.650.710.690.260.220.460.510.550.50

Glyndon LIDARPond Branch LIDARGlyndon PhotogrammetricPond Branch Photogrammetric

Kernel Size (metres)05/29/0206/28/0208/22/0205/30/0206/26/0208/22/0205/29/0206/28/0208/22/0205/30/0206/26/0208/22/02

1-0.1024379375-0.2160221966-0.05432280690.15303328190.01863639890.00405342880.45538263050.29940646540.07753901960.12280286650.0256000639-0.0421502605

30.0338397515-0.05850078080.319923907-0.0965837793-0.2050147854-0.21820269870.46908013240.32513847160.09101069790.1351085680.0319896557-0.0419767203

50.43692196290.29548054320.4154837123-0.1532202509-0.2321189388-0.21536956990.47211684940.34845700150.05143531840.15842509140.0464872485-0.0361184013

70.52596215680.34068674580.2737285493-0.1815675472-0.2322967953-0.20782785310.48845918780.36955391730.04956880350.18722893640.0667423795-0.0255512852

90.5983532740.374628190.2551553211-0.2665210579-0.326869259-0.3165241230.47256826130.36440043350.02195604320.21648363540.0898850721-0.0123252387

110.74670017720.56968389330.3238456809-0.2823789106-0.3691327028-0.37110842410.47341585130.36498885510.01796304010.27030068510.13753744870.0280686388

130.75060121880.52906665430.281300497-0.2708117901-0.3733514484-0.38821796480.4667123690.35191048940.00760119490.33205697120.19601926910.0839381493

150.73015777190.47085631230.1772287592-0.2453946662-0.3520972494-0.38297306830.46777219310.34669451040.00501789620.38343185020.24793782030.1356344582

170.68540820030.40524442870.1062366012-0.2269786135-0.3382085716-0.38386374780.46878080760.33950483610.0130693830.42810255020.29378210020.1807041203

190.65923356890.37109198010.0841178066-0.2133463045-0.3300768347-0.38919871440.46646240990.32887582330.00619088580.45910931250.32647293610.2107002761

210.62565186310.33542334650.0859838822-0.2101504093-0.3279808647-0.39093247140.46799826170.326856663-0.00382549230.46213584620.33064605030.2071411506

230.61981229020.31555316470.0967391499-0.1944041063-0.3034338274-0.36064722120.48488334010.3416513036-0.00717890820.46926279250.33940953820.2103217556

250.64075350530.33375191490.1073207311-0.1914021328-0.3027103713-0.35672814560.4950741140.3440935549-0.00961910560.47930129930.35093581010.2178636308

270.68425264010.38868034110.1589812855-0.1951607647-0.3051783585-0.35528188130.5038462740.3456192671-0.01356164130.49832109880.37138241920.2361727583

290.70016253010.41141729020.1831203203-0.2138851495-0.3286063632-0.37874894330.50932844730.3473335119-0.0221817520.51594718820.39047815480.2535398048

310.69550347990.3982364340.1932290598-0.2153365257-0.3312964789-0.38100927810.51184668820.3468934012-0.03246630670.53277576250.40887324930.2708362119

330.68116656260.39721228720.2076995394-0.2043957306-0.3259897295-0.37345383840.51281692710.3459100843-0.04219043490.55083417230.42916653970.2906202614

350.64454318970.37069825280.1932199563-0.195480557-0.3212342677-0.36230797670.5143664420.3487428925-0.0483501480.57110895010.45461268170.316711861

370.65014487760.36892722290.2205284349-0.1814397097-0.3085447109-0.34500532070.51660427460.3525015936-0.05574168520.58836310710.47991430070.3437822993

390.630511180.36731969390.2137869094-0.1632199963-0.2908219336-0.32462530280.51474810220.3565538181-0.05999810610.60808882520.50418318750.3676406201

410.61107472030.36018290460.2007474377-0.1609507981-0.2880864537-0.31978567830.51844394090.3596777103-0.05786951310.62594004710.52399154840.3864090095

GlyndonPond Branch

AvgthetaTMI-Theta Corr.AvgthetaTMI-Theta Corr.

2/1/020.45407212430.603395462/12/020.32514472290.87

2/8/020.43033268070.70218526932/21/020.31687484140.84

2/15/020.40492817570.72850118292/28/020.31012270060.85

2/22/020.39178401510.64816940613/7/020.33385069610.93

3/1/020.37313865590.55507067323/15/020.32719585970.77

3/8/020.41385719880.65715065743/29/020.3330019860.86

3/29/020.44904162560.74995845734/4/020.32229244490.87

4/4/020.4378330770.71062450954/11/020.3269122820.89

4/11/020.40862515120.68020688734/18/020.2947729870.87

4/17/020.40976798410.69056000694/24/020.32653323770.85

4/25/020.43610559790.67539714655/3/020.3540656250.65

5/9/020.4139334390.6877528585/8/020.31304742220.88

5/16/020.35870981240.57556087675/14/020.30799418540.78

5/21/020.39628362270.57012491375/20/020.3332398710.84

5/29/020.45758130690.74670017725/30/020.33308279790.84

6/6/020.35046784310.56217867096/7/020.30812131460.82

6/12/020.31630006890.52422104896/12/020.23536620750.84

6/19/020.35669306670.44091974296/19/020.27516499340.86

6/28/020.25236107710.56968389336/26/020.21558350180.89

7/11/020.2546389160.34993478677/11/020.19509432320.86

7/19/020.18905617310.32700303277/24/020.16475377110.89

8/1/020.17098047720.39039751938/15/020.11437196540.91

8/15/020.11864684960.27235456088/22/020.10325055660.89

8/22/020.09434200960.3238456809

AvgthetaTMI-Theta Corr.AvgthetaTMI-Theta Corr.

Avgtheta1Avgtheta1

TMI-Theta Corr.0.90839417551TMI-Theta Corr.-0.42339443841

0GLYNDONPOND BRANCH

113.03221029250.9313464609

231.48216709865.3485896754

327.8785634958.9941458222

415.957052943413.7307078233

56.145871899312.666311868

62.887819326211.2293773284

71.39454523028.6216072379

80.65407873637.4507716871

90.3208688146.2001064396

100.20979883995.5082490687

110.03702332474.7099521022

1202.6343799894

1302.6343799894

1401.9425226184

1501.4635444385

1601.7030335285

1701.3038850452

1801.0111761575

1900.9845662586

2000.3991484832

2100.2927088877

00.2394890899

GLYNDONPOND BRANCH4GLYNDONPOND BRANCH

43012050.46867676934.0458530007

5935807614.607092641827.2083614295

621521411733.619746914547.5724881996

71630407825.464771129513.7221847606

874587911.63880643652.9332434255

937733105.88970473361.1126095752

1020317113.1713794720.5731625084

1112522121.95281987190.7417397168

127743131.20293704111.4497639919

137019141.09357912830.6405933918

14400150.6249023590

15150160.23433838460

1620170.0312451180

64012966

Further Moments of the DistributionWhile measures of dispersion are useful for helping us describe the width of the distribution, they tell us nothing about the shape of the distribution

Further Moments of the DistributionThere are further statistics that describe the shape of the distribution, using formulae that are similar to those of the mean and variance1st moment - Mean (describes central value)2nd moment - Variance (describes dispersion)3rd moment - Skewness (describes asymmetry)4th moment - Kurtosis (describes peakedness)

Further Moments SkewnessSkewness measures the degree of asymmetry exhibited by the data

S: sample standard deviation If skewness equals zero, the histogram is symmetric about the meanPositive skewness vs negative skewness

Further Moments SkewnessSource: http://library.thinkquest.org/10030/3smodsas.htm

Further Moments SkewnessPositive skewnessThere are more observations below the mean than above itWhen the mean is greater than the medianNegative skewnessThere are a small number of low observations and a large number of high onesWhen the median is greater than the mean

Further Moments KurtosisKurtosis measures how peaked the histogram is

The kurtosis of a normal distribution is 0Kurtosis characterizes the relative peakedness or flatness of a distribution compared to the normal distribution

Further Moments KurtosisPlatykurtic When the kurtosis < 0, the frequencies throughout the curve are closer to be equal (i.e., the curve is more flat and wide) Thus, negative kurtosis indicates a relatively flat distributionLeptokurtic When the kurtosis > 0, there are high frequencies in only a small part of the curve (i.e, the curve is more peaked)Thus, positive kurtosis indicates a relatively peaked distribution

Further Moments KurtosisSource: http://www.riskglossary.com/link/kurtosis.htmKurtosis is based on the size of a distribution's tails. Negative kurtosis (platykurtic) distributions with short tailsPositive kurtosis (leptokurtic) distributions with relatively long tailsleptokurticplatykurtic

Why Do We Need Kurtosis?These two distributions have the same variance, approximately the same skew, but differ markedly in kurtosis.Source: http://davidmlane.com/hyperstat/A53638.html

How to Graphically Summarize Data?

Histograms

Box plots

Functions of a HistogramThe function of a histogram is to graphically summarize the distribution of a data set The histogram graphically shows the following: 1. Center (i.e., the location) of the data 2. Spread (i.e., the scale) of the data 3. Skewness of the data 4. Kurtosis of the data4. Presence of outliers 5. Presence of multiple modes in the data.

Functions of a HistogramThe histogram can be used to answer the following questions: 1. What kind of population distribution do the data come from? 2. Where are the data located? 3. How spread out are the data? 4. Are the data symmetric or skewed? 5. Are there outliers in the data?

Source: http://www.robertluttman.com/vms/Week5/page9.htm (First three) http://office.geog.uvic.ca/geog226/frLab1.html (Last)

Box PlotsWe can also use a box plot to graphically summarize a data setA box plot represents a graphical summary of what is sometimes called a five-number summary of the distributionMinimumMaximum25th percentile75th percentileMedianInterquartile Range (IQR)

Box PlotsExample Consider first 9 Commodore prices ( in $,000) 6.0, 6.7, 3.8, 7.0, 5.8, 9.975, 10.5, 5.99, 20.0 Arrange these in order of magnitude 3.8, 5.8, 5.99, 6.0, 6.7, 7.0, 9.975, 10.5, 20.0The median is Q2 = 6.7 (there are 4 values on either side) Q1 = 5.9 (median of the 4 smallest values) Q3 = 10.2 (median of the 4 largest values) IQR = Q3 Q1 = 10.2 - 5.9 = 4.3

Example (ranked) 3.8, 5.8, 5.99, 6.0, 6.7, 7.0, 9.975, 10.5, 20.0The median is Q1 = 6.7Q1 = 5.9 Q3 = 10.2 IQR = Q3 Q1 = 10.2 - 5.9 = 4.3

Box PlotsRanked commuting times:

5, 5, 6, 9, 10, 11, 11, 12, 12, 14, 16, 17, 19, 21, 21, 21, 21, 21, 22, 23, 24, 24, 26, 26, 31, 31, 36, 42, 44, 47Example: Table 1.1 Commuting data (Rogerson, p5)25th percentile is represented by observation (30+1)/4=7.7575th percentile is represented by observation 3(30+1)/4=23.2525th percentile: 11.7575th percentile: 26Interquartile range: 26 11.75 = 14.25

Example (Ranked commuting times):

5, 5, 6, 9, 10, 11, 11, 12, 12, 14, 16, 17, 19, 21, 21, 21, 21, 21, 22, 23, 24, 24, 26, 26, 31, 31, 36, 42, 44, 47

25th percentile: 11.75 75th percentile: 26Interquartile range: 26 11.75 = 14.25

Other Descriptive Summary MeasuresDescriptive statistics provide an organization and summary of a datasetA small number of summary measures replaces the entirety of a datasetWell briefly talk about other simple descriptive summary measures

Other Descriptive Summary MeasuresYou're likely already familiar with some simple descriptive summary measuresRatiosProportionsPercentagesRates of ChangeLocation Quotients

Other Descriptive Summary MeasuresRatios # of observations in A# of observations in Be.g., A - 6 overcast, B - 24 mostly cloudy daysProportions Relates one part or category of data to the entire set of observations, e.g., a box of marbles that contains 4 yellow, 6 red, 5 blue, and 2 green gives a yellow proportion of 4/17 or colorcount = {yellow, red, blue, green}acount = {4, 6, 5, 2}=

Other Descriptive Summary MeasuresProportions - Sum of all proportions = 1. These are useful for comparing two sets of data w/different sizes and category counts, e.g., a different box of marbles gives a yellow proportion of 2/23, and in order for this to be a reasonable comparison we need to know the totals for both samplesPercentages - Calculated by proportions x 100, e.g., 2/23 x 100% = 8.696%, use of these should be restricted to larger samples sizes, perhaps 20+ observations

Other Descriptive Summary MeasuresLocation Quotients - An index of relative concentration in space, a comparison of a region's share of something to the totalExample Suppose we have a region of 1000 Km2 which we subdivide into three smaller areas of 200, 300, and 500 km2 (labeled A, B, & C)The region has an influenza outbreak with 150 cases in A, 100 in B, and 350 in C (a total of 600 flu cases):Proportion of AreaProportion of CasesLocation QuotientA 200/1000=0.2 150/600=0.25 0.25/0.2=1.25B 300/1000=0.3 100/600=0.17 0.17/0.3 = 0.57C 500/1000=0.5 350/600=0.58 0.58/0.5=1.17

Documents

Graphical Summary of Data Distribution Statistical View Point Histograms Skewness Kurtosis Other Descriptive Summary Measures Source: