Watersheds 101Presentation Notes
Hands on experience that you can take back to your classroom. Meaningful. Link back to community.
http://streamsidescience.usu.edu
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Introductions. Great way to introduce watersheds and can integrate into all grades and subjects. About – Utah Stream Team manual has great science and programs, redeveloped for teacher use – lesson plans, ideas to do w/data Developed SSS and Bugs Don’t Bug Me for kids. Fun activities getting kids engaged and excited
AGENDA
• WHAT IS THE CONNECTION BETWEEN WATERSHEDS AND WATER QUALITY?
• WHAT CAN YOU MEASURE AND WHY?
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Ask the kids and get interesting answers – “Shed that holds water”
WHAT IS A WATERSHED?
WATER DRAINS TO A COMMON POINT.
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Common definition….all water drains to a single point. Note that groundwater may not follow same pattern. – breaks boundaries The geographic unit that makes the most sense with respect to water quality Have teachers put hands together to make a “watershed”. Thumbs are the mountains. We use this technique to teach children about watersheds.
WATERSHEDS ARE DEFINED BY STRUCTURE AND BY FUNCTION
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Structure – How is it formed? Function – What does it do? We’ll be talking about both of these in this mapping project To a large extent, you’ll be mapping structural components for your project. But the structure very much affects the functioning. Water quality, biological characteristics of the water, etc. represent the response of the structural components
ELEMENTS OF WATERSHED STRUCTURE
Functions of watersheds
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Watershed as whole, not just water, but sed, soil, nutrients, bio material Collect water, but also nutrients (eg acid precipitation), organic material (migration in), wind blown soils, etc. Process soils – soil formation, modification/ process geographic forms, plant material produced and stored, used by animals, etc. etc. Water processed in some ways, but mostly we think of storage….in different reservoirs (groundwater, subsurface soil water, in plants and animals, in atmosphere, in lakes, reservoirs, streams, wetlands. Transportation: of water via streams but also evaporation, movement of animals, runoff, groundwater, etc. Other transport issues: animal movements, soil erosion, minerals, metals, nutrients, etc. moving through the watershed (through plants, soils and water). Pollutants being transported to water. Continually moving and changing, depositng sediments in new areas
• Watersheds are nested
• The scale you work at depends on the question you want to answer
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Can use two peoples’ hands as watersheds to demonstrate nested watersheds. Examples – Mississippi R vs Backyard pond
What is causing “dead zones” in the Gulf of Mexico?
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For example….dead zones in the gulf of Mexico refer to the anoxic areas on the floor of the gulf. About the size of Massachusetts. Huge impacts on shellfish and other fisheries. Caused by over-fertilization, excess nutrients Drains 41% of continental US, ag runoff and treated wastewater from urban areas Sources are all agricultural applications and combustion engines in the gulf’s watershed/….especially since nitrogen is so soluble, it moves easily out of shallow groundwater into the river and on to the gulf. Algae blooms, dies, then decays. Decay process consumes oxygen.
What is causing the scum in my back yard pond?
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Scale is much smaller. You can see the probable influences for this small pond .. Horses, other animals, possibly fertilizers and septic systems in these small acreages. Can’t just look at a single issue. Must use and ecological approach.
WATERSHEDS ARE THE LOGICAL GEOGRAPHIC UNIT FOR PLANNING:
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Watersheds do not follow political boundaries. This causes jurisdiction problems within states and counties.
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Stream Order helps characterize types of streams
How does a river change as it moves from headwaters to base of watershed?
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Location of water in watershed determines storage/movement/residence time How streams change as they move through a watershed…. stream flow at a certain point. Small headwater stream vs large low gradient stream Ask for images – what are differences as go downstream? (canopy, size, shape) 1st order – more input from outside stream. 3rd order more solar energy, fore feeding and growing directly in the river Changes….stream continuum issues. Shading, Slope/velocity, width to depth ratio, oxygen concentrations, nutrient inputs, temp Autochtonous (rocks) vs allocthonous (sediments, nutrients) inputs Different food and methods of foraging… Processing of materials (shredders at top and primary producers/filter feeders at bottom)
How to “delineate” a watershed…
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Introduce the concept of a stream reach. Note that for water quality purposes, the water that comes in at the top of the reach is another contributor. As you go through the watershed from the headwaters to the main stream, the structures and functions change (e.g. substrate size, vegetation patterns, temperature, size of stream). Like tree w/branches
DELINEATE YOUR WATERSHED
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Activity - Need three colors… start with the largest tributary and work up.
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Again, you can see the upstream influence of Jordan River water leaving Utah Lake. Note, that in “real life” a lot of the red streams are probably in ditches, pipes or canals by the time they get down to the river as it moves thru SLC. Human influences – changing structure, piped underground, dried up and used before make it to R Can get topo maps online, or from sporting goods store, trim down maps to manageable size, laminate
DELINEATE WATERSHED
• . INSTRUCT STUDENTS TO USE THE BLUE MARKER TO TRACE THE MAIN CHANNEL (MAIN STEM) OF THE BEAR RIVER. HAVE STUDENTS START FROM THE RIVER’S MOUTH AT THE GREAT SALT LAKE AND CONTINUE TO THE HEADWATERS IN THE UINTA MOUNTAINS WILDERNESS AREA.
• 2. HAVE STUDENTS USE THE RED MARKER TO TRACE THE TRIBUTARIES OF THE BEAR RIVER. TO DO THIS, THEY SHOULD START AT GREAT SALT LAKE AGAIN. EACH TIME THEY ENCOUNTER A TRIBUTARY CONNECTING DIRECTLY TO THE BEAR RIVER, WHICH IS NOW TRACED IN BLUE, THEY SHOULD TRACE THE UNMARKED TRIBUTARY FROM ITS MOUTH TO ITS HEADWATERS WITH A RED MARKER.
• 3. WITH A GREEN MARKER, REPEAT THE PROCESS FOR ANY SMALLER TRIBUTARIES FOLLOWING THE ONES MARKED IN STEP 2 (I.E., STUDENTS SHOULD USE A GREEN MARKER TO TRACE THE SMALLER TRIBUTARIES THAT LEAD INTO THE LARGER TRIBUTARIES MARKED IN RED). ACTIVITY 1: DEFINE YOUR WATERSHED JOURNEY THROUGH THE BEAR RIVER WATERSHED © 2006 PROJECT WET INTERNATIONAL FOUNDATION 30
• 4. FIND A SPOT ABOVE THE TOP OF EACH RIVER MARKED IN RED OR GREEN AND MARK IT WITH A PURPLE DOT TO INDICATE THE DIVIDE. USE THE EXAMPLE OF A SHALLOW BOWL TO EXPLAIN HOW TO IDENTIFY THE DIVIDE OF THE WATERSHED. THE RIM OF A BUCKET INCLUDES ITS HIGHEST POINTS, JUST LIKE A WATERSHED. FOR THE BEAR RIVER WATERSHED, HAVE STUDENTS MARK THE DIVIDE POINTS ON THE OUTSIDE OF THE WATERSHED ONLY. REMEMBER THAT STREAMS FLOW FROM HIGHER ELEVATIONS TO LOWER ELEVATIONS. THUS, EACH TRIBUTARY OR STREAM ACTUALLY BEGINS AT SOME POINT ON THE LAND ABOVE THE HEADWATERS, USUALLY A HILL, MOUNTAIN, OR SOME OTHER HIGH POINT. THESE HIGH POINTS DIVIDE THIS WATERSHED FROM THE ONE(S) NEXT TO IT.
• 5. HAVE STUDENTS TRACE THE DIVIDE BY CONNECTING THE DOTS WITH THE PURPLE MARKER. START AT THE MOUTH OF THE BEAR RIVER AT THE GREAT SALT LAKE AND MOVE IN A CLOCKWISE DIRECTION AROUND THE MAINSTEM. CONTINUE TO CONNECT THE DOTS ALL THE WAY AROUND UNTIL THE PURPLE LINE MEETS ITSELF BACK AT THE GREAT SALT LAKE.
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We all know the big water cycle picture….water moves through different reservoirs. The amount of time in these reservoirs varies enormously. All processes important in watershed functions. Structure of the watershed will affect each component of the water cycle. Driving force for the water cycle is the sun.
NATURAL HYDROGRAPHS:
Oct -------------------------------------------- Sept
Fl ow
(c fs
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Graph of flow at a point in a river over time. Note: Oct – Sept is a hydrologic “water year” Ask class what the pattern would look like around here. What is normal? – snowmelt and spring rains Show – Runoff period vs baseflow (fed by shallow gndwater) Area under curve represents volume/reservoir over time Cfs – Cubic feet per second.
NATURAL VARIABILITY
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We tend to talk about average years, drought and wet years. BUT…Note how variable streams flow can be between years (7 fold difference between years). Notice different types of runoff patterns within a year. An “average” year may not have even occurred during this window of time. What is average? This is the Little Bear River at Paradise, UT.
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25426
25427
25428
25429
25430
25431
25432
25433
25434
25435
25436
25437
25438
25439
25440
25441
25442
25443
25444
25445
25446
25447
25448
25449
25450
25451
25452
25453
25454
25455
25456
25457
25458
25459
25460
25461
25462
25463
25464
25465
25466
25467
25468
25469
25470
25471
25472
25473
25474
25475
25476
25477
25478
25479
25480
25481
25482
25483
25484
25485
25486
25487
25488
25489
25490
25491
25492
25493
25494
25495
25496
25497
25498
25499
25500
25501
25502
25503
25504
25505
25506
25507
25508
25509
25510
25511
25512
25513
25514
25515
25516
25517
25518
25519
25520
25521
25522
25523
25524
25525
25526
25527
25528
25529
25530
25531
25532
25533
25534
25535
25536
25537
25538
25539
25540
25541
25542
25543
25544
25545
25546
25547
25548
25549
25550
25551
25552
25553
25554
25555
25556
25557
25558
25559
25560
25561
25562
25563
25564
25565
25566
25567
25568
25569
25570
25571
25572
25573
25574
25575
25576
25577
25578
25579
25580
25581
25582
25583
25584
25585
25586
25587
25588
25589
25590
25591
25592
25593
25594
25595
25596
25597
25598
25599
25600
25601
25602
25603
25604
25605
25606
25607
25608
25609
25610
25611
25612
25613
25614
25615
25616
25617
25618
25619
25620
25621
25622
25623
25624
25625
25626
25627
25628
25629
25630
25631
25632
25633
25634
25635
25636
25637
25638
25639
25640
25641
25642
25643
25644
25645
25646
25647
25648
25649
25650
25651
25652
25653
25654
25655
25656
25657
25658
25659
25660
25661
25662
25663
25664
25665
25666
25667
25668
25669
25670
25671
25672
25673
25674
25675
25676
25677
25678
25679
25680
25681
25682
25683
25684
25685
25686
25687
25688
25689
25690
25691
25692
25693
25694
25695
25696
25697
25698
25699
25700
25701
25702
25703
25704
25705
25706
25707
25708
25709
25710
25711
25712
25713
25714
25715
25716
25717
25718
25719
25720
25721
25722
25723
25724
25725
25726
25727
25728
25729
25730
25731
25732
25733
25734
25735
25736
25737
25738
25739
25740
25741
25742
25743
25744
25745
25746
25747
25748
25749
25750
25751
25752
25753
25754
25755
25756
25757
25758
25759
25760
25761
25762
25763
25764
25765
25766
25767
25768
25769
25770
25771
25772
25773
25774
25775
25776
25777
25778
25779
25780
25781
25782
25783
25784
25785
25786
25787
25788
25789
25790
25791
25792
25793
25794
25795
25796
25797
25798
25799
25800
25801
25802
25803
25804
25805
25806
25807
25808
25809
25810
25811
25812
25813
25814
25815
25816
25817
25818
25819
25820
25821
25822
25823
25824
25825
25826
25827
25828
25829
25830
25831
25832
25833
25834
25835
25836
25837
25838
25839
25840
25841
25842
25843
25844
25845
25846
25847
25848
25849
25850
25851
25852
25853
25854
25855
25856
25857
25858
25859
25860
25861
25862
25863
25864
25865
25866
25867
25868
25869
25870
25871
25872
25873
25874
25875
25876
25877
25878
25879
25880
25881
25882
25883
25884
25885
25886
25887
25888
25889
25890
25891
25892
25893
25894
25895
25896
25897
25898
25899
25900
25901
25902
25903
25904
25905
25906
25907
25908
25909
25910
25911
25912
25913
25914
25915
25916
25917
25918
25919
25920
25921
25922
25923
25924
25925
25926
25927
25928
25929
25930
25931
25932
25933
25934
25935
25936
25937
25938
25939
25940
25941
25942
25943
25944
25945
25946
25947
25948
25949
25950
25951
25952
25953
25954
25955
25956
25957
25958
25959
25960
25961
25962
25963
25964
25965
25966
25967
25968
25969
25970
25971
25972
25973
25974
25975
25976
25977
25978
25979
25980
25981
25982
25983
25984
25985
25986
25987
25988
25989
25990
25991
25992
25993
25994
25995
25996
25997
25998
25999
26000
26001
26002
26003
26004
26005
26006
26007
26008
26009
26010
26011
26012
26013
26014
26015
26016
26017
26018
26019
26020
26021
26022
26023
26024
26025
26026
26027
26028
26029
26030
26031
26032
26033
26034
26035
26036
26037
26038
26039
26040
26041
26042
26043
26044
26045
26046
26047
26048
26049
26050
26051
26052
26053
26054
26055
26056
26057
26058
26059
26060
26061
26062
26063
26064
26065
26066
26067
26068
26069
26070
26071
26072
26073
26074
26075
26076
26077
26078
26079
26080
26081
26082
26083
26084
26085
26086
26087
26088
26089
26090
26091
26092
26093
26094
26095
26096
26097
26098
26099
26100
26101
26102
26103
26104
26105
26106
26107
26108
26109
26110
26111
26112
26113
26114
26115
26116
26117
26118
26119
26120
26121
26122
26123
26124
26125
26126
26127
26128
26129
26130
26131
26132
26133
26134
26135
26136
26137
26138
26139
26140
26141
26142
26143
26144
26145
26146
26147
26148
26149
26150
26151
26152
26153
26154
26155
26156
26157
26158
26159
26160
26161
26162
26163
26164
26165
26166
26167
26168
26169
26170
26171
26172
26173
26174
26175
26176
26177
26178
26179
26180
26181
26182
26183
26184
26185
26186
26187
26188
26189
26190
26191
26192
26193
26194
26195
26196
26197
26198
26199
26200
26201
26202
26203
26204
26205
26206
26207
26208
26209
26210
26211
26212
26213
26214
26215
26216
26217
26218
26219
26220
26221
26222
26223
26224
26225
26226
26227
26228
26229
26230
26231
26232
26233
26234
26235
26236
26237
26238
26239
26240
26241
26242
26243
26244
26245
26246
26247
26248
26249
26250
26251
26252
26253
26254
26255
26256
26257
26258
26259
26260
26261
26262
26263
26264
26265
26266
26267
26268
26269
26270
26271
26272
26273
26274
26275
26276
26277
26278
26279
26280
26281
26282
26283
26284
26285
26286
26287
26288
26289
26290
26291
26292
26293
26294
26295
26296
26297
26298
26299
26300
26301
26302
26303
26304
26305
26306
26307
26308
26309
26310
26311
26312
26313
26314
26315
26316
26317
26318
26319
26320
26321
26322
26323
26324
26325
26326
26327
26328
26329
26330
26331
26332
26333
26334
26335
26336
26337
26338
26339
26340
26341
26342
26343
26344
26345
26346
26347
26348
26349
26350
26351
26352
26353
26354
26355
26356
26357
26358
26359
26360
26361
26362
26363
26364
26365
26366
26367
26368
26369
26370
26371
26372
26373
26374
26375
26376
26377
26378
26379
26380
26381
26382
26383
26384
26385
26386
26387
26388
26389
26390
26391
26392
26393
26394
26395
26396
26397
26398
26399
26400
26401
26402
26403
26404
26405
26406
26407
26408
26409
26410
26411
26412
26413
26414
26415
26416
26417
26418
26419
26420
26421
26422
26423
26424
26425
26426
26427
26428
26429
26430
26431
26432
26433
26434
26435
26436
26437
26438
26439
26440
26441
26442
26443
26444
26445
26446
26447
26448
26449
26450
26451
26452
26453
26454
26455
26456
26457
26458
26459
26460
26461
26462
26463
26464
26465
26466
26467
26468
26469
26470
26471
26472
26473
26474
26475
26476
26477
26478
26479
26480
26481
26482
26483
26484
26485
26486
26487
26488
26489
26490
26491
26492
26493
26494
26495
26496
26497
26498
26499
26500
26501
26502
26503
26504
26505
26506
26507
26508
26509
26510
26511
26512
26513
26514
26515
26516
26517
26518
26519
26520
26521
26522
26523
26524
26525
26526
26527
26528
26529
26530
26531
26532
26533
26534
26535
26536
26537
26538
26539
26540
26541
26542
26543
26544
26545
26546
26547
26548
26549
26550
26551
26552
26553
26554
26555
26556
26557
26558
26559
26560
26561
26562
26563
26564
26565
26566
26567
26568
26569
26570
26571
26572
26573
26574
26575
26576
26577
26578
26579
26580
26581
26582
26583
26584
26585
26586
26587
26588
26589
26590
26591
26592
26593
26594
26595
26596
26597
26598
26599
26600
26601
26602
26603
26604
26605
26606
26607
26608
26609
26610
26611
26612
26613
26614
26615
26616
26617
26618
26619
26620
26621
26622
26623
26624
26625
26626
26627
26628
26629
26630
26631
26632
26633
26634
26635
26636
26637
26638
26639
26640
26641
26642
26643
26644
26645
26646
26647
26648
26649
26650
26651
26652
26653
26654
26655
26656
26657
26658
26659
26660
26661
26662
26663
26664
26665
26666
26667
26668
26669
26670
26671
26672
26673
26674
26675
26676
26677
26678
26679
26680
26681
26682
26683
26684
26685
26686
26687
26688
26689
26690
26691
26692
26693
26694
26695
26696
26697
26698
26699
26700
26701
26702
26703
26704
26705
26706
26707
26708
26709
26710
26711
26712
26713
26714
26715
26716
26717
26718
26719
26720
26721
26722
26723
26724
26725
26726
26727
26728
26729
26730
26731
26732
26733
26734
26735
26736
26737
26738
26739
26740
26741
26742
26743
26744
26745
26746
26747
26748
26749
26750
26751
26752
26753
26754
26755
26756
26757
26758
26759
26760
26761
26762
26763
26764
26765
26766
26767
26768
26769
26770
26771
26772
26773
26774
26775
26776
26777
26778
26779
26780
26781
26782
26783
26784
26785
26786
26787
26788
26789
26790
26791
26792
26793
26794
26795
26796
26797
26798
26799
26800
26801
26802
26803
26804
26805
26806
26807
26808
26809
26810
26811
26812
26813
26814
26815
26816
26817
26818
26819
26820
26821
26822
26823
26824
26825
26826
26827
26828
26829
26830
26831
26832
26833
26834
26835
26836
26837
26838
26839
26840
26841
26842
26843
26844
26845
26846
26847
26848
26849
26850
26851
26852
26853
26854
26855
26856
26857
26858
26859
26860
26861
26862
26863
26864
26865
26866
26867
26868
26869
26870
26871
26872
26873
26874
26875
26876
26877
26878
26879
26880
26881
26882
26883
26884
26885
26886
26887
26888
26889
26890
26891
26892
26893
26894
26895
26896
26897
26898
26899
26900
26901
26902
26903
26904
26905
26906
26907
26908
26909
26910
26911
26912
26913
26914
26915
26916
26917
26918
26919
26920
26921
26922
26923
26924
26925
26926
26927
26928
26929
26930
26931
26932
26933
26934
26935
26936
26937
26938
26939
26940
26941
26942
26943
26944
26945
26946
26947
26948
26949
26950
26951
26952
26953
26954
26955
26956
26957
26958
26959
26960
26961
26962
26963
26964
26965
26966
26967
26968
26969
26970
26971
26972
26973
26974
26975
26976
26977
26978
26979
26980
26981
26982
26983
26984
26985
26986
26987
26988
26989
26990
26991
26992
26993
26994
26995
26996
26997
26998
26999
27000
27001
27002
27003
27004
27005
27006
27007
27008
27009
27010
27011
27012
27013
27014
27015
27016
27017
27018
27019
27020
27021
27022
27023
27024
27025
27026
27027
27028
27029
27030
27031
27032
27033
27034
27035
27036
27037
27038
27039
27040
27041
27042
27043
27044
27045
27046
27047
27048
27049
27050
27051
27052
27053
27054
27055
27056
27057
27058
27059
27060
27061
27062
27063
27064
27065
27066
27067
27068
27069
27070
27071
27072
27073
27074
27075
27076
27077
27078
27079
27080
27081
27082
27083
27084
27085
27086
27087
27088
27089
2
2.2
2.2
2.3
2.3
2.3
2.5
2.5
2.5
2.5
2.5
3.7
6.7
12
21
25
28
28
28
31
34
36
37
39
40
41
45
46
45
45
45
46
47
46
46
45
46
47
52
57
61
59
56
54
54
52
52
51
50
49
48
49
50
48
47
48
44
44
43
41
42
43
44
46
50
53
60
74
37
5.7
5
5
4.7
4.7
4.7
4.7
4.7
4.7
5
5
5
6.1
70
287
269
130
150
189
181
134
105
77
21
8.5
6.7
70
201
207
216
253
301
328
324
287
257
231
210
185
169
167
151
142
150
167
185
177
169
171
175
179
165
151
142
142
159
144
110
131
144
159
177
187
193
195
167
115
68
41
23
17
12
8.5
8.1
8.1
8.5
9
7.8
4.2
4.2
4.5
3.7
3.7
3
2.3
2.5
2.5
3
2.3
2.3
1.9
1.9
2.2
1.9
1.7
1.3
1.2
1
0.8
0.7
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.7
0.6
0.6
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.8
0.8
0.8
0.8
0.8
0.9
1.3
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.9
1.2
1.7
1.7
1.2
1
1
1.2
1.6
1.3
1.2
1.2
1
1.5
1.7
1.7
1.7
1.9
1.7
1.7
1.2
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.6
0.6
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.8
1.2
1.6
0.9
0.8
0.8
0.8
0.8
0.8
1
1
1.3
1.3
1.5
1.3
1.2
1
0.9
0.8
0.7
0.6
0.6
0.6
0.5
0.4
0.4
0.3
0.3
0.3
0.3
0.3
0.4
0.3
0.4
0.5
0.5
0.6
0.6
0.6
0.8
0.7
0.7
0.7
0.7
0.7
0.8
0.8
0.8
0.8
0.8
0.7
0.8
0.8
0.9
1.6
1
1.2
1.2
1.2
1.5
1.7
1.9
1.9
1.7
1.7
1.7
1.7
1.7
1.9
1.9
1.9
1.9
1.9
1.9
1.9
1.9
1.7
1.7
1.7
1.9
1.9
1.9
1.9
1.9
1.9
1.7
1.7
1.7
1.7
1.6
1.6
1.9
1.9
1.9
1.9
1.9
1.7
1.7
1.7
1.7
1.7
1.7
1.9
1.9
1.7
1.7
1.7
1.7
1.7
1.7
1.9
2
2
2
2
1.9
1.9
1.9
1.9
1.9
1.9
1.9
2
1.9
1.9
1.9
1.9
1.9
2
2
2
2
2
2
2.2
2.3
2.3
2.2
2
2.2
2.2
2
2.2
2
2
2.2
2.3
2.2
2.2
2.5
2.5
2.3
2.3
2.3
2.3
2.5
2.5
2.5
2.8
2.8
2.8
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.3
2.3
1.9
0.9
0.9
0.8
0.8
0.9
1
1.5
1.6
1.6
1.6
1.7
3.5
3.5
3.3
3.3
3.3
7.4
57
96
108
102
96
90
84
85
96
96
86
80
70
76
98
112
105
86
72
65
58
50
40
32
24
19
17
7.8
3.5
3
2.8
2.5
2.5
3.7
4.7
6.1
4.7
3.7
3.3
3.3
4
3.7
3.5
3
2.8
2.5
2.8
2.3
1.9
2.2
2
2
2.2
2.3
2
2.2
1.9
1.7
2.5
3
2.5
3.5
2.5
1.7
1.5
1.3
1.3
1.3
1.3
1.2
1
1.2
1.3
1.9
2.5
1.9
1.2
0.8
0.8
0.8
0.8
0.8
1.2
1.3
1.2
1.2
1
1
1
1
1.2
0.9
0.9
0.8
0.8
0.8
0.8
0.8
1.5
1.2
0.9
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
1.2
1.7
1.2
0.8
1.2
0.9
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.9
2.2
3
2.3
2.2
2.2
1.9
1.7
1.6
1.3
1.2
1.2
1.3
1.3
1.2
1.2
1
1
1.6
1.3
1.2
1.2
1.2
1
0.9
0.9
0.9
0.9
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.6
0.6
0.6
0.6
0.6
0.6
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.6
0.6
0.6
0.6
0.6
0.6
0.8
0.9
1
1
1.3
1.3
1.3
1.6
1.7
1.5
1.7
1.7
1.7
1.3
1.6
1.3
1.2
1
1.2
1
0.9
0.9
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.9
0.8
0.8
0.8
0.8
0.8
0.9
1
1
1
1
1
1.2
1.2
1.2
1
1
1
1
1.2
1.2
1
1
1
1.2
1
1
0.9
0.9
0.9
1
1
0.9
0.8
0.8
0.8
0.9
0.9
0.6
0.6
0.5
0.6
0.6
0.5
0.5
0.7
1.6
1.6
1.6
1.6
1.6
1.6
1.6
1.6
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.9
1.7
1.7
1.7
1.7
1.7
1.7
1.9
1.9
2.2
2.2
2.2
2
2
1.7
1.7
1.7
1.7
1.7
1.9
1.9
1.9
1.9
1.9
1.9
1.7
1.7
2.5
119
432
427
379
324
282
282
273
260
242
227
207
193
177
161
146
133
120
102
93
88
84
79
74
73
76
76
76
79
79
76
74
70
35
3.7
3.7
3.7
3.7
4
4.2
4.5
4.2
4.5
4.5
4.5
4.7
4.7
112
238
195
150
153
205
266
262
262
262
262
260
260
260
260
262
324
384
406
508
612
675
591
481
520
554
551
545
548
597
660
669
639
600
574
388
177
182
200
135
169
305
374
364
328
296
269
242
214
173
140
108
86
110
155
148
138
127
135
150
153
167
183
201
203
197
187
197
199
177
185
169
146
129
117
100
72
50
37
28
14
5.4
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
0.9
0.9
1.1
1
0.9
1
1.6
2.7
1.8
1.3
1.1
1
0.9
0.8
0.7
0.6
0.7
0.8
0.8
0.7
0.7
0.7
0.7
2.1
1.8
1.8
1.6
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
2.1
2.5
3
6.5
15
17
11
4.1
2.1
1.7
1.5
1.3
1.3
1.2
0.8
0.8
0.8
0.9
2.3
1.8
2.3
1.7
1.3
1.2
1.1
0.9
0.9
1.1
1.6
1.4
1.2
1.1
2.1
3.2
5.2
6.2
8.7
8.4
8.1
7.8
6.5
4.1
4.1
4.1
4.1
4.1
4.1
3.8
4.1
4.9
3.5
1.5
1.4
1.3
1.4
1.7
1.7
1.6
1.6
1.6
1.6
1.6
1.4
2.3
2.4
1.5
1.1
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.6
0.5
0.5
0.5
0.5
0.5
0.7
0.7
0.7
0.7
0.7
0.7
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.5
0.5
0.5
0.5
0.6
0.5
0.5
0.7
0.7
0.7
0.7
0.6
0.6
0.6
0.6
0.6
0.5
0.5
0.5
0.5
0.6
0.6
0.6
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.9
1.9
1.9
1.9
1.9
2
2
2
2
1.9
1.9
2
2
2
2
2
2
2
2
2
2
1.9
2.3
4.9
3.3
2.6
2.1
2
1.9
1.9
1.9
1.9
1.9
2
2.8
3.6
3.6
3.5
3.5
3.3
2.8
2.8
2.8
2.8
2.8
2.8
2.8
2.8
2.8
2.8
2.8
2.6
2.3
2.4
2.6
2.6
2.4
2.4
2.4
2.4
2.4
2.4
2.4
2.4
2.4
2.4
2.6
2.6
2.6
2.6
2.6
2.6
2.6
2.8
2.8
3
3
3
3
3.1
3.1
3.5
12
28
46
51
54
54
59
123
170
139
116
98
82
72
66
65
72
69
70
72
85
98
94
96
108
121
137
154
143
131
123
119
110
100
96
101
106
114
127
127
129
127
121
105
88
78
80
82
69
66
61
52
40
33
28
28
34
86
65
27
9.4
4.3
3.8
3.3
3
3.1
2.6
2.1
2.8
3.1
11
21
36
38
36
36
40
37
34
27
25
25
26
24
17
8.1
3.8
3.5
3.1
4.6
2.4
2.3
1.7
2
2
1.9
1.7
1.9
3.1
2.8
3.3
2.8
2.6
2.4
2.3
2.1
2
1.7
1.6
1.9
1.9
4.6
9.1
6
2.8
2.6
1.9
2
2
2.1
2.1
2.1
1.7
1.5
1.3
1.3
1.3
1
1
1
0.9
0.8
0.8
0.8
1.1
1.7
1.9
3.1
2.8
2.3
2.4
3
3.1
2.8
2.6
2.3
2.8
3.5
7.8
13
10
5.2
2.3
2.3
2.4
1.9
2.1
2
2
1.5
1.3
1
0.9
0.8
0.8
0.8
1.4
1.5
1.6
2.3
1.9
1.5
1.4
1.3
1.1
1
0.9
0.9
0.8
0.8
0.8
0.8
0.8
0.8
0.7
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.8
0.8
1
2.4
2.6
2.4
2.4
2.4
2.4
2.4
2.6
2.6
2.6
2.6
2.6
2.6
2.6
2.6
2.6
2.4
2.6
3
2.5
2.4
2.4
2.4
2.6
2.6
3.1
3.1
3
2.8
2.8
2.8
2.8
2
0.8
1.1
1.3
0.9
1.5
2.8
3
3
3
3
3
3
3
3.1
3.1
3.1
3.1
3.1
3.1
3.1
3.1
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
2.8
2.8
3
3
3
3
3
3
3
2.8
2.8
2.8
2.8
2.6
2.6
2.8
2.8
2.8
2.8
3.1
3.1
3
3
3
3.1
3.1
10
25
25
56
99
97
94
94
93
91
88
86
85
83
82
79
77
75
73
70
69
66
65
64
62
61
57
32
3.6
3.5
3.5
3.5
3.5
3.5
3.5
3.5
3.5
3.5
3.6
3.6
3.8
3.8
3.8
3.8
3.8
3.8
3.8
3.6
3.8
3.8
3.8
4.1
4.3
4.3
4.3
4.6
4.6
4.9
34
64
62
61
60
59
59
59
57
56
56
55
55
56
57
59
59
61
62
61
64
68
198
273
270
262
258
258
258
258
252
228
79
5.2
3.8
3.5
3.5
4.1
6.2
6.2
7.9
40
89
142
188
193
179
202
211
199
188
233
260
270
273
301
310
320
371
359
351
262
243
286
296
286
250
221
186
164
138
118
104
69
47
33
40
45
42
36
89
209
252
252
243
221
197
182
156
146
167
216
231
226
207
204
177
148
116
96
77
64
53
33
14
5.2
4.9
4.6
4.1
4.3
4.3
6
4.3
3
3
2.6
2.3
2
2.3
2.8
2.3
2.1
2.3
2.1
2.3
2.3
1.6
1.7
3.1
3.6
2.4
2.1
2.1
2.3
2.3
1.7
1.7
1.9
1.7
1.4
1.3
1.4
1.4
1.3
1.1
1.1
1.6
2.4
2.8
3.3
2.6
6.2
14
6.5
2.4
4.6
15
13
3.1
2
2
2
2.6
2.4
2.6
1.9
1.7
1.9
1.9
1.4
0.8
0.7
0.7
0.8
1.3
1.9
2.4
2.6
3
2.1
1.9
2
2
1.7
1.8
2
1.4
1.5
2.1
1.5
2.4
1.4
1.3
0.9
3
7.6
7.9
9.6
9.6
9.6
9.6
9.6
9.6
9.6
9.6
7.6
1.3
0.8
0.7
0.7
0.6
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.6
0.7
0.7
0.6
0.6
3.5
5.2
2.1
2.1
2.1
2
2
2
2
2.1
2
2.1
2.1
2.1
2.1
2
2
2
2
2
2
2
2
2.1
2.1
2.1
2.1
2.4
2.3
2.3
2.3
2.3
2.4
2.3
2.3
2.3
2.1
2.1
2.1
2.3
2.3
50
83
79
66
65
64
62
61
60
60
59
59
91
175
243
252
240
228
219
204
190
175
109
65
186
162
144
135
120
110
100
90
85
80
75
72
70
70
68
67
66
66
66
66
66
68
66
66
66
70
90
108
148
162
152
140
130
114
114
108
97
94
89
83
77
76
76
73
73
72
72
70
70
72
73
75
73
73
73
75
80
79
76
73
73
72
70
70
70
72
70
69
66
64
61
60
60
60
57
56
55
55
55
55
55
54
54
56
56
56
64
77
106
142
146
146
144
144
144
144
144
136
127
120
77
4.1
3.1
45
97
3.6
3.1
3
3
3.1
3.6
69
114
189
243
273
351
359
399
457
489
492
460
440
334
293
291
288
286
283
280
204
169
171
177
193
207
216
223
216
207
197
188
94
46
52
57
61
66
72
75
66
59
53
48
19
7.2
6
5.7
6
6
5.4
4.6
4.6
4.1
4.9
4.6
3.5
3.3
3.1
3.1
3.1
3.5
4.3
3.8
3.6
3.1
3.1
2.1
1.4
1.1
2.1
1.6
1.7
1.4
1.1
1.1
1
1.1
1.6
2.1
2.4
3.1
3
2.3
2.6
3.3
2.3
5.7
13
14
13
14
14
14
12
3
2.3
2.1
2.3
1.6
0.8
0.9
5.4
10
13
14
13
2.8
1.7
2.1
1.5
1.3
1
1.6
2
2
1.4
2.1
1.5
3.3
8.6
7.9
7.2
7.2
7.2
7.2
7.9
5.7
2.6
2
1.7
1.7
1.5
2.6
2.6
3.5
5.2
12
14
14
14
14
14
13
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
57
86
89
89
88
86
86
80
114
152
148
144
140
134
130
125
123
120
116
111
106
102
101
96
94
91
85
82
75
68
65
62
61
59
57
64
82
77
82
79
76
75
79
97
114
116
113
109
104
101
97
93
91
89
88
85
85
83
83
83
83
85
85
83
80
77
73
70
69
69
68
69
69
69
70
70
70
70
73
83
86
86
83
80
79
77
76
76
75
75
73
73
73
72
72
73
72
69
68
68
68
65
65
66
68
68
68
66
68
66
72
80
77
75
73
70
66
65
69
69
69
69
68
69
70
72
72
70
70
70
70
70
70
69
69
68
68
68
68
68
69
72
72
69
68
68
69
70
72
77
83
86
88
94
106
118
51
5.7
5.2
5.2
5.2
5.2
47
83
85
86
89
94
99
102
158
214
214
214
211
209
207
207
204
83
44
64
120
231
226
93
65
82
78
160
120
41
6
40
131
173
171
104
18
94
154
182
193
199
186
173
164
158
148
140
171
226
216
184
154
134
113
94
80
68
56
44
25
13
7.6
5.7
4.9
4.9
5.6
7.2
6
4.1
4.6
4.3
4.6
6
4.6
4.9
4.6
4.6
4.9
4.9
4.6
4.3
4.3
3
3.1
2.3
2.6
2.8
3.3
2.3
2.1
1.6
1.9
2.3
2.8
2.6
3
3
3.1
2.6
2
1.6
1.4
1.3
1.2
2.5
1.6
1.5
2.1
2
2.9
1.9
4.6
8.5
2.2
1.8
1.2
0.9
0.8
1.3
1.7
1.5
1.4
1.2
1.1
2.3
2.2
2.2
1.5
2.1
2.6
2.6
2.4
2.4
2.2
2.1
1.8
1.9
1.9
1.6
1.4
1.3
1.7
1.8
1.5
2.1
15
14
12
2.4
1.6
1.6
1.2
0.7
0.6
1.2
1.9
1.5
1.6
1.3
0.9
0.8
1
0.8
0.8
0.8
1.1
0.6
0.7
0.6
0.5
0.7
0.6
1.1
1.4
1
1.1
1
0.6
0.5
0.7
0.8
0.6
0.5
0.5
0.8
1.1
0.4
0.4
0.3
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.7
0.9
0.3
0.2
0.2
0.2
0.3
0.7
0.4
0.8
2
2
1.6
1.6
1.6
1.6
1.3
1.1
0.5
0.4
0.4
0.3
0.3
0.4
0.4
0.4
0.4
0.4
0.5
0.4
0.4
0.5
0.5
0.7
1.3
1.6
1.6
1.6
1.7
1.6
1.5
1.5
1.5
1.5
1.5
1.5
1.7
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.6
1.8
1.6
2.1
2
2
2
1.9
1.9
1.9
1.7
1.7
1.8
3.8
11
19
26
31
36
38
39
38
37
37
40
41
41
42
43
43
43
42
41
41
42
43
42
41
40
39
38
40
40
40
41
41
41
41
40
40
41
45
52
53
53
51
50
49
49
51
55
55
53
51
50
49
47
46
45
44
43
42
42
42
44
46
46
48
49
48
46
44
44
44
44
45
49
49
49
50
53
55
55
54
52
50
49
48
38
22
24
26
28
29
30
23
4.5
3.8
3.5
3.5
3.5
3.2
3.4
3.1
3.1
3
3
3.3
3.1
3.1
3
3
3.1
3
29
92
111
118
142
174
160
122
99
108
171
255
245
238
202
195
193
180
183
188
176
167
163
159
173
200
187
185
185
186
243
288
293
320
361
415
440
423
399
382
412
438
404
390
488
558
587
611
631
658
654
630
561
504
455
418
291
212
219
225
213
203
201
203
218
231
249
257
282