HYDRAULIC GEOMETRY OF STREAMS & INTRODUCTION OF ELEVATION AS THE NEW STREAM CLASSIFYING PARAMETER RAJAN JHA, EIT, VIRGINIA TECH ADVISOR : Dr PANOS DIPLAS

Outline Hydraulic Geometry of streams - An Overview Stream classification system- An Overview Compilation of hydraulic geometric field data- UK, US & Canada streams Grain size (D 50 ) based statistical analysis of the field data Elevation based statistical analysis of the field data Overall conclusion of this study 2

Hydraulic geometry of streams – An overview Hydraulic geometric equations describe the quantitative variations of stream properties with changing discharge. [Ferguson, 1986] Leopold and Maddock (1953) established following hydraulic geometric relations in power form: w = aQ.5 d = cQ.33 v = kQ.17 Hydraulic geometric variables considered in this study : Aspect ratio, channel slope & Sinuosity (All dimensionless) 3

Defining the hydraulic geometric terms Aspect Ratio (Ar)– For any channel or stream, it is defined as the ratio of bankfull width to bankfull depth 4

Defining the hydraulic geometric terms Channel gradient (Sc) – For any channel or stream, it is defined as the ratio of drop in the elevation per unit horizontal length 5

Defining the hydraulic geometric terms Sinuosity (P) – For any stream reach, it is defined as the ratio of actual sinuous length (channel length) to the shortest straight line distance (valley length). 6

Compilation of hydraulic geometric field data 7 CountryRegions covered # Data points Type of streams covered based on grain size Canada Yukon, British Columbia, Alberta, Manitoba, Saskatchewan 92 Sandy, Gravel & Cobble UK Wales, Scotland, Staffordshire, Lancashire, Herefordshire, Durham county 74Gravel & Cobble USAArizona, New Mexico, Oklahoma, Navajo, Missouri, Virginia, Maryland, West Virginia, New York, Montana, Washington state, Florida, Georgia, Alabama, Tennessee, Colorado, Michigan, Kentucky, 707Sandy, Gravel & Cobble

Stream classification system –An overview More than 20 different stream classification systems have been proposed till date Streams have been classified on the basis of bed material, patterns, age, sediment inputs, orders etc Rosgen (1994, 1996) developed a new approach to channel classification system where he divided the channels into four hierarchical levels Even with the existence of so many available classification systems, none of them have been accepted universally till date 8

Research Objectives Calculating most probable values of Ar, Sc & P occurring together in nature for each stream type : sandy, gravel and cobble Introducing “elevation above mean sea level” as the new parameter for stream classification system Identifying trends existing in the behavior of stream variables (Ar, Sc & P) while moving upstream 9

Median grain size (D 50 ) based analysis of hydraulic geometry of streams Brief Outline: Dividing field data into sandy, gravel & cobble groups Application of joint probability distribution on Ar, Sc, P of each group Finding MPVs of the hydraulic variables for each group occurring together Analyzing 3-Dimensional plots 10

D 50 based distribution of cumulative data 11

Sandy, Gravel & Cobble streams 12 Cobble streams Sandy streams

Modal values of Ar, Sc & P for each stream type Probability density functions of hydraulic geometric variables were estimated for each stream type and modal values were calculated 13

Joint probability distribution of Ar, Sc & P Using kernel density estimation and smoothing on a fine grid in statistical software R, joint probability plots in 3 dimensional forms were also obtained for each stream type The peak in the plots represent the most probable values (MPVs) of the three variables [Ar, Sc, P] occurring together in the nature for each stream type 14

Joint probability 3-D plots for sandy streams 15 [Ar + Sc][Sc + P][P +Ar]

Joint probability 3-D plots for gravel streams 16 [Ar + Sc][Sc + P][P +Ar]

Joint probability 3-D plots for cobble streams 17 [Ar + Sc][Sc + P][P +Ar]

Most probable values of Ar, Sc & P occurring together 18

Elevation based analysis of hydraulic geometry and establishing it as the new stream classifying parameter Brief Outline: Dividing complete field data into 14 fine elevation ranges Calculation of Modal values of Ar, Sc & P for each range Formation of final fine elevation zones and calculating MPVs for each zone Classifying sandy, gravel and cobble streams on the basis of the 5 elevation zones 19

Grouping of data into 14 fine elevation zones 20

Modal values calculated for 14 elevation ranges 21

Formation of final 5 elevation zones 22

MPVs calculated for each of the 5 zones 23

3 Dimensional Probability density plots 24 Presented for highest elevation zone : 5000 ft & above Rest all zones followed similar distribution behavior [AR + Sc][Sc + P] [P+ AR]

Elevation based classification of sandy, gravel and cobble streams 25 SandyGravelCobble Elevation range (ft) MPVs [AR, Sc, P] 0-250[10.0,.05, 1.36] [16.5,.10, 1.16] [31,.25, 1.19] [37,.25, 1.14] 5000-above[24.0,.4, 1.19] Elevation range (ft) MPVs [AR, Sc, P] 0-250[11,.20, 1.34] [16.0,.35, 1.19] [23.0,.45, 1.19] [38.0,.50, 1.14] 5000-above[19,.8, 1.16] Elevation range (ft) MPVs [AR, Sc, P] 0-250[11,.35, 1.27] [16.0,.35, 1.14] [28,.60, 1.16] [41.58, 1.16] 5000-above[26, 1.15, 1.12]

Summary & Conclusion Statistical analysis is a strong tool in understanding the co- relation and interdependency existing amongst the stream variables Elevation provides a consistent framework for grouping streams on the basis of its hydraulic characteristics. Thus elevation based classification can be considered as the new morphology based stream classification system. 26

Summary & Conclusion Elevation based classification provides a logical progressive expression of trends occurring in channel characteristics. MPVs can be very useful for engineers while designing canals, channels and obtaining representative dimensions for laboratory and numerical modeling 27

Acknowledgement Dr Panayiotis Diplas- Professor & Department Chair, Civil & Environmental Engineering, Lehigh University, (Previously at Virginia Tech) Dr Shrey K. Shahi- Stanford University NCHRP – National Cooperative Highway Research Program (Funding Agency) 28

Dedicated 29 Dedicated to those who lost their lives in the tragic incident called “Himalayan Tsunami”, June 2013, India. More than 5700 people died and many still missing

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