PEAK-FLOW IRAYEL-TIME CHABACTEBISTICS CP THE PBASER BIVB,
ERI?ISB COLUHBIA
Anne Shuttf eworth
B,Sc. (bons) , University of Males, 1979
THESIS SUB BITTED IN P ART1 AL PULPILL!IEWF OF
THE REQfJIREElENTS FOR THE DBGREE OF
MASTER OF SCIENCE
in the Department
of
G eo gr ap hf
0 Anne Shuttlenorth 1984 SIRCW PRASZR UNIVERS ITfl
Fefrruar y, 1984
A11 rights reserved. This vork may not be reproduced in whale or in part, by photocopy or other means, without permission of the author.
ISBSIOACT
A tine-area model was developed to synthesise hydrographs
for the Fraser River, Eritish Columbia. These hydrographs
reflect the size and sbape of the tributary basins, and the effects of storage aud attenuation are incor~oratedby the use of pluskingum f lcod routing technique, As each tributary is added
to the Fraser River f lw, its relative importance to the
mainstrean peak is assessed. The effects of the timing and
magnitude of tributary inputs are shown to be critical in determining the time of absolute peak-flow. Apparent travel t isaes between gauging stations for rainfall
events vere examined for the pexiod 1971 to 1980. Travel tiaes were derived fro@hourly discharge data which were obtained
directly f rotn streamflow recorder charts. A negative relaticnshi p between discharge and travel time should exist where river flow mechanics dominate, hut no decisive patterns were found, either on an annual or seasonal basis. Wave celerity
ap~earedto be very fast in many cases, and in several others,
the upstream peak occurred after the downstream peak. This
behaviour is predicted by the time-asea model, Therefore it is
concluded that it is basin morphology and not translation that exerts the primary control upon runoff patterns in the Fraser
Ea sin.
Beal hydrograph changes in time and space can be interpreted using the model as a means to infer the source area
of runoff. When data are grouped according to the spatial
iii distritution of precipitaticn, trends between discharge and
travel time can be identified, for cases where substantial
tributary inputs between two stations do not domi~tethe
time-of-peak, It is concluded that the time-area taodel is a
useful tool for interpreting travel time characteristics of the
Fraser River flood waves.
ACKIPO1 LBDGBIlSDTS
Sincere thanks are offered to Ted Hickin, ay Senior
Supervisor, for his guidance, patience and support. Alsc warm thanks go to Hike Roberts and Brian Sagas for their help and advice, and to Professor Olav Slaymaker for kindly acting as lay external examiner,
I would like to say a special thank-you to Oliver Nagy of the Water Survey of Canada data section f cr making data acquis it ion a gleasure, and thanks also to Gary Schaeff er of the Atmospheric Envifon~entService.
Many thanks to everyone who has given me their salued friendship and support in the recent years, especially: Elelen,
Larry, Steve B, Chris, Bark, Bick, Plo, Brent, Careen, Joan, Ron,
Pat, aschi, Gary, Steve G, Geir, Cathy and Lorraine.
I thank you all,
Last, but not least, 1: wish to thank Richel for his encourageaent, love and understanding. TABLE OF CONTEBTS ~pproval...... ii Abstract ...... iii Dedication ...... v BckuouPedgenents ...... v i List of: Tables ...... ,...... I.. ix List ot Figures ...... x 1. Background to study ...... 1 1.1 Introduction ...... 1 1.2 Hydrclogical Background ...... 2 1.3 The Problem Defined ...... -24 1.4 Organisation of the Study...... 28 I1 . Physical Envircnment of the Fraser Basin ...... -29 2.1 Physical Characteristics a•’ the Fraser Basin above Hope ...... 29 2.2 Neteorclogical Conditions ...... -41 2.3 Hydrometeorologica 1 Divisions and Highflow Regionalisation ...... 51 I11. The Fraser Biaer Tiae-Area Bodel ...... 54 3.1 Introduction ...... 54 3.2 Mode I: The Basic Plodel ...... -54 3 .3 irlode 11: Rainfall Simulation ...... 70 3.4 Hode 111: Snowleelt Adaptation ...... 74 3.5 Nodes ZV. Y .VI. Regional Ada pions ....,...... -78 3.6 Discussion of generated data ...... -80 FV . Peak Flow Times ...... I..87 U.1 Introduction ...... I...*..87
vii 4.2 Data Ccllection ...... -88 4.3 OhServ~dPeak flow Travel Time relationships .... -91 4.4 In•’luence of neteorologica 1 Conditions ...... 100 4. 5 Observed and model generated velocities ...... 106 4.6 Time-area model hydrcgra phs and Ff aser River hydrographs compar~d ...... 109 4.7. Discharge/Travel Tiae relationships for selected precipitaticn source areas ...... -114 Y . Discussion ...... 122 5 .7 Im~crtantControls on Time of Peak ...... 122 5.2 Use of the Time-Brea flodef to interpret Travel Times ...... 127 5.3 Further Uork ...... 130 5.4 Conclusions ...... 135 Appendix ...... 138 Bibliography ...... 144
viii LIST Of TABLES
TABLE PAGE Physiographic Regions ...... 33 Shape characteristics of subbasins ...... 37 frasfr Basin drainage densities...... 39 Percentage of precipitation occurring with f ronts present ...... 41 Clia atic characteristics of the frase r Basin subhasins ...... =...... 50 Seasonal runoff peaks ...... 51 Peak Discharge for dif fereet va iues of .. expressed as a percentage of the value for ~~0.2...... 64 Time of peak with various x values ...... 55 Model variations ...... 80 Time of peak derived from model ...... 81 Apparent travel times ...... 81 Source of main peak volurse ...... 82 Gauging station details ...... 89 Discharge-velocity relaticnshi~s...... 96 Travel tiaes and eeteorological conditions ...... 104 Travel tiae statistics ...... 107 Yelocity cora~arisons...... 107 LIST OP PPGURES
PIGUAE PAGE Typical area-discharge relationship for a stream and its in•’hence on wave celerity ..,...... , 21 Stage-travel time rela tionship ...... 21 Flow Chart of The Probles ...... 27 Elevaticn of the Fraser Basin ...... 30 Physiographic Regions cf the Fraser Basin ...... 32 Subbasin locations and shapes ...... 36 Average Precipitation Distribution in the Fraser Basin ...... 43 Locations of climate and gauging stations in the Fraser Basin ...... 46 ~fydrometeorologicalRegions of the Fraser Easin ...... 52 Time-ar~aPlap of the Fraser River ...... 56 Simple time-area histograms for the Fraser River to gauging stations ...... 58 Instantaneous unit hydrographs for the Fraser Basin to the gauging stations ...... 60 Hydrographs representing each subbasin ...... 61 Fraser River hydrographs at successive confluences ... 62 Co~parativehydrcgra~hs produced in all modes at four gauging station locations ...... 72 Discharge-travel tilae relationships ...... 92 Fraser River hydrographs ...... 712 Disc harge-t rave 1 ti me ref ation ship ky source region of precipitaticn ...... 115 I, Background to study
--1.1 ------Introduction
Belatively feu sturlies have addressed the prable~of flow
travel time variations vithin a watershed (Pilgrila, 1977). Studies have tended to polarize, either toward exaining the effects of geoaorphic characteristics upon response time (lag
tiate) , or considering changes in flood wave shape as it passes along a channel. In a large basin houever, both aspects are import ant in deterriniag peak flow travel tines.
Travel time is defined by Linsley, Kohler and Paulhus
(1949) as the elapsed ti~ebetween flood wave crests at two stations, They noted the lack of constancy for a given reach but suggested travel tine behaved in a regular fashion: being long at low stages, decreasing to a minimont at atoderate stages, and
increasing somewhat to stages above bankfull, Between reaches, travel time will vary depending on hydrologic and hydraulic differences. However, the regular rela tionship between travel
tiae and di=charge can be disrupted by laa jor tributary inputs and a nonun iforra preci~itation distribution,
In this study, a tine-a rea model of the Fraser bas in is used tc interpret peak flow travel time irregularities for
rainfall events, The Praser Basin is irregnlarly shaped, contains contrasting hydroneteorological regions and supplies numerous tributaries to the Praser River. Therefore it per~its an examination of the way in which spatially limited Frocesses are incorporated into the cverall basin response. Time-area concepts were used to simulate a series of contrasting preci ~itation inputs which uer e Bodif ied to Instantaneous Unit Hydrographs using the Rasking ura flood routing technique, Peak flow travel times, derived froa the model, then can be used to interpret real travel time irregularities. The mcdel helps to identify where river flow mechanisms are dolainant and where other factors need to be considered.
12.1 Crainage Basin dodels and the Bpdrograph
The land compooeet of the hydrologic cycle is described by
More ( 3969) as consisting of a ~reciritatioainput that is
"distributed through a number of storages by a series of transfers leading to outputs of basin channel runoff, eva~otranspirationand groundwater". W hydrograph represents the time distribution of that runoff from a drainage basin and
Rogers (1972) noted that its peak corresponds to flow arriwing froa the maxiaum basin width. The hydrograph is therefore an integral of physiographic and cliaat ic variables (Roberts and Klingeman, 1970) . The relationships between basin features, cliraatic inputs and the hydrograph are documented or implicit in nurerous papers, including those c•’ Butler (1977). Howard and
Smith (1977) and Ueyman (1975).
Runoff reaches a river by numerous routfs which Hewlett and ffibbert (1965) classified either as quick or delayed flow in order to avoid aaking process assumpticns, The asonnts translated by the differing means depend nltirsately on basin characteristics, but quick flow generally corresponds to storm runoff. A hydrograph represents basin rescone to a storm and therefore bydrclgra ~h shape reflects basin storage a red its influence on travel tiees. NuHierous aethods of hydrogra ph anafy~isare available (Chow, 1964) but the unit hydrograph of
Sherma n (1 932) rersains the most widely used technique. Sherman suggested that a unit bydrogragh is specific to a given basin and that it can be used to understand individual basin processes, The theoretical bases of the unit hydrograph have
been nuch debated. For example, Heerdegen (1973) questioned the rigidity of the assumptions, However, despite the problems, it still Froves to be a valuable titethod, Physical ~odelsof watersheds have been used to exalsine simple relationships between basin characteristics and runoff
(for example Roberts and Klingeman, 1972; Black, 1970 ; and
Black, 1972)- Subsequent studies focussed on the similarities
between laodels and basins, These models illustrate the
relationships to be expected far ideal, reduced scale conditions and hence may be limited by problettls of hydraulic silrrilitude, They are useful tocls for understanding simple basin Frocesses
and are conceptually of great importance. Simple sathematical modeling using correlation and regression techniques has had only limited success (Vorst and
Bell, 1977). Correlaticns obtained are rarely applicable to a
range of regions and possibly lieited by poor mathematical representation of the relationships, Linear mthesatical models do not explain several im~ortantfeatures including the
non-linear relationship between ~eakdischarge rate and
precipitation intensity (Wooding, 1965) , Preliainary studies of
non-linearity in laboratory channels were made by Anorocho (1963) and subsequently Kulaedaiswamp, 196U; Snyder, #ills and
- Ste~hens,1970; Reed et al, 1975; Pilgrim, 1976; and Singh and
Woolhiser, 1976, A linear rainfall-runoff relationship is satisfactory for large basins but more deviations from linearity are cbserved in saaller basins (Wang et a1,1981) , Coapu ter technology has enabled advances in the synthesis
of ua tershe d processes: the Stanf crd Watershed Rodel IV
(Crawf ord and Linsley, 1966) is a classic example. As models become atore sophisticated, parameter optiaisation makes them more spcific to tbe catchment for which they were developed, as exenplified in models of the ?!ease (Bultot and Dupriez, 1976)
and the Praser (Quick and Pipes, 1976a)- Vorst and Bell (1977) cautioned that paraaeter values outside the range of streamflow
data used Bay not t~ rdiable. The scale of a study is important, both spatially and
temporally. For the micro-scale, an examination of the physical
corsglexi ties of the watershed is necessary. At the macro-scale,
genera 1 trends in parameters are investigated, 3 llowing
descriptions to be simplified. While it is well known that basin
size influences runoff, an understanding of the implications of different scales is important for data transfer. Pilgrim and
coworkers (1982) examined the effects of catchment size on
hydrological relations and concluded ge lleral pat terns between large and small catchments exist, but they are not sitsple and well defined,
Tools for predicting the hydrograph characteristics of a
- watershed abound, ranging from sitsfle, empirical precipitat ion - runcff relations to complex routing techniques (Rurphey et al, - 1977). Clnt if. recently, spatial processes in hydrology have been
relatively neglected in contrast to the aultitude of studies of
tempcral stochastic processes ((3rd and Bees, 1979). Hany studies- are 1iraited.because they consider hydrographs at only one point
in the riper system and assume that a single storm produces a
si~glef food hydrograph, The concept of multiple inputs however, is attracting Bore attention, for example, Baudsley and Tagg
(1981) and Buthnan and Wilke (1982). 1-2.2 The Tine-area concept
Geomor pholcyy controls the time taken for translation of flow and ultimately influences hydrograph shape (Gray, 1965), One of the earliest attempts to quantify the relationships among flood hydrograph characteristics and the size, shape and gradient of a drainage syste~was that of Borton j1932). Hore recently, Vorst and Bell (1977) found that the distance travelled tothe outlet is usually significant ia predicting flood response time. Singh 11975) showed tine of concentration to vary vith the space-time distribution of rainfall, Ne reports
Bulvany (1 850) as ~ossiblyteing the first to show clearly the relation between t it~ecf concentration and maximuta runoff,
The time taken for an actual drop of water to travel througb the systen can be used to construct a tiee-area map of a basin, By assuming that f lov velocity remains constant, iscchronesl can be placed objectively at equal distances from the basin outlet. Laurenson (1964) proposed that the titre interval betueen preci~itationand its ef f rct at the outlet was a more realistic interpretation than the actual travel time of a water droplet,
A tiae-area histogram way be used to siwlate an Instantaneous Unit Hydrographz at the basin outlet (Clark, 1945;
Nash 1957; and Dooge, 1959) , The concepts are well founded since area is undisputedly corrdated with runoff volume and distance with the titee crdinates of the hydrograph. In experilaental work with physical zodels, ~6mec(1972) found full confirmation of time-area concepts. Clark (1945) claimed that the method allows the ident ificat icn of elements in the hydrograph attributable to certain parts of the basin, The method involves applying flood routing techniques, designed to mathematically simulate flows using storage modifications, This assumes that it is possible to separate watershed translation and storage effects, The foraer
allows pure translaticn (inflow curve = outflow curve) via the stream network to the outlet based solely cn chanoel travel tislle. At the outlet the translated flow is daarped by the incorporation of storage effects. This is achieved by ronting the flow through a hypothetical linear reservoir3 producing an outflow hydrograph for a basin.
The first attempts were based ltlainly on an assumed constant translation speed and uniform precipitation distribution, Clark
(1945) obtained unit hydrographs which were net perfect, but within------the accuracy------usually attainable in runoff ca lculations, 2 The hydrograph of runoff fro~an infinitesiloally small period of precipitaticn that would result from an inch of water spread uniforlslily over an area and then allowed to runoff,
3 Chow (196L)) describes a linear reservoir as a fictitious reservoir in which storage is dependent on outflow, and a finear channel as a fictitious channel in which the time necessary for translation of a discharge through a given channel length is constant, necessarily produce more accurate results for flood flows than aeasureoaent of a gecmorphic parameter, such as area, frcm a map,
Clark (1945) considered large drainage areas by deriving unit hydrographs for each subbasin, and then routing these to a main stream point, Kirkby (1971)) suugested that output frola a large drainage basin is damped relative to the input and therefoee the prediction of storm hydrographs for large areas is successfnl because of the daaping. In view of this, he also suggested that there were few advantages to be gained by including sore detail than necessary, N ash (1957) proposed that a drainage area can be simulated by a number of reservoirs in series, Studies prior to Nash, had implied this concept but not mentioned it explicitly (Chow,
1964)- The Nash model however, sap not yield satisfactory results in basins with a large delay time between precipitation excess and coaaencement of surface runoff. This is because the model i~ based on storage routing alone, and only makes indirect use cf the translation property [Kulandaisvamy, 1964) . To incorporate the translation eleaent, Dooge (1959) re~resenteda tasin as a series of alternating linear channels and reser~oirs, In simple term, a channel allows pure translation and a reservoir incorporates storage effects allowing hydrograph shape to change, In Dooge8s tttodel, subareas delimited ty isochrones are re~resentedby a linear channel in series with a linear reservoir, Outflow from the linear channel is determined from a tiae-area diagram and added to the outflow from the preceeding subarea. The sum then provides inflow to a linea r rese rvoi r. Unfortunately, the X nsta ntaaeous Unit Hydfo graph solution that results is mat hemat ically complex and not easily solved for practical FurFoses.
As computer facilities expanded, more complex mathematical funct ions were handled. For exaaple, Manderville and 0' Connell
(1973) introduced time variant versions of the linear channel and linear res~rvoirto produce hydrographs that are not governed by the harsh assum~tioasin Unit hydrograph theory. Ragan 11966) attempted to introduce local inflows but model oversensitivit~caused many problems, making it unsuitable for a basin such as the Fraser,
Generally, a time-area gtodel produces simple but reliable hydrographs, The Clark version has been used in many subsequent studies including the well-repected Stanford Watershed Hodel IV of Crawford and Linsley (1966). In 1973, both the-area concepts' and Muskingum flood routing were used in the BEC I nodel of the
U. S. Army Engineeering Corps (Viessman, 1977) , 1.2. 3. Flood flouting
This is a technique for predicting teraporal and spatial variations of a flcod wave as it traverses a river reach or reservoir (Viessaan et al, 1977). Flood routing was originally defined as the deterainaticn of a hydrograph from an upstream hydrcgraph [Ding, 1974) and the first reference to what is considered to be a real application of routing a long a river uas by Graeff, in 1833 (Viessman et al, 1977) , Elost procedures have been developed since 1900; the majority being of a hydrological storage nature involving solutions based upon inflow and outflow hydrographs, Inflow hydrographs may be substituted by precipitation data or lagged input f ro5 time-area histograms. A second category of flood routing consists of hydraulic methods hased on equations for unsteady flow in channels, Hydfologic flood routing methods calc uLate the volume of water temporarily stored in a reach. Natural streams of ten have high channel resistance and storage capacity which modify a wave as it traverses the reach, Ideally, the sate of storage in the reach should equal the difference between ordinates of input and output hydrogra~hs, A negligible loss or gain in total volune is assumed, and the equation of continuity applied,
The best known hydrologica 1 flood ro a king technique is the Huskingum method which views channel storage as having two constituents: prisla storage de~endson output and wedge storage reflects the difference between ingut and output. During flood
uave advance, input is greater than output producing a uedge of storage. Ccnversely, output becomes greater than input during f locd wave recession and a negative wedge results, The method assumes a unique relationship between stage and discharge, a
storage constant (x) that is acceptable for all flows and a
storage time constant [k) that is reasonably close to travel time within the reach. That is, k and x relate channel storage to input and output,
The kinematic wave theory [Ligh thill and Ilhitham, 1955)
offers an another approach, A kinelaatic uave has constant
aapfitude and only one velocity at each point in the wave,
- Canvection- diffusion principles were originally def bed by Hayarrti (1951) who recognised that irregularities in channel - geometry affect flood waves and attempted to slake allowances for
them. However, this method has disadvantages which make it
incom~atiblewith a tiae-area model, For example, the problem of'
evaluating channel gecmetry ir~egularitiesis imlaense and the the method can te applied only tc a limited range of discharges.
Alsc, iaa jor tributaries cannot be included unless routing is from tributary to tributary and therefore problems arise in poorly gauged areas. Resistance to flow, storage and channel irregularities
govern outflow f roe a reach and can lengthen the time base and
lower the crest of a stom hydrograph, This resnlts in
attenuation, The ~ilodelingof wave attenuation ho~ever,presents problems to both flood routing methods discussed here. For exampl~, the prediction of attenuation by the Pluskingum method is not easily reconciled with the assumption of a unique stage-discharge relation. The kinematic wave solution may not be ap~ropriate either, because Henderson (1 966) suggested that kinematic wave velocity may not occur during attenuation, Wave subsidence is usually more iaportant in shallow sloped rivers t ha a in steep mountain streams.
S iople snatheeatics are inadequate for nonuniform channels of comple~section with varying slope and roughness. Even if these irreg ularities are assessed by extensi ve, costly surveys, they are sufficiently dynamic to liait the use of any data set, Also, the wave itself is usually an interiaediate between pure translation and pondage and canaot be def i~edsimply, Routing in natural channels is therefore highly cartlplex, but assumptions can be ~adeto liait the effect, of channel irregularities.
The #uskingum metbod is cne of the most satisfactory, and theref ere popular, techniques of flood rotlting (National
Environmental. hesearch Council, 1975) and its relevance today is ernphasised by Pilon and Cheng (1 983) . The wodel has an overall sim~licity,both concepkually and pract ically, Chow ( 1964) suggested that alt bough the method is not exact, it is adequate, es~eciallyfor flood control ~lansand designs. Also, this method can include tributaries that are poorly ganged.
Theref ore, the nuskingue method was chosen for the Praser Basin ti me-area model, The nu sking urn Rethod.
Developed by G-T-McCarthy (1938) through studies of the
Muskinqum Conservancy District by the U.S. Army Corps of
Engineers, the Buskingum method is based on the continuity
equation (1) I-O=ds/dt
where X=in flow O=outf low ds/dt=changes in storage Storage in a given channel reach deplnds on inflow, outflow and
other hydra nlic characteristics of the cha nnel section. It can
be expressed as: s = ,[xxI'i+(l-x,&l a
where S is storage,
- a and n are constants reflecting stage-discharge at the end of the reach, b and ra represent stage-voluae characteristics, +? and x defines relative weights of I and 0. The Pluskingum method assuntes a/n = 1 and lets bla = k. The value
k is a storage constant for the reach and thus
s = K [XI., (1- x) q In application, equation (2) is expressed in the finite form
therefore fro@equation (3)
which, when substituted in (4) becomes the Huskingum routing equation:
in which and C,+C, +C,=I,O
Routing involves solving equation (6) for successive ti me increments. Deteraination of constants,
T he #uski ngum me thud assufaes a unique stage-discha rge
relationship, so x should allow the volume stored to be the saw
f cr both rising and falling stages, fjsually, x varies between
0.0 and 0-5, If storage is a function of outflow alone, as in a
- reservoir, x=O,O, Vhen nc storage occurs, FO. 5. In the latter case, inflow and outflow carry equal weight, and hydrograph - shape is not changed (pure translation) Clark (1945) routed a - . cosine curve using x values between 0.0 and 1.0 and fonnd x was
responsible for changing peak mgnitude, The constant k
indicates the time required for the centre of mass of a flood wave to pass from an u~strealapoint to a desigrated point
downstream. It is theref ore a function of reach length and wave
veloci ty IS trupczewski and Kundzewicz, 1980) and usual1y
approximates the travel titpe through a reach (Viesstttan et al,
1977)-
- If actual input and output hydrographs for a reach are
available, k and x can be d~ter~inedby trial and error, This
involves plotting graphs fron equation (3) for: a series of x values. The best x value plots the narrowest hysterisis loop,
and k equals the reciprocal of the slope through this loop. Unfortunately, the data available for the Fraser River do not permit this approach. There are rsany lateral inputs bet ween
continuous gauging stations, and althcugh these inputs may be measured daily, they are too infrequent to be useful. Brakensiek
(1963) calculated coefficients by using the section rating
function and conveyance data for ungaugea watersheds, but
concluded t hat nursesoas assulaptions limited their utili ty. By assuming the input hydrograph to be an isoceles triangle,
Overton (1966) deter~llinedk and x from aa analytical solution of the output hydrcgra~hshape. Clearly this lsethod is not
- practical for the large, irregularly shaped Fraser Basin. He found that k was related to the shap of the inflow hydrograph - and the lag tise between the inflow and outflow hydrograph - peaks, whereas x was a function of k and attenuation. Also,
because of the sensitivity of hydrograph shape in small
catchments, he found that k and x varied for each storttt.
The #uskingum methcd can be applied to aany problenrs, when the aodel deficiencies are understood, and Bore importantly , where the deficiencies are not critical (Strupczewski and
Kundzeuicz, 198 I), Singh and HcCann (1980) found agreement among
vriters that the effectivertess of the Buskingum method depends
on the accuracy with which the parameters are estimated,
Although they found significant changes in k and x, depending on
the aethod used, they concluded that no method had any particnlar advantages. Diffesent investigators use different initial conditions to determine k and x [Singh and BcCa nn, 1989). This hinders coseparison of the methods and the utility of the results,
Dooge et a1 (1982) advocate the estimation of fluskingum pa ralaeters from georaetric and hydraulic characteristics of the reach in the absence of in~ntand output data. They attempted to establish relationships f cr any cross-sectional shape and any friction law. Although small differences in the values of k and x resulted, they suggested the real values vculd lie between the extremes, Hethcds using hydraulic characteristics can incf ude nonlinearity becanse k and x can be varied with discharge, Ponce and Yevjevich (1978) prefer to vary k and x in time and space, depending on flow variability, However, they quote Kousis 11978) who suggested calculations are relatively insensitive to x and therefore it can be constant. Chon (1964) considered a variable x to be a refinesent that is seldoe necessary. The nature of k is agreed upon by many hydrologists (Strupczewski and Kundzewicz, 1980) but the nature and values of x are mere inconsistent. In soiae cases, a negative x way be calculated, Theoset ically, this is detatakle because cfassica 1 hydrology views x as a measure of wedge storage, but
Stru~zeuskiand Knndzevicz (1980) conclude a negative x is admissikle in =thematical modeling. In general, x increases with increasing input rate and decreasing output rate, The routing time t is critical. Theoretically, t must be
small relative to cther time elements and sufficiently short to validate the assumption of a linear relationship between hydrograph ordinates- The routing period is normally assigned
any convenient value between the limits k/3 and k (Viesseaan et a1 , 19 77). However, errors introduced when t=k are insignificant
coepared vi th the inaccuracies cf the basic storage assumption
(Nash, 1957)- Long reaches are often simulated unsatisfactorily
and Strupczewski and K uedzewicz (1980) prefer a cascade of mdels. This concept was used in the Eresent study.
Because k and x depend on the method of estiaaation, it is difficult to determine the best values. Also, in a natural
- systea , constant values are suspect. Clark (19 45) was criticised in the discussion of his classic paper for using uniform
velocity to establish isochrones. Be examined various
refinements, but his resalts were not improved, Clark suggested
this was caused simply by two wrcags making a right; the second y*wrongxtbeiog the use of a single k value, nhile his answer may
not be tuatheiuatically acceptable, it is an adequate solution for
this method, Therefore average values of k and x seei reasonable when lcng rivers are silaulated. 1.2.4. U. B, C, Hodel of the Fraser Basin
Funding frora the Eritish Columbia Disaster Relief fund
SUFFO~~~~developmental work on watershed and flow models of the
Fraser basin by Quick and Pipes l1972, 1975, 1976a, 1977). The computer mcdel consists of two major parts: the first is a watershed model, run on continuously updated aeteorological information to combine botb rainfall and snowmelt rnnoff parameters, and the second part routes flow through the channel network, including lakes and reservoirs,
The model has been in operation for several years now, and is a reasonably gocd ~redictorof runoff volume and timing for the system. Based on the total water kalance, the model coefficients are held constant through the season and from year to year, Quick and Pipes considered this im~ortantfor producing reliable short and long term forecasts, Indeed, the principle uses of the @ode1 are forecasting and planning.
Quick (1965) noted that it is difficult to guantif p runoff due to the cum~lexityof snowmelt. Therefore, much study of the phenomenon was necessary at the outset. Area-elevat ion ba nds wefe delilfii ted to allow a pertinent distribution of temperature and precipitation elements. The soil moisture deficit is then used to apportion runoff to three different flow routes which are distinguished by speed of transfer. In physical terms these routes represent direct runoff, intesflou and grcunduater, Routing of the fast component is based on the conce~tualmodel of Nash (1957) with an additional linear storage reservoir for the medium component. A linear storage reservoir is used to accumulate the slow in~utwhich is subsequently released as recess ion flow,
The watershed model was designed to use a sparse data input, nevertheless, estimating inputs frcm the precipitation station network in the Fraser Basin is still difficult, As well, the numerous influences upon the water balance require constant revision, The flow nodel USES mean daily rives discharges and thcrefor~the Huskingum nrethod is unsuitable because the travel time hetween stations is less than one day (the routing period), Theref ore, a nonlinear kinemtic wave method was developed utilising routing ccef ficients calibrated froa stage-discharge and stage-velocity curve data for each section, This method of calibration avoided problems created by the addition of large amounts of ungauged lateral inflow. The model is flexible because it allows travel time and channel storage to be independent, However, real travel time and ti~edifference between two peaks at two successive stations may not fie the saw, The Eresent study examines time differences between peaks at successive gauging stations and requires rain-produced floods with discrete inputs rather than snowaelt,
A major problem of the U.B.C. aaodel is the use of Bean daily streaaflov data, Hourly data should be more reliable since travel times b~tweenstatio~s are usually less than one day, Velocity usually increases with stage, therefore area - discharge curves are usually concave upwards (Linsley e t al,
1958) [figure 1.1). For a wave enclosed within the banks of a
rectangular channel, it can be shcwn that the speed of the wave crest is greater than at its foot. Therefore, a hydrograph
rising limb at a downstream point will be steeper than its ccunterpart upstream (N-E.R.C., 1975) . The speed of flood wave movement is great1y influenced by slope, roughness, and
hydraulic radius of the channel, Therefore, small inbank floods
- will travel faster than a flcod that overtops the channel. - Linsley et a1 (1949) suggest that minimum travel tiste occurs at - modera t~ stages (figure 1.2) ,
Have velocity or celerity may be calculated by Chezy or
Ranninq f oraulae, tut the result ieg relationship with water velocity is contingent on the particular formula utilised, and channel shape. Therefore, neither snpplies a finite solution, Alternatively, celerity [c) of a atonoclinal risinrj flood wave can be expressed as: c=ag d A where Q=discharge &=area
This is known as the Rleitz-Sedd~n law. It assumes that the wave has a ~ermanentform and therefore there are @any doubts as to
its applicability, Quick and Pipes (1976b) however, found that - slopes of secants OA and 08 represenf water velocities for sections 1 and 2 - slope of secant AB represents wave celerity
(after Linsley, Kohler and Paulus, 1958)
FIGURE 1.1 Typical area - discharge relationship for a st ream and its influence on wave celerity
( after Linsley, Kohier TRAVEL TIME and Pauius, 19L9)
FIGURE 1.2 Stage - travel time relationship dQ/db tutds to overestiaate wave speed,
Ideally, peak travel time is a direct function of head. In general use theref ore, equation (2) can be applied.
where C=wave celerity v=water velocity g=acceleration due to gravity y=water head
Although this equation is good for a moaoclinal save, it is guestionab le when applied to a normal flood wave,
Okservations suggest wave celerity is between 1.4 and 2-0 times greater than the water velocity (Liosley et al, 1949). Probleias exist in the calculation of wave celerity in real rivers because of channel nonunifortuitp, Quick and Pipes (1 W6b) suggest gauging stations are often located above a contracted section and theref ore reflect the velocities at these sections.
Conversely, wave celerity is influenced more by the slower sections and thus, direct calculation of velocity is difficult. During attenuation, the observed speed cf the flood peak remains dependent on celerity, but it is also influenced by hydrograph shape (I.E.B.C., 197S), As peak curvature decreases, wave velocities nay depart frog kinematic expectations because outflow is no longer aerely dependent on water depth. Wow, neither discharge nor head remain constant, Subsequent calculation E nnst consider the wave as having progressively decaying amplitude. Approximations usual1y yield adequate results, kut crude simplificaticn may hide important natural variations and care must be exercised. The main ~ethcdsof measurement of travel times are by
timing coloured dye or radioactive tracers in the flow, and by
inter~retingwater level records. Pilgrim (1976 and 1977) used isotope tracer methods to examine travel times and their relation to flood runoff and flood storage, Therefore, isochrone
spacings are determined froa the travel time of the water and
not speed of flood wave movement. His studies re vealed an
initial positive increase of travel time to fairly constant
values at medium to high discharges. Tracer analyses are usually
re=tricted to slaall watersheds with limited tributary additions, and prior to this study, to low flows.
Stall and Hiestand (1969) estimated contaminant travel
- times in Illinois streams froe hydraulic geometry relations with reasonable accuracy but generally found the computed travel tirtte
to ke the minimum expected, especially at low flows. In Britain
however, Brady and Johnson (1981) only found a good agreement
between travel times measured by radioactive tracers with others derived theoretically, at relatively high flows.
Gergov (1971) proposed a method of determining travel time
from t te Chezy formla, utilising hydraulic strea la ex~ressions and requiring relatively unif orta time - space precipitation distribution. Therefore the methcd is usually better for smll
ho~ogeneousbasins. However, he suggested that the inf1 uence of
storm distribution and area of flood formation may have
considerable effects on travel tie values for a streaa with major tributaries; this notion is central to the present study. The difference between tine-cf-peak at two consecutive stations can be attributed directly to •’lo& wave velocity,
and/or to basin and river network controls on generating ~axiltlua runoff. In the former case, a regular relationship to discharge should be expected on which tc base pmdiction. In the latter case, a knowledge of basin geoaorpholgy and of meteorological features are required to understand travel time irregularities.
#hi le engineering analyses of river syste~srevolve around successful prediction of flow, science seeks explanation of flov phenomena, By explaining and understanding the processes involved, more reliable predictions should be provided.
As hasin heteorogeneity increa ses and the likelihood for
complete storm coverage decreases, the strength of the
relationship between preci ita at ion and runoff diminishes, An additional protlera in the Fraser Basin is that precipitation variability in both spatial and temporal frames at the higher levels is inadequately recnitored by the sparse distribution of weather uctations. Therefore sin~leinpnt - output analyses are restricted, In contrast to the hyiholcgic approach, mathematical flood routing tsethcds require input hydrographs to produce dewnstreatft outflow hydrographs. Such models can on1 y be as good as the input data and the validity of the assuilptions inherent
in the methods, Within a basin of the plani~etricand vertical dimensions cf the Fraser, many diverse hydrclogic conditions exist. The basin heteorogenei ty allows highf lows to be generated b y different causes in spatially distinct areas, Therefore the effects of trikutary inputs, and the consequences of transfers through contrasting hydroaeteorologica1 regions, on a mainstream flood wave may be studied for a range of discharges, It should be noted that much precipitation falls as snow in the Fraser
Basin and thus a high percentage of runoff is produced by spring melt, To model this process, detailed information of snowpack conditions and energy inputs over the tasin are required, While snowmelt p~oducesa general rise in river level, rainfall is typically associated with a flood wave, Therefore, it should be emphasised that only ~eakscaused by rainfall will be used in an analysis of travel tiiies. for a small, simple channel, a relaticnship between travel time and discharge kight be expected, as described by Linsley et ' a1 (1958). However, given the different generating processes operating at any particular ti= in the large, coaplex Prasef Basin, it is reasonable to suggest that for a specific event, flow in the rain channel will not behave in a simple mathematically defined Banner, Hornover, travel tire will be in•’fuenced by the contrasting hydrometeorclogica 1 features of its tributaries. Thus it is suggested that the mcst significant variable in peak timing is a function of relative overland distances between sources and leain channels, That is, the time of concentration f cr each sptial distribution of precipitation,
A mod~lbased on time-area considerations is develc~edin this study to simulate a series of contrasting inputs, in order to increase our understanding of the relative imrortance of the main tributari~sand their effects upon aainstreaa hydr cgra ~hs
(figure 1.3). Data for real events were obtained from continuous recording gauge stations operated by the Water Survey of Canada on the Frasfr River. This involved a detailed analysis of the recorder charts to obtain ties and discharges of river flow on an hourly basis, together with an interpretation of meteorological conditions. Real hydrographs, in certain cases, exhibit characteristics that can be interpreted by the model,
Therefore a series of hydrographs reflect the im~ortant tributaries for an event, and can be used to infer the region of precipitation source. This in turn can ke verified by
meteorclogical data, allowing a reclassification of events by source area of precipitation,
The main cbjective of this study is to laodel Fraser River hydrographs using the time-area concepts of Clark (1945) and
Muskingnetl flood routing. The model hydrographs are then used as an aid to the ioter~retatioaof peak flow travel time irregularities bet ween gauging stations. Within this central theme, there are several secondary objectives,
1. To exaraine the ways in which tributary inputs affec-t main channel flow volu~aesusing simple tiae-area concepts.
2. To comFare Fraser River hydrographs with hydrographs from TIME AREA MODn
Basin divided by equi-distant isochrones and areas between them measured I - I Areas weighted (dependent on mode) and a 1 I series of time-area discharge diagrams I I produced for subbasins I I I 2nd subbasin nth subbasin input input
1 1st subbasin 1 +hydrograph
I I- - Fraser river 2nd subbasin I hydrograph hydrograph I REAL EVENTS I I I Fraser river nth subbasin hydrograph at I leve1 I
etc. recorder
discharge
M1 Muskingum flood routing Peak time Peak time -assuming pure Q Q translation plus storage at the outlet
M2 Muskingum flood routing -assuming storage QUALITATIVE included along the channel COMPARISON the time-area mcdel and identify characteristics attributable to loca lised storm inputs,
3. lo assess the degree to which peak travel time is related to
discharge in the manner suggested by Linsley et a1 (1949).
4. To deterlnine if time differences between peaks at successive
mainstream stations result ~redominatelyf row flood wave
transla tion or the int€grated effect of geomorphic controls on runoff.
These objectives will be pursued in accordance with the
f ollcwing format.
This study is arranged in five cha~ters.Chapter 2 - describes precipitation and runoff, based on a review of the
pertinent hydrologic characteristics of the Praser Basin. The
third chapter introduces the basic time-area ~odelof the Fraser '
Basin, its variations and irttplications for tributary
contributions. In the fight of this, Chapter 4 exaaines real
peak events on the Fraser River. Conclusions drawn front the
above are presented in the final chapter together with a
discussion cf the illfpurtant controls on time-of-peak and the use
of the timearea model for inter~retingflood peak "travel - timen. The work is concluded with a discussion of several poten tially use•’ul research directions snggested by the present results. XI, Physical Enwironment of tbe Fraser Basil
--2.1 PhvsicaL C__haracterist& of the Xraser Basin above Hope
The Fraser Basin above Rope drains approximtelp one quarter of south - central Eritish Columbia. This 218,000kmaarea ex tends from the Dnited States border at 49O north, to 5fPnort h, and it is bounded to the east by the Rocky Mountain divide and to the west by the Coast Hauntains. The elevation range is quite striking, for ~xaaple, ninety ~ercentof the basin is higher than Prince George 1665 metres above sea level (a.s.1)) , and two percent lies at elevations higher than 2400 metres a ,s. 1,
(Bruce, 1964) [figure 2.1)- Prom Red Pass to Hope, the fraser river is approximately 1200kn long, and flows through regions with diverse relief, clinsate and vegetation,
2 .I .I, Physiography
Pbysiogra~hicregions are identified by similarities of relief and lithology, arid fairly uniform land cover; therbp unif yirig the controls on hydrological processes. Physiographic differentia tion can be attributed to the evolution of the landscape at several scales, Ryder (198 1) recogn ised three distinct temporal and spatial scales responsible for the FIGURE 2.1 Elevation of the Fraser Basin
8 * kilometres geolsor~holcgyof the southern part of the Coast Hountains of
Britis h Columbia. The aldest and most extensive landf orns were produ cfd by tectonic activity and subaeria1 denudation during the Tertiary. Subsequent landforms developed more locally witbin this framework, reflecting differences in climate and relief. During the Pleistocene, the existing laadforms were modified by the effects of continenta 1 glaciation, Landscape details have been mcdif ied locally since t te last extensive ice-cover
(approximately 10,000 years 3. P. ) and therefore the landscape today is a composite form ~roducedat all scales. Reduced glaciers still exist in the highest parts of the kasin, but present trends of advance and retreat are contradictory (5 laymaker and Wacpherson, 1977). Most glaciers are now retreating, but a few show signs of advance, especially in tbe Coast Mcuntains. Generally, ablation is occurring more rapidly in the Rocky Rcuntains than the Coast Hountains
(Slaym aker , 19 7 2a) ,
The physiographic regions of British Columbia were definitively described by Holland (1964). Eight of his 18 regions are represented in the study area (figure 2.2) and the pertinent features of each region are summarised in table 2. 1. Physiographic regions are clearly apparent in regionalisation a•’ hyd~olireteorologicalfeatures as will be shown later. FIGURE 2.2 Physiographic Regions of the Fraser Basin
-KEY: A =Coast Mountains
Ci= Northern Interior Plateau Cii= Sout hern Interior Plateau Di= Columbia Mountains Cariboo range Dii=Columbia Mountains Monashee range E =Rocky Mountain Trench 0 50 100 150 F =Rocky Mountains kilometres
32 i h 0a3 d E aagad; 5u . . U rl c a5 071 C U d aJ cd 0 oarnu)rnG u kUSd aU-4 U 9) 0 orl
3 il-d 4aJm k-e * 2, 1-2 Basin Diaens ions a nd conf iguration
The absolutf size and shape cf the basin govern the distance runoff Bust travel to the mainstream, and resistance to flow controls velocity. These parameters are genera lly accepted as inflencing time-of-~eak and steepness of a flood hydrograph,
Several studies have attempted to define the importance of basin size and shape to runoff, for example Renard and Kefpel, 1956;
Pilgrin et al, 1982; and Alexander, 1972, Alexander also investigated the relationship between area aad tiae of concentration for a basin, and his results COK~~SFO~~well with
Linslep et a1 (1958) and Hoyt and Langbein (1955). The Fraser Easin consists of several contrasting ~egions,and because the relationship between basin area and runoff, should be examined in areas of similar climate and physiography, each sub-basin should ke treated separately.
Pilgrim et al (1982) found a correlation between basin size and the geo~ur~holcgicalvariables describing its physical f om,
However, basin shape may influence the strength of this relaticnship. Rnrphey and his coworkers f1977) fomd a coabination of basin shape and size to he one of the best gecmor~hicpredictors of hydr cyra ~h fea tures in the southwest
United States. Unf ortunately, it is difficult to quantify this highly irregular and markedly variable parameter, The effects of basin shape upon the timing of a flood peak are only qualitatively understood, Bell and Vorst (1 981) suggest that shape is of ~ostuse in "between basinH studies and in multi-variate analyses where it is necessary to express the coabined effects of many paraaters. This quality is used in time-area studies where shape and size are the most important de~~riptorsof each subbasin.
The general geometric sha~ecf small watersheds is between ovaid and pear shape (Gray, 1961) but in the Fraser Basin, subbasins are rarely of the classic form. The ideal pear-shaped basin is restricted to small or first order tributaries like the
Nahatlatch. The deformation and crenulaticn of the basin p~rintetorreflects locations of small tributaries within the basin (figure 2.3) . As basin size increases, shape departs from the ideal, The Chilcotin and Quesnel basins for exaaple, are broadest at their headwaters, Elongated basins are tuostly large, for example the Fraser River to Hansard, the tiorth Thompson
(excluding the Clearwater) and the Stuart basin, but small tasins like Williams Lake river, are also represented in this class {table 2.2). Hovever, the shape variations perceived are ' dependent upn the scale of exa sir;a tion.
The overall shape of the Fraser Basin is complicated by the sharp Lend in the Fraser River near Prince George. This causes the north-east region of the basin to be folded back upon itself, and ri ver length [excluding aea ndering) then exceeds the length dirension of the basin, Therefore, runoff is in•’luenced by tasin shape, not only because the vhole basin is effectively elongated, but also because irregularly shaped tributary basins produce non-synchrcnised inputs to the main streain. FIGURE 2.3 Subbasin locations and shapes
kilomet res
36 ----'Iable 2,2 Shape characteristics f *let ted subbasins
Shape Size Tributary Region sq. km of 1 Pear Nahatlatch Fraser Baker Cr, Praser
Offset- Bridge Praser Coast ,Yl tns Pear Split Pear P ra ser I Square Clearuater N. ThompsonI Columbia il tns Eroad- C hilcot in Praser headva terr Q uesn el Fraser Naz ko Hest Road
E longa ted Praser to Colmbia ntns Hansard A dams S.Thoapson Columbia atas N, Thompson Thompson Cof rn bia fltns S taar t Necha ko NmZsP* Pilliams-Lake Fraser H.1 .P. Pillow f raser hI.1.P.
note: N,I,P, is Northern Interior Plateau S,I, P, is Southern Interior Plateau
In a rsisrilar manner, the density of tributary streaas determines runcf f speed. Chanaef spacing, or drainage density1 develo~sin rezgonsf to mean annual ~recipitationand influences the outflow of precipitation excess, Hence, drainage density is intrinsic is the time of concentration after a storm and in the --I------1 term coined by Borton (1945) to describe the ratio of total length of streams within a basin to total basin area, time taken to travel through a basin to the mainstream, A high drainage density allows faster reaoval of surface runoff and a corresponding peak discharge increase and lag-time decrease.
Gregory and ilalling (1968) suggested that the dynamic nature of drainage density, that is, its ability to expand and contract dependent cn preci~itation conditions, should be included in studies wherever possible.
The problem of deter mining drainage densit y are n nmerous and well-docnnented (HcCoy, 1971 ; Gardiner, 1979; and Richards,l979). Carlston and Langbein (1960) recsgnised that drainage density is the reciprocal of the mean orthogonal dista ace be tween channels, Theref ore,
Drainage Density = 1.4 14 4 L (1)
where N is the number of intersections between a randomly orientated sampling net L is the total length of sam~linglines,
Mark (1974) examined the theory and empirical evidence, including samples from southern Eritish Columbia, and concluded that equation (2) was more applicable,
Drainage Density = 1.571 & L
Drainage density within the Praser Basin was estimated for this study using Xark's 11974) method, Sa~pleswere taken fron a
1: 1,000,000 scale map compatible with the time-area model, for each of the five h ydroaeteorological regions (table 2.3). lable 2.3 Praser Basin drainaqe dewit_i_e_s ------we --- -- Region Drainage density (kWkm')
Southern Interior Plateau 0.15 Northern Interior Plateau 0, 16 Eountains - Cariboo Range 0. 18 flountains - Eionashee Hange 0-18 Mountains - Coast 0.19
At this scale, the differences between regions are small, but nevertheless reflect a reasonable pattern, These figures may be interpreted in ccnjunc tion bith table 2.1, The Coast Mountaios have the highest drainage density, despite being saapled on the
leeward side, They also have the highest discharge intensity, Drainase densities for the tuo eastern mountain saa~lesarc! only slightly lower, as are tkeir discharge intensities. Together, these mcuntain ranges cover 20.5% of the f raser Basin. About 73% of the basin lies in the Interior Plateau which has a very law discharge intensity and numerous lakes, At the scale of
1:1,000,000 the drainage density measure does not reflect this
contrast, This is ~cssiblydue in part to the inclusion of all intermittent streams, because it is assumed 'that the whole basin contributes to high flow conditions. However, the dynamic nature of the streaaa network and the incorporation of lakes into the drainage density index need to be examined further, These
resultz represent t be seso-scale of drainage densities (Gregory and Gardiner, 1975) b~causfthey reflect both Bean annual pr ecipitat ion and litholog y/topography. Gardiner (1 979) noted
that biases introduced by scale and location are still probable, The value of the drainage density index is widely
acclaimed, but Black (1970) and Dingaan (1978) indicafx? that it
may not be sensitive e~oughto indicate runoff behaviour. Despite the problems, drainage density remains the most I significant measurement of drainage basin ator~h010gy (Richards,
1979) and it is a useful integrative index reflecting physiography, soil developnaent and vegetation. fiuggedness ineasures the cornkination of drainage density and maximum ref ief and therefore ex yresses slopes within a basin
(Flelton, 1957)- Black (1970) shoved steeper slopes result in
faster runoff, shorter tiae of concentrat ion and higher maximuat
flows, In the Praser Easin, differences between the drainage
- density indices for the Interior and the mountains would be increased by the ruggedness measure, Ruggedness is also
interrelated with increased amounts of precipitation received in areas of higher relief. --2-2 Heteorological Qaditions
Precipitation and temperature are both highly spatially
variable at any time in the Fraser Basin, The hydrolcgy of the
basin is further influenced by the interaction of precipitation
and temperature in winter and their effects upon snow
distribution.
2, 2. 1 Precipitation
Host precipitation in the Fraser Basin is frontal in
% origin, bringing wides~readpreci~itation especia fly in winter, - Orographic effects teed to increase the intensity of frcctal precipitation by reducing the speed of de~ressionsystem movement. In su~~r,frontal activity is weak and less frequent,
but Walker (1961) found a large proportion of summer
precipitation still falls when fronts are present (table 2.4)-
Jan Apr Jul Oct
Vancouver 9 9 83 92 9U Reve fstoke 98 80 48 88 Prince George 100 75 U 1 95
After Walker(1951) Boist air predcminately approaches t he Fraser Basin from the southwest, and thus perpndicularly to the Coast flountains resulting in high precipitation on the windward slopes and aridity to the lee side (figure 2.4)- Hoisture is reduced for a considerable dista ace dovnuind of the barrier in Washington and Oregcn (Schern~rfiorn, 1969) . This is also apparent in the Fraser Basin but the aridity of the Interior Plateau is interupted by the Coluabia Hountains where precipitation is induced again,
The irregularity cf a barrier is reflected in the lee side precipitation pattern- In the northern Interior Plateau, for exatsple, generally higher precipitation is attributed to uplift of iaoist air that has ~assedover the lower section of the Coast Mountains Letween 53'~ and 5S01? (Ingledov, 19b9) . Also, gaps in the Coast Wountains, allow moist air to penetrate into the tiechako Valley (Wallis, 1963)-
P recipitation usually increases with height (Barry and
Chorley, 1974) but Riehl (1965) shoved a steepr precipitation gradient on the leeward side of Pacific Northwest motlntains. In the Fraser Basin, a ~'spilloverueffect Pay occur and the
Nechakc, Lillooet and Bridge subbasins, for example, have steep pr~cip itat ion y radients to @axiia urn values at t he Coast Eou ntain boundary, The Chilcotin basin is an exception because it does not drain the high precipitation areas west of the Coast
Rountains, Otherwise, the lee effect is masked only where convection precipitat icn is irttportant. FIGURE 2.4 Average precipitation distribution in the Fraser Basin
# a kilometres ISOHYETS in mm (after Fariey, 1979) Walker (196 1) generalised the levels of l~axiaum precipitation, but noted that terrain differences in British colutnbia produced many local variations. The value of such
generalisations is questioned by Glennie (1963) and March and
coworkers ( 1979) . kilson, Vaides and Rodriguez-Iturbe (1979) examined the reliability cf models subject to spatial variations
cf precipitation. They found the errors in a predicted hydrograph were greater for short, intense or localised storas than for thse of frontal origin. 1n winter, amounts of ~recipitationover the whole basin can be related to direction of upper air flow, This is not the
case in suEtrer when precipitation Bay be more localis&,
Orographic effects, f cr exaaple, may trigger convective instability and convective thunderstoras which a re associated
with a variety cf flow directions and amounts received (tialker,
1961). Also, the passage of a cold low in suamnter can in duce
local ~recipitation. Hage (reported in Walker, 196 1) deduced that cold lcws cause intense uplift and thus intense local
precipitation within British Colulabia. The resulting runoft from such events aay be of local im~ortance,but F~O~UC~only a limited resFonse in the mainstream Praser. The mcre localised
nature of storms helps ex plain precipitation variability in the
Interior.
The annual pattern of precipitation distribution in the
Fraser Basin is greatly in•’luencfd by the ~ountainousria and
topography within the basin. However, the use of mean annual preci Fitation tigures is coatplicated when examining sin gle events. This is because maximu& precipitaticn is partly governed by the degree tc which contrasting air masses penetrate the
tasin and therefore it does not occur everywhere at the same t time (gallis, 1963)- The resulting precipitation distribution within the Fraser Basin is therefore highly variable. Unfortunately, climate stations lccated predoiuinately in river
F valleys and the more accessible areas, provide aa insufficient
network for a thorough evaluation [figure 2.4)-
2. 2.2 Temperature
Te~peraturesin the Fraser Easin a re primarily modified by
- the distribution of notmtain chains, and the effects of continentality. Although, radiation receipt is highly variable
in rugged topography, teaperatures generally vary with altitude within the Iirasfr Basin. The direction of air flow influences
seasonal values of daily ntaximua and siniraua tem ~eratures;an
effect that is especially noticeable in winte~when north and northeast winds lover the temperature. Easterly continental
winds in suamaer and southerly ~aritiaewinds in the winter can
increase temperatures, These are very genera 1 trends, hooever and micro-clisat ic effects cause ~uchvariabif itg,
In the absence of cli~atestation data, average lapse
rates, typically about 6.~~~/1000metres are used to interpolate
tea ~eraturcs between staticns. The presence of an inversion
cofa~licatestheir use however, because large temperature changes FIGURE 2.5 Locations of climate and gauging stations in the Fraser Basin
oprecipitation only k i lometres @ (Walker, 1961)- This is relevant for evaluating potential
I snowselt, i
2. 2.3 Snowfall and its influences on Praser Basin runoff
During the winter months, snou covers the higher elevations of the mountainous Praser Basin f Lank$ and remains as snowpack
until tem~eraturesrise sufficiently to allow ael t and
subsequent runcff. The mountains of the Cariboo and Coast
Wountains receive most of their snowfall in spring, but the
remainder of the basin has a winter snow r~axi~tlua[Wallis, 1963). Snow accuaulation tends to correlate with elevation but
scow depth at any point de~endson the afllount of drifting. The
loner limit of snowcover, or the snowline, is dynautic and constantly changing through winter, Snonline fluctuations affect the amount and timing of delayed runoff and therefore storage
time is highly variable and difficult to evaluate,
As winter progresses, the snowpack compacts under its own weight and looses soae water directly to the atmosphere by
evaporation or subliaation. The nature of the snow varies and
theref ore potential runoff is best aeasured by its water
equivalent. Loi jens (1972) found elevation and slope acccounted for most variance of annual maximum snow-water equivalent in Eanff National Park, Heavy basin-wide snow~teltin the Fraser Basin is often
triggered by the incursion of varm upper air flows from the southwest. Melt begins first in the south of the basin and then in successively more northern areas as arctic air is displaced by warmer maritme air, To the lee of the Cariboo mountains, significant localised ~eltingcan be induced by transverse upper winds ~roducinga Chinook effect (Pollack and Bellows, 1972). On a diurnal basis, the amount of melting depends on the net heat exchange b~tweenthe snowpack and its environment. Snowlselt during rainfall is a dominant hydrolcgic process in western Oregon (Harr, 1981) but further north within the Praser Basin it is usually liar ited to the Warner southwest [Wall is, 1963) and the lowr elevations (Woo and Slayntaker, 1975). The timing and magnitude of the freshet is of great concern to the residents of the Praser Basin, especially in the populcus area below Hope, Glennie (1963) ~e~o~tedan old wives * tale that a high flood on the Fraser is pceceeded by a fine, cold Indian
Sulataer the previous year. The temperature and water content of the soil in the previous October can influence the available
~oisturein the spring, and thus freshet size. On the other hand, Bruce (1 964) suggested the sequence of tern ~eraturesf rotll April to June was the critical factor in the generation of a f locd. The majority of snowtaelt runoff originates in the
Interior Plateau where snowfall is moderate and winter
temperatures often fall to -35-C (Quick, 1965)- In the north-east of the basin, as much as 80 percent of annual precipitation falls as snow producing the bulk of runoff in spring [En gineer ing Division, 1972) . Wayleu and Woo (1983) examined highf lows produced by snowaelt in three diverse subbasins of the Fraser, In a basin representing the sout fiern f nterior Plateau and in a subalpine basin cf the Ronashee mountains, the mean date of peak flows occurs near the end of May. In the basin representative of the Columtia mountains the date was almost a rnontb later.
Snowcover is so beteorogenous that only estimates can be made of its extent, and the artlonnt of melt at any time, Relationships b~tweensnow cover area and saowaelt runoff differ for each type of geomorphological catchment (Gupta et al, 1982).
Several methods for estimating aelt exist however. For example, tempratme-index methods are considered to kc the best in large, forested basins (Gray, 1970), together with 'phase-routing1 which effectively slows the flou by varying storage constants. The U. B. C. Eraser Basin nodel (secticn 1.2.4) iccr~oratesth~se ideas, In sumiaary, snowmelt varies both tetn~orallpand spatially in the Ffaser Basia. The contribution of meltwater to runoff is
therefor^ very difficult to predict and inpossible to evaluate precisely from ~eteorologicalrecords.
T he above review of meteorofoyica 1 conditions in the fraser
Basin has h jghliqhted regicnal differences and thus each tributary basin of the Fraser has contrasting hydrotaeteorological character ist ics , These a re pre.sen te d iu table 2. 5. Climatic Precipitation max group snow
UFF= alpine even winter- Frascr hu mid spring
Stuart alpine sumaer spring autumn arctic
Nechako hursi d winter srring autumn conti- nental
#.Road su P ser s~ring N/ A
Cuesnel dry and even spring s pring hu mid coat i- nental
Chilcot in dry sumer spring autuisa cont i- nen t a1 Br idge al~ine winter snianter autumn maritime Ncrth alpine winter spring autumn Tho@pson humid E dry con- suamer tinental
Sout k as North %inter spring autuisn Thoat FSOB su QI Ber
T~CSFSU~ alpine winter sprin g sutu~n aaritime G dry summr conti- nental note: spring=8arcb, Apr il, Ray Butu&n=Sep, Oct, Nov adapted froa Wallis (1963) 22 Hvdrome teoroloqical Divisions 2nd g iqhf low Reqionalisa tion
PIany facets of the basin affect the volume and speed of ru ncff gene ration; some change daily, ethers remain more constant. Haps of mean precipitation, mean temperatures, and physiographic divisiops often reveal common divisions which
Waylen (198 1) grouped into hydrometeorologica1 regions [figure
2,6). Physiogra~hicboundaries defined the three mountain zones, while vegetation indicators divided the Interior Plateau,
Slaynaker ( l972a) noted the control of physicgra ~hyupon clinate, veyetatian and hydrology, Annual discharge hyd rographs of Fraser Biver tributaries exhibit corresponding differences in the im~crtanceof seasonal peaks [table 2,6),
Based on cbservations that gauging stations in siailar areas shov corresponding annual discharge patterns, flow data can be regioaalised to aid data transfer to nngauged areas. Soae success in regionalisation has been achieved despite differences in basin character ist ics an4 chance variations
Physiographic S~ring neyion snow itle It ablation I rain I Coast Htns Yes Yes Yes Cascade Htns El Yes - Y es Cascade atns E Yes - - Skeena Pl tns Y es - Pe s C~inecaBtns - - Yes Interior Yes Plateau Columbia 8 tns Y es Eocky Ht as Yes FIGURE 2.6 HydrometeorologicaI Reg ions of the Fraser Basin
kilometres sampling. In British Columbia, Leith (1976) regressed ten variables with mean annual flood, He concluded the method was reasonably effective in large basins, but he was unable to identify important physiographic parameters, Leith used a contputer data Lank containing ~hysiographicand hydrological data for 1 OkaZgrids. Data collection is described by Kreuder
(1979) , but this laborious task is not yet complete. The grid square method was also used in the South Thompson Basin by
Gbedkoff (1 970) tc im~roveseasonal Bean flow estimates by including evaporation and snow course data,
Uaylen (1981) modeled the frequency characteristics of
Praser Basin highf lows. He coatpared results from anaual and partial duration series by using probability distributions to estienate parameters for a regrouping procedure. Para~etervalues were then regressed OB basin and climatic data for each group. Uaylen achieved partial success which he attribut~dto the inccrporation of both spatial and tem~oralmeasures,
Strong regional differences ia the range of highf lows within the Praser Basin have been identified by the studies described atovr. Tte pbysiogca~hicand climatic controls on these variations will also influence daily runoff patterns. The sub-basins mill produce hydrographs reflecting cantrasts in the quantity and tising of stors discharge. This, in turn, is i uportant for Fraser river flood wave translation because inputs may not be synchronised. An understanding of regional differences therefore helps ex &lain peak flow characteristics, 111, Tbe Praser River Pime-Area lode1
3.1 ------In troduction
The model developed in this study was designed to generate hydrograph tiae-of-peak data at four stations on the Fraser
River for varied input conditions, The model is based on a series of time-area histoyraias which provide a series of lagged inflows to a flood routing eyuaticn. The result is an estislation of a ccmplete hydrograph vhich can be ccriipred to real hydrographs, The basic model was produced froa a simple time-area map of the Fraser Basin. Subsequent variations were made to repres~ntmean annual ~recipitaticn, snowmelt and three regional st crms.
--3.2 ---Mode 2~ Basic Hodel
3.2. 1, Description
To construct the time-area nr ap at a scale of 1: 1 ,oao,ooo, dividers were used to lace isochrones equal distances apart along the riwers, The isochrones deliai t areas vithin which rainfall has sensibly equal travel distances to become runoff. A total cf 49 areas were deliait~d,@any being segmented into a number of Fraser tributary basins because of contrasting flow directions (figure 3.1) , The iscchrones were constructed on the basis of equivalent horizontal distance, and therefore water travel time, or velocity through each section can be varied conveniently. On the basis of Water Survey of Canada meter notes, the mean velocity of the Fraser River at Hope was found to be approximately twice that recorded at Upper Praser river stations. Although velocity differences way reflect channel conditions adjacent to the gauge, it was conside red necessary to increase velocities increiaentally below Shelley.
The construction of isochrones allowed a detailed visua 1 exaaination of the Praser Basin streala network. Of ten, subbasin shape dominates the pattern of isochrones, In the Interior Plateau, lover drainage densities a1low a simpler arran geaent of isochrcnes, as in the Uest Road, Chilcotin and Bonaparte basins, In a few aountainous basins such as the acGregor and North Thompson, isochrones are arranged simply, but this contrasts with the niajority of subbasins where topography and stream network complicate the patterns, for exa a~le,the Fraser Basin above Hansard and the western Mechako basin,
Isochrone positions are contrclled more by drainage channel pattern than drainage density, The extent to which small streams affect isochrones depnds on ieap scale and the chosen, horizontal spacing along the channels. The complexity of a time-a rea diagfaa increases v ten neighbcuring st reams flow in opposing directicns, for example the headwater areas of Nechako, FIGURE 3.1 TIME-AREA MAP OF THE FRASER BASIN
kilometres South Tholrtpson and Stuart basins and also the Fraser Basin above
Hansard. A pure, dendritic stream pattern dl1 not displace isochrones significantly from an arc, but drainage density itself may affect the subsequent cafculations. Unfortunately, ne tvork con•’igurat icn and drainage density are too interrelated to allow examination of the quantitative impacts of one alone, Basin drainage density is inherent in time-area modeling because it expresses the relative amount of time that runoff spends in channels rather t ban in athe r, much slower routes.
Theoretically, isochrone spacings shonld be wider where drain age density is high because there, the potential runoff speed is faster (all other tkings being equal). Therefore, a sirttilar drainage density thronghout a basin is preferable for time-area modeling, as discussed in section 2. 1.2,
At the scale of the ti=-area model described here, the inter-regional dif ferfnces in drainage density are not especially high. T her €fore, before giving drainage dens itp more attention in a time-area model, quantitative studies are required to deteraine if it is proportionally Bore important than other topcyra ghicd variables,
After construction of a time-area map, the areas between ad jacent isochrones are measured by pla nit~eter, These areas were used to construct time-area histograms at four points on tile Fraser River, corresponding to Water Survey of Canada continuous recording gauge locations {figure 3,2), At this stage, kasin storage is not included and the diagrams only represent travel a) HANSARD b) SHELLEY
0 110 110
c) TEXAS CREEK d) HOPE
TIME (hours)
FIGURE 3.2 Simple time -area histograms for the Fraser Basin to the gauging stations times / distances,
Hydrographs are produced by applying a Bean value for basin precipitation1 to the whol~watershed, The lagged area - precipitation values are then input to the fluskingurn flood routing procedure, Instantaneous unit hyd rographs for t he same four lccations are shorn in figure 3.3. bihile the resultant hydrographs reflect the overall basin conditions, they do not allcw an interprotation of the relative importance of t he contributing subbasins. Therefore a time-a rea histograa of each tributary was routed to a hypothetical linear reservoir situated at its Praser Diver confluence (figures 3,4), The resultant hydrogra~hkecoaes inflow to the Fraser River and is then routed to the next ata jar confluence or gauging station using ;4 uskingusa coefficients. This allows the effects of natural attenuation to be incorporated if igure 3.5)- Each tributary hydrograph in turn, is added to the fraser River flow at the corresponding time. See figure 1.3, Eeterminati on and sensitivity of Huskingum constants,
As described in section 1.2-3, several methods of determining x and k exist, but all need either input and output hydrcgraphs or field studies to determine fi ydraulic paraaeters.
Each method results in slightly different values and is often based on different initial conditions, The problea remias, which is the most representative? ------lassuaed to be instantaneous {duration = 0 hours), a) HANSARD b) SHELLEY
) TEXAS CREEK
TIME (hours) FIGURE 3.3 Instantaneous unit hydrographs for the Fraser Basin to the gauging stations 6 0 dl -KEY: a) flow from Hansard at Shelley b) other inputs to Shelley
55 d)Quesnel river e) Chilcot in river f) Bridge river g) North Thompson h) South Thompson i) Thompson at Lytton
TIME (hours)
FIGURE 3.4 Hydrographs representing each subbasin
61 n a) at Shelley b) at West Road river r IV)
c) at Quesnel river d) at Chilcotin river
e) at Bridge river f) at Thompson river
(hours)
FIGURE 3.5 Fraser River hydrographs at successive confluences
6 2 and x from output, an d adequate infor rmticn rega rding h pdranlic character istics are not availakle. Therefore, the empirical average of 0-2 was used for x and travel times based on average velccities used for k, The choice of mean values say counteract and balance oatural variations along the Fraser River. Witnout extensive field work, the utility of waccurateyspoint values would he suspect and it is argu~dtheref ore that under these circuenstances, and given the available data, averages for k and x are the appropriate choices, Iheref ore, it uas necessary to exa mine ~ossibfevariations caused by ckanging k and x values. Owerton (1966) found that inflow hydrographs varied for each storei in small catchments and k and x varied likewise, In the present study, k and x Mere considered iadifferent to stora characteristics owing to the large size of the Praser Basin. Overton also exaained the effects of naultiple routings on the prameters and found no significant changes in the routed hydrogra~hwhen k is less than the t im to peak of the input hydrograph, Also, the the of peak of the outflow hfdrogra~hdid not change when x was between 0-0 and 0-5. This is relevant for the Fraser River Time-area model since peak tiaings are of utmost importance in the determination of apparent travel times.
Values of x were varied in ane of the regional modes of the Praser River tittle-area model to identify gossible changes in the results. When tributary tiltlearea inputs ace routed to the Fraser River, all the storage is incorporated at the confluence using x=0,0. Therefore variable x values can be incorporated only when routing on the Fraser River itself, As x was increased from 0.0 to 0.3, peak magnitude also increased (table 3 .I) ,
Fraser River Peak I at Shelley with Shelley at Q uesnef with Quesnel at Thorapson with Thompson at Hope
However, the change appeared insnff icient to change dom inant peaks, and therefore apparent travel times, It is interesting to note that when another tributary is added, peak discharge remains the sarae regardless of the x value. This is because tributary inputs dominate and govern peak time, regardless of
Fraser River discharge, Also, the degree of variati.cn in discharge tends to become slealler toward Hope, I! his is possibly because the hydrograph becorns brcader with each input, and therefore subject to less attenuation than a sharp peak,
Despite small peak discharge changes, time of peak is rarely altered (table 3.2) iaa~lyingthat although the hydrograph my be altered slightly, the time ordinates are preserved. This is of paramount importance to the Fraser River time area model. Praser Biver x value Peak I 0.1 1 0.15 1 0.2 1 0.25 at Shelley with Shelley at Q uesnel with Quesnel at T hompson with Thompson at Hope
The shape of hydrographs produced by each x value are very sispiilar, and the most noticeable effect of x is the degree of attenuation, Shar~input hydrogra~hsare attenuated sost, especially by low values of x. However, once incorporated into the Fraser River flow, th~differences are soen counteracted. Rttenuaticn between tributaries, and thus gauging stations, will be important in deterlining peak volumes, Long distances between tributaries enatle considerable reduction of an upstrea~ peak, In some cases, the effect may be sufficient to allow a smaller input downstream to dominate the overall hydroqra ph a nd therefore affect the tiaing of inaxintua flow, This method jives an ismedia te impression of the relative importance of each tributary input in producing a mainstream flood peak, with obvious ~fa~licationsfor future iucnitoring, 3-2.2. Basic Model Interpretation
The input to Hansard takes the form of an almost regular hydrograph, except for a brad peak from its elongated basin
(figure 3,tca). At Skelley, the shcrter contributing area produces a sharp, symmetrical peak with a tieaebase half that of Hansard (figure 3.4b). When the translated flow from Hansard is added to the Shelley input, the Shelley waters form the dominant peak because they are combined with the Hansard ri-sing limb ffiyure 3 -5a) . The Hansard ~eakbecomes a blip on the Shelley recession liab, Depending on the relative importance of flows froin each subbasin, the tine-to-peak has the potential to change quite considerably (see section 3.6)- The Nechako and Stuart river inputs were included as average values for all versions of the model after a visual exaaination of the recorder charts of the Nechako at Isle Pierre which is relatively near the Fraser confl uence.
The Yest Road tr ibutasy basin is disproportionate1y broader in the oiddle. This produces a very steep and sharp h yd rograph
(figure 3.4~) which drains into the Fraser River before the arrival of tbe Upper Praser (Hansard and Shelley). The two peaks are cf almost equal volume and either the West Road trikutary or the Upper Fraser is ca~ableof altering the balance between peaks, That is, the maximum recorded peak on the Eraser at the
Qest Road confluence may be asscciated with the West Road river alone, the Upper Fraser contribution alone or some combination of botk.
The Quesnel river drains the windward Cariboo mountains and
the eastern Interior Plateau. Its basin is broadest in the upper
reaches hnt it is shorter than the West Road basin (figure
3.4d)- Therefore when the Quesnel is added to the Praser, the
bulk of its discharge arrives in synchrony with the West Road
peak. At this point on the Fraser, the first peak is accentuated
and dominates the scmewhat attenuated second peak f rota the Upper Fraser (figure 3.5~). Hinor inputs fro@ small tributaries can
increase flows ahead of these arain peaks, but may be
insign if ica lrt i r! the owrall h ydrograph,
The next tributary of significance is the Chilcotin.
Draining the vestern edge of the Coast Rountains, the basin is
also widest at its headwaters. Basic titae-area considerations
produce a Rreversedn input hydrograph {figure 3. 4e) whose main
input is delayed, Despite the delay, its waters are a supplementt
to the rising limb cf the first Fraser peak (tigure 3,Sd)
because of the travel tiate f rols the Quesnel tributary, However,
the desertified nature of the Chilcotin basin would considerably
alter its real contribution and tiaing, In the basic model, it
is suggested that the cotabina tian with the nnderestimated
Quesnel allows a reasonable simulation of the whole basin.
The Bridge basin is also widest near its headwaters (figure 3.4f) , but its relative shortness allows most of the flow to enter the Fraser before the peak flows described above [figure 3,Se). Beca use the headwaters are glacially-fed, the actual amount oi input is difficult to determine with a time-area method. The generally high precipitation received in the basin should negate any reduced flow fro@the glacial areas, for the lasic aodel-
The gauging station at Texas Creek which is a short dista ace below the Bridge conf hence, receives a three- peaked flow according to the model- This is fewer peaks than were deterained by routing the whole basin timearea inputs to Texas
Creek, Attenuation bouever, wrges inputs considerably. The absolute timing of ~axiraumpeak is flexible within a few hours but different ratios cf in~utscould alter the peak of im~ortanceand consequently titee-to-peak data.
The North Thompson river has a broad headwater catchaent draining the southern Cariboo, The upper reaches consist of lakes draining icefields, and sc the real unit hydrograph frotir this basin roba ably does not reflect the broadness, The length of the basin causes the time-of-peak to be lagged [figure 3.4~3). The South Thompson river drains the Honashee Mountains and its basin is also broadest at the headwaters but much shorter [figure 3.5%)- The South Thoapson peak appears as a blip on the lorth Thompson river hydrogra ph rising limb at their confluence.
Lakes are of such importanc~in t he Tbolrt~scnbasin, but the degree to which they reduce and delay peaks can not be assessed easily and incorporated within the simple principles of the reodel. Below the junction of the North and South Thompson rivers, the Eonaparte to the north and the Wicola to the south supply the bulk of local flcws. Therefore the flow added by the whole Thompson basin to the Fraser River has two peaks arriving laarginally before the paks created in the Bridge catchment and middle Fraser area respectively. The Thompson river supplies a major input to the fraser,
This causes backwater effects, which as noted by Clark (l9&5), alter the storage relationships in th at reach, T keoretica lly, the PI usking us x component should be changed to accoaaodate backwater, but the average value of 0-2 is assumed throughout the ntodel in the absence of contrary empirical evidence.
The first Thompson peak wdrownsfl the Fraser and the Bridge creates a small blip afterwards. The tining of the arrival of flow fro& the Eridge basin therrefore may be critical if flooding is imminent. The second Thompson ~eaksupplements the main Fraser flow. Again, tising nay be critical, After these aain peaks, the steep falling limb of the hydrograph is interupted by a plateau caused by attenuated Upper Fraser flow,
Ey the time the flood wave has reached the Hope station, the first pak has attenuated considerably and acts as a 18warningfl high before the aain peak. Ces~itethe relatively low level of the U~prPras~r waters, its rcle in prolonging high level conditions could ke problematic in terms of overbank flooding. ---3.3 --Hode z;Rainfall Simulaticn
3.3. 1, Description
In many real situations, a ~odelas descriSed in the previous secticn, is inadequate, Therefore, the first adaptation
of the model incorporates the spatial variation of precipitation. !feteorological data show an uneven distribution of amounts and ti~ingof precipitation for wcst events, Rean annual pfecipitaticn values were used to veight ~reci~itation
amounts received by each isochrone-deliai tea area, The resultant hydrcgra ~h enables an interpretation of the rela tive tributary addit ions, by acccunting for the retness or dryness of each
subkasin, As such, the model remains relatively crude, The
contributions of Interior Plateau tributaries are possibly still
overestimated because the Bean annual precipitation figures represent total precipitation, not the proportion froa a given precipitation event, This is noteworthy because aost of the
sumiuer precipitation in the Interior Plateau is fro^ local
convect iona 1 storms, while elsewhere, f ronta 1 precipitation is
aost important. a ntultitude of variations are possible, but the aim of this
inode was to simulate kasic hydronmteorulogical differences.
Regions of 'highflcn, deliaited on the basis of mean annual flood series siteilarity, have been siicwn to correspond closely to Bean
annual precipitation isohyets (Haylea, 1981) , feigh ting in terms of mean annual ~recipitationis therefore relevant to man annual flood volulaes and consequently, runoff yield, Also,
vegetation responds to mea n annual ~recipitationand theref ore, I runoff coefficients fcr a large area will be related to amount
of precipitation in a secondary and less direct manner. A
logical extension of this ~cdewould be to assign precipitation
contributions to the three seasons of interest: spring, sunitler
and autumn,
3 -3.2. Interpretation
The main features illustrated by this simulation were not
significantly different fror the basic model. When all the area
above She1ley contributes to the Fraser River flow, the tiae of
the peak reflects maximum in•’low below Hansard (figure3 -6f), The
Hansard basin produces a larger runoff voluae f roa increased
precipitation in the mountains (figure 3.6e) and forms a lsore
pronounced seccnd pak in the flow at Shelley, The West Road
tributary provid~sa lower peak vclume preceeding the IJpper
Fraser ffous, Saall changes of the West Road river input volume were simulated. Although minor effects were visible on the
tliainstream Praser, attenuation ha r lsade the changes practically insignificant rhen the flow arrives at Hope.
The height order of the first and second fraser River peaks
are reversed by high runoft from the Quesnel basin, An
irregularly shaped input hydr cgra ~h is contributed from the arid GAUG l NG STAT ION NAME: Hansard Shelley Texas Creek Hope
b) c) 3 a) 2 m
0 A .A
TIME (hours) KEY TO CONTRIBUTING SUBBASINS: h=Hansard q = Quesnel n= North Thompson s= Shelley c=Chilcot in s= South Thompson w=West Road b= Bridge t=Thompson FIGURE 3.6 Comparative hydrographs for all modes at gauging stat ions Chilcotin river basin kccausc the driest region borders the
Frasrr and therefore most of its runoff arrives late. The Chilcotin addition coincides with the Quesnel rising limb and produces a tvin-pronged initial peak cn the Praser. The balance
Let ween dominating pakz appears very delicate. The ref ore, the recording of an instantaneous peak for example, could be altered by several hours depending on storm characteristics.
High temperatures and the lack of precipitation in the
Chilcotin basin and the area around the Praser / Tholtrpscn confluence cause secondary effects. Evaporation and vat er withdrawals for irrigation Bay cause some reduction of river discharge. Occasionally, water also will be required to fight fcrest fires in this very hot, dry region.
The Bridge river discharges into the P raser River before the arrival of upstream ~eaks,despite having its highest runoff delayed, This produces a multi-peaked hydrograph at Texas Creek (figure 3,6g) , In the Thotapson basin, considerable contrasts exist between high volume runoff front the aountainons headwaters and barely significant runoff bel~wKamloops. The North Tho~pson river input reflects an increased supply from the aountains, but
the South Thompson input is still mare sensitive to the effects of basin shape. Combined, they produce one large, steep-lirabed peak,
At the Thompson-Fraser confluence the inputs seem well
spnchrcnised: iaplying that the high runoff production areas lie sirsila r travel times away iu both basins, The combination of the Bridge and lower Thompson flows produce a minor first peak. The
main peak is produced by the UFpr Thompson, Quesnel and West
Road together. 'ihe volume and peak timing of the North Thompson river are of major significance in this mode, Because it drains higher elevations however, it is feasible to suggest some runoff
Ray be held as snow occasionally. In this case, the peak may be reduced or delayed or a co~binationof toth. At Hope, one major peak is clear and compared with the basic model, the Upper
Fraser flow is more substantial (figure 3,6h) ,
--3.4 --Mode ---111: Snownelt Ada~taticn
3 4 1 Description
The problea of evaluating snowrselt was discussed in chapter two. Clearly, any sodel using meteorological inpnts can only hope to reasonably estiaate the runoff component due to snoumeft, Snowaelt in the Praser Basin is of prime importance in producing the annual peak flow and theref ore, it should not be neglected, Bucb additicnal information vould be necessa ry to
analyse snowselt but this is incompatible with the time-a rea sodel developed in this study.
Only one case of snowmelt is therefore modeled here. The appropriate scenario suggests that cold temperatures prevail at the time of a storm, resulting in snow only at the higher elevations, Temperatures rise after the storm enabling total
74 melt of the new snow. In this mode, the snowmelt runoff is
1agged accordingly and distributed over a twenty-four hour period to simulate a diurnal melting regime, Yoo and Slaymaker
(1975) found diurnal runoff cycles to be pronounced in a small catchment in the Southern Coastal fiountains of British Ccfumbia.
Pl ode I11 is tberefore concerned with minor delays caused by snowfall rather than general basin melt. This phenomenon is more likely to occur at either end of the winter season, Variations were considered but would roba ably not justifiably it~provethe nodel. Examples include a weighted increase in snow with elevation on an already weighted precipitation index, to account for the percentage of sncv to rain; or routing some percentage of the runoff via greater storages and with lcnger trav~ftimes,
The summary cf snow survey measurements from 1935 to 1975
(British Columbia Hater Investigatios Branch, 1975) was inspected, but no easily definable pattern of snow (water equivalent) distribution could te determined, Ronitoring amounts of snowfall is obviously a great advantage. A visual analysis of river gauge recorder charts, revealed that a tex thook h ydrograph shape only existed in late summer and autumn especially at Rope and Texas Creek, This illustrates that snowmelt is incrementing flaw volume in the early part of the year. The events later ia the year therefore, allow an exanination of basin processes without snowmelt coeaplica tioas. One of the salient differences to mode I is the sensitivity of the rela tively small basin above Hansard to diurnal melt fluctuations (tigure 3.6i). As voluees becoae higher downstream, the diurnal variation becones negligible. The effect at Shelley is nct so erratic because simulated snowmelt is less from the generally lcwer altitude drainage area (latitode effects were ignored). T he coabination of Raasard and Shelley reflects the time of peak frora the area contributing to Shelley, but hecause of decreased vcluare in the Hansard rising limb, the Shelley peak occurs after the maxi~u~at Hansard [figure 3.6-j). Snowmelt in the region above Hansard produces a secondary, seal1 rise on the falling lisb.
The Rest Road river: input shows very little difference to previous modes. Snowmelt arrives rela ti velp late and is absorbed into the first peak from the Upper fraser, Substantial snounelt also arrives late from the Qnesnel basin and joins the second peak flow. 0 bviously the inter~layof factors sould determine the dcainant peak and thus, apparent travel time of peaks ktw~entwo minst ream stations. Attenuation merges the peaks more closely near the Chilcotin river confluence. The C hilcotin adds mcst input late because its highest runoff is frorrr the extreme west and also subject to small snowmelt delay. ffouever, the resultant input jcins the Fraser river before the upstream ~eaks. When the Chilcotin peak was varied in terms of arrival time, substantial differences occurred in the Fraser to the extent of a ltef ing a hy~otheticalinstantaneous peak. The Bridge river input coincides with the early Chilcotin peak, Diurnal effects again seem to be important in this basin. The h ydrograph of the Fraser at Texas Creek is dominated by highf low contributions from the Quesnel basin If igure 3, Sk), The snowmelt mode causes large changes in the Thompson input due to initial storage and subseguent release of snowmelt,
The input has an extended timebase and a rtiuch lover peak, but it sti 11 coincides vit h t be first peak on the Fraser, #hen all flows are suatlmed at this point, the snovntelt acts to
"f ill-in-the-lowsm in the rainfall mode h ydrograph, Theref ore at
AoFe, the h ydrograph shows one major rise and fall, with a small recession limb plateau created by Dpper Fraser runoff (figure
3-61). The hydrograph has a broader peak with the total volu~e distributed more evenly than in previous modes.
From t be three aodes described above, it is apFarent that the highest peak at any pcint on the Fraser River usually
CUE~~SFU~~Sto a particular in~utupstrea~. The hydrograph at
Hope is the summation of all basin input: attenuated and summed.
Therefore, to detersine true peak travel time, it is necessary to identify the input to which the Bcpe peak corresponds. #hen only daily data are available, or the concern is with maximm discharge, aa analysis of peak travel times will be unrealistic for the hole basin, --3.5 --nodes gV,V,VI= Regional &aptions In a catchment with the size and hydrometeorological variety of the Fraser Basin, it is unlikely that precipitation is received everywhere and commences at the same time. Therefore, three stcrm centres for smaller areas were s iatulated, utilising ueighted precipitation values,
!!lo_! was concentrated on the Rocky Hountain Trench to examine attenuation and peak travel times when unaffected by inputs between Hansard and Hope. The broad hydrogra~hwas on1 y slightly attenuated, but compared with the aorrea 1 volunes at
Hope, its arrival nay not be noticeable (figures 3.61s to 3.6~). --IY ade 1 deposited precipitation on the vest (windward) side of the Cariboo range. A small area upstream of Hansard, supplied a short, sharp, low peaked input [figure 3,6q), Yhen a small input from above Shelley is added to the Hansard flow, its peak dominates, In this instance, time-of-peak at Shelley is the same as at Hansard if igure 3. 6r), Therefore, apparent flood wave travel time is zerc hoors, A large, steep peaked input from the
Quesnel basin joins the Fraser before the Upper Praser flow and forms the dominant peak, The North Thompson river basin produces a sharp, but broad based peak, Although it is greatly attenuated at the Prasrfr confluence, its volome is still significant and its arrival coincides with the Qnesnel flov [figure 3.6s). The
Upper Fraser input is now lost within the recession li~band one large, broad peak is observed at Hope (figure 3.6t). Because the ThcItI~son river flows doninate, an analysis of travel times between Texas Creek and Hope would be incongruous, ---Bode --VI sieulated a storm that was a supposed spill-over effect from the Coast Rountains, providing a series of inputs
between Shelley and Texas Creek (figures 3.6~to 3.6~).The West
Road river headwaters develop a very peaked input hydrogra ph which is almost completely attenuated on entering the Fraser,
The Chilcotin basin also generates a steep geak whose arrival at the Praser coincides with the West Road river input, producing a wide peak. The area of the Bridge basin affected by the storm creates substantial runoff. Its peak occurs before the arrival of upstream flcw (figu~3.6~) but the relative balance with the
second peak is probab fy governed by local sturn characteristics,
It is feasible that a storm moving from the northwest would
reduce the separaticn between the two peaks. Conversely, a storrtt approaching fros the southwest may separate them. Hovever, storm nrovemeat is generally fast in relation to runoff speeds and
hydrograph shape Bay not alter drastically. It is suggested that timing differences are substantial only when precipit at ion events occur in close succession.
The hydrogra~hsfro@ regional siraulations [modes IV,V,VI) seen LESS sensitive to changes in tributary input timing than
when the whole basin produces runoff. However, it is possible to envisage many scenarios depending on relative interactions. 3.6 Discussion pf generated datp
First, it should be restated that this model is dependent
"totally on the concept of isochrcnes and consistent proportions F j of runcff generation throughout the basin. Time-area concepts were tested in six modes as summarised in table 3.3.
Table 3.3, Nodel variations, --- --a------FIode no. flodel description
I basic unadjusted model of whole basin
areas weigh ted by Bean annual precipitat ion index for whole basin
sno wfall at higher 1evels witheld from calculations, follov~dby later melt and release of runoff IV I local storm centered over Rocky Mountain Trench V loca 1 storm on nindaard side of the Caribon mountain
VI overspill effect on fee of Coast mountains
Generally, hydrcyraphs remain very similar for events involving the whole tasin, Hydrographs at Texas Creek are the most varied in all but two cases, illustrating the io~artaaceof tributary
inputs in the reach below Shelley, Addition of the Thoa~son river at Lytton tends to smooth the hydroyfaph and heighten the a~xinaura peak.
The model illustrates the iraportance of tributary input
timing for determining time-of-peak (takle 3.4) Time-of-peak thus appears related to tributary input. Therefore, the term
"travel times" is a misnomer for this system because basin Hansard Texas ShelleyI Creek flcde I: 50 node 11: 50 Bode 111: 28 Flcde IV: 73 Wode V: 28 Mode VI: --
(in hours from coeraencement)
,,Table -L3 5 gmaren_t awes Raasard to Shelley to Texas Cree Shelley Texas Creek to Hope
#ode I: -20 +82 +50 node 11: -1 5 +95 +17 aiode 111: + 6 +67 +56 Bode IV: + 5 +51 t39 #ode V: +I 1 +90 + 5 Rode VI: +51 {in hours f roa cosaeacement)
characteristics totally suanp rost flood wave movement {table
3.5). Undoubtedly, some ele~aentof wave progression will be expex ienced cn the F rase& but predict ions using crest tra vel times are not reasonable, Peak tilne differences however will be referred to as travel times throughout this study, because these ideas are ccapatible with data collected and ideas of strea mi low in general,
Differences between the six modes reflect the relative importance cf the tributaries. The dominant source of peak at each station is presented in table 3.6.
Table 3A Source of gpin ~ggkvolume Fraser River at Shelley Creek
Rode I:
Mcde If:
Hode 111:
Hode IV:
Hode V: Bode VI:
Key: E=Fraser basin above Hansard, - S=contribution added between Ransard and Shelley, W=Yest Road river, Q=Quesnel river, C=Chilcotin river, 8=Wort h Thota~sonriver, St=South T holapson river,
The following can ke concluded.
1, A negative travel ti= between fiansard and Shelley exists
wha the input betveen Hansard and Shelley is donainant. The
peak at Shelley can only be later than Ransnrd when either its contributing area sapplies an insignif ica nt inf low, or
tho Hansard volulae is delayed [snowmelt), It is unlikely that the peak at Shelley will occur after the peak at Hansard for vides~readrainfall events,
2. A negative travel tirrte betveen Hansard and Shelley allous
ap~arentlyslower travel times between Shelley and Texas
Cr €eft. This is because Texas Creek shares the salae overall to peak tining than arrival of an upstream floodwave.
3, B slow travel time between Shelley and Texas Creek can occur r also, if only the lower sections of the Hansard and Shelley i - subbasins provide runoff. Then, runoff has shorter distances P to travel and the peaks at Hansard and Shelley are
relatively early compared to peaks at Texas Creek.
4. Travel times decrease between Shelley and Texas Creek in
rnode 111 because the Texas Creek peak receives runoff fro& a large area that i+not subject to substantial snowmelt delay
[high elevation sncvfall case) and therefore there is a relatively early peak at Texas Creek.
5, The shortest travel tilae between Shelley and Texas Creek is
when a flood is produced only above Ransard, This suggests
that tributary additions in this reach delay the peak. For mode IY (no additicns), on other reaches travel times for
each reach are central to the range of derived valnes,
6. Between Texas Creek and Hop, travel time is highly
variable, The relative isportance of the lhoa~sonis
paramount, The shortest travel tilae occurs when the Thoa~son input is such more important than the Fraser flow. This is
becaus~the '~~CEFSU~is a shorter basin, its time-to-peak is
earlier and theref cre, acst of its volume arrives at Hop
relatively fast. This is especially clear for a storm
centered over the Cariboo mountains because runoff
generating areas of the Thompson are closer tc Rope than those of the Fraser, Slow travel times for this reach occur when the Thom~sondoes not contribute,
7. When all the Lasin operates together, the slowest travel
times are recorded. This suggests inputs from all subbasins
are significant in the timing of the Hope peak.
These conclusions were deduced from relatively siaple cases involving one storm. As the nuaber of storms increases, the runoff pattern and resultant hydrog ra ~hsbecoae more complex.
The areal extent of a storm is of prime interest because tributary hydrograph shapes retfect basin shape and size, and, the s~atialcharacteristics of grecipi tation. Bogers I19721 however, found that a reasonable variation in preci~itation amount and intensity within a general stora had little effect on the shape of the surface runoff hyd rograph.
The arrival time of tributary peaks appear ilxrportant in Fraser River hydrographs, therefore they were exarained briefly,
1 n most cases for the eiddle Fraser, each tributary arrives before the main upstream peat and accounts for a substantial proportion of Fraser volume at that time. Overall, sreall timing changes of one tributary will not drastically alter the resultant Fraser River hydrograph, Also, as the Fraser becomes larger, it beccaes less sensitive to the smaller tributary inputs,
From takles 3. 3 and 3-4, it is apparent that negative travel times between fiartsard and Shelley occur when the Fraser Basin above Hansard does not contribute to the =in peak.
Therefore, time of peak at Shelley is not dependent on the arrival of Hansard flow. As the Hansard flow becomes more important, travel times can become positive. The Shelley peak input coincides with the arrival of the rising limb of the Hansard hydrograph and this cof&3bination prcduces a large peak tcforr the arrival cf pat Hansard discharge, @hen the Mnsard peak arrives, its effects are minimised because there is little additional runoff to Shelley at this tittte, Therefore, the
Shelley input must be reduced for the Hansard peak to dominate at Shelley.
The relation between runoff volumes and Shelley peak titsing was exalsiner? using mode 11, ghea runoff is received from the whole basin, the volume bel~~ffansard must be 40% of norleal to allow the Hansard peak to dominate, This would require a storm across the centre of the Fraser Basin, that did not extend much north of Hansard. If only the western part of the area betueen Hansard and Shelley is contributing, a 50% reduction in runoff is required, This is due to t fie configuration of the subbasins-
The HeGregor river confluence with the Praser River is below
Hansard, but its basin lies parallel to the northern part of the
Hansard basin, Here, high runoff is generated from the mountain slopes. Cl~arly,the phenoiaenon of negative travel times is acceptabl~, because t ilse differences ketueen peaks are not depndent on wave celerity. The tie-area model and its variations Frovi.de a useful
tool for inter~retingPraser River hydrographs, Ey doing this,
the model has achieved its ~otential, It is restricted by its
simplicity; real world complexities need highly sophisticated
models to enable predictions. It provides an invaluable aid, however, to understanding gauging station water level data used in the analysis of travel tiae. L Eased on an understanding of how hydrcgraphs at selected E i points along the Fraser River are produced, strea elow data can
be analysed with more insight, The time of occurrence of each peak uas extracted from streamf lcw recorder chart data, and
apparent travel tines were derived frcm the time differences
between peaks at two adjacent stations. It is postulated that
travel times are governed by discharge if peak timing is
determined by flood wave mvement alone. In the absence of such a relationship, it is ~ostnlatedthat basin geomorphology is an important ccntrol on runoff resFcnse. Thi s chapter comm ences
with a revieu of the details of data collection methods- Peat
flow data are then used to exanrine the nature of a relationship between discharge and travel tim for the Fraser river. Finally, meteorclogical chasacteristics are integrated in an atteapt to
r educe wnoise" and ex~lainanonalies, ---4.2 ---Data ---Collection
4.2.1 Streareflow data and gauging stations
Streamflow data were obtained from the Water Survey of
Canada vhich currently operates 1841 active stations within the Fraser Easin, This study requires a continuous record of stream levels to define hydrograph shape precisely, but unfortunately most stations supply only one reading per day, Hourly water levels therefore were obtained directly from the existing continuous recorder charts for Fraser River gauging stations between 1970 and 1980, These data were converted to discharges by use of the appropriate rating tables and a justntent factors, The prerequisites described above reduced the nureber of useable stations to five [table 4.1). Subsequent analyses were performed for each reach between adjacent gauging stations,
Station locations are illustrated in figure 2-4, Of these, the station near the Fraser headwaters is situated on noose river but its contribution to the Praser River, and its location near the source were considered acceptable for inclusion here.
The Texas Creek and HGFe stations axe classified as having regulated flow following the corapletion of the Kenney Dam on the
Necbako river in 1952. The dam reduced the effective drainage area------of the ------Fraser Basin by 14000 knt' because Alcan diverted the 1Surface Water Data for British Columbia, 1982, pnblished by the Inland Waters Directorate, Ottawa 1983 -- Stn, name la ti tude Years of S,S.U. longitude record (1) datum (2)
floose .river 58-80 nat
Psaser river 70-80 nat at Hansard
f raser river 50-80 nat at Shelley
Frasrf above 51-80 reg Texas Creek
Praser siver 50-80 reg at Hope
(1) nat = natural flcu, reg = regulated flow (2) the Geological Survey of Canada datula in eaetres, stored water to Kitinat, The records at Isle Pierre (08JC002) ,
40 km above the Fraser River confluence, were assessed and i~pliedthat this tributary had introduced no sizeable flood waves into the Fraser during the study period, despite periodic spillway opaings at the dam, The yearly station discharge fattern shows a general increase to a late spring aaximum and then a gradual decline to winter levels. This is probably due to the moderating influence of lakes, especially in the Stuart basin,
The Hope gauging station is often used as the key station to the Fraser, Its reccrds, dating to 1912, are considered to be the most reliable on the Fraser, and it is situated sufficiently inland to be above the daily tidal fluctuatioas, 4.2.2 fleteorological data
T fiese were ~rovidedby the Atmospheric Environment Service.
The Praser Basin has 105 meteorological stations (figure 2.4) supplying precipitation data on a daily basis, P recipitatioa is rrcorded as rain or sncu after 1977, but prior to this, tempratures are required to estimate snowfall.
Published daily values provide a static iapression of precipitation distribution. Therefore, for several days before
and after each streamf low ~eak,frontal movements, cold lcw digressions and Upper Air flow ptterns wer tracked on six-hour surface charts and twelve hour Upper air charts,
Slay~aker(3972b) found a trend of increasing f raser River
discharge at Hope from 1952-1 969 despite an expected reduct ion due to retention behind the Renney Dam. Although he found no statistically significant preci~itationincrease, he deduced that acre precipitation, especia lly snovf all in the upper ungauged areas, caused the higher discharges. This could occur following a northward shift in the arean position of the Arctic
Front, allowing moist Facific air to exert a greater influence
in central Eritish Colueabia. However, this is difficult to monitor because of the rarity of high elevation meteorological
stations. The Barkerville station in the Cariboo Mountains is therefcre important and its data are key inputs for flood
predictions and the U.B.C. aodel. The theories discussed in sect ion 1-2, indicate a negative, relat ionshi~between discharge and travel time should exist,
Eotb travel. times in hours and the velocities necessary for flood waves with corresponding travel times, were exanined for a dependence upon actual d ischarge values. No decisive pa tterns could te deterrsined between the two sets of variables, either on the basis of a whole year or when split by season. The seasonal
division was made to differentiate between different runoff genera ting processes. Spring events with a substantial snowpelt contribution,
Smaller scale snmrner events caused by localired storms and increas cd water losses during transfer,
Autumn rainfall-runoff events due to increased iron tal activity.
At this stage in the study, only cases with positive travel times between two stations were considered, In aost cases, only a qualitative analysis was atteatped due partly to the lack of clear relationships exhibited by the data (figure 4-1)- The
inr~licationzfrom analysis are presented in table Q.2, This table highlights general trends but nct f irrs rela tionships and additional observations subsequently will to discussed. -r1 -C, Discharge in m3/s Discharge in m3/s
Discharge in m3/s Discharge in rn vs
i; Table 4,2 Discharge/travel time relationships
Reach Whole Year Spr iny Autumn
large Q range as annual as annual as annual for medium 'IT
broad Q range as annual as annual very broad with short 'IT nega ti ve trend, low slope
broad Q range large TT negative as summer with short TT range for trend, low medium Q slope, broad scatter
broad (; range as annual with short TT
key: Q=discharge, q'i=travel time, RP=Red Pass, H=%ansard, S=Shelley, TC=Texas Creek, Ho= Hope
On an annual basis very little can be determined about the
nature of an association between discharge and travel t be,
exce~twith regard to the range of both variables. With the
exception of annual data for the reach between Red Pass and
Hansard, most discharge values can occur with relatively short
travel times [figures 4. L2a, 4.1.3a and 4.1,4a), The rsaxirnu~
discharge range an the reach between Bed Pass and Aansard occurs
central to the spread of travel tirse values [figure 4.1. la), For the Hansard to Shelley reach it appears that the longest travel times occur at medium discharges, contrary to the predictions of
Linsley et a1 {lW9), Annual data suggest travel tines are not The freshet peaks are the highest in all reaches [figures
4.1. Ib, 4. 1.2b, 4. 1.3b, 4.1 .4b) r While it is possible to comment i on a few Feints on the spring plots, there are nore exceptions
than genera 1 rules. At this time of year the observed
unpredictability of travel tilties is prokably resulting from
spatially and teaporally uneven inputs,
In suamer, the broadest range of travel times occurs at low
discharges for the upper two reaches (figures 4.1.1~and
Q. 1-2c). For the Shelley to Texas Creek reach (figure 4.1-3c) a
vague trend of shorter travel times with higher discharge is indicated, possibly responding to localised convect iona 1 storms,
This ccnclusion is based on the nature of most suinmer
precipitation in the Shelley to Texas Creek region, and
observations frola the model developed in the study. The &ode1 implies that travel ti- vill not be dependent on discharge when
there is ba sin-wide precipitation, but that a relationship can emerge for s ma 11, localised storms. In autumn, low discharges appear to occur only with
relatively long travel times for the aiddle two reaches [figures
4. 1,Zd and 4.1,3d), but the pattern is still confnsed (figures
4.1,ld and 4,1*4d), Pcr the total river length between the
extrene stations, travel time appears to be totally uncorrelated with discharge,
The importance of the Tho~ti~sonriver input to the Fraser
Eiver belor Texas Creek led to an exaaination of discharge and travel time relationships h~tweenSpences Bridge and Hope. The patterns exhibited here were no better than those on the Fraser River itself. In general, the search to establish pat terns between discharge and travel time seem fruitless. Considering discharge at only one station may contribute to the paucity of results because travel times. %tillrespond to conditions along the whole section. Thesef ore, several tests were made to incor~oratedischarge values for Bore than one point. The first approach required the computation of peak difference, that is, the volume by which the ~eakhas increased downstream. This measure should account for lateral inputs which may confuse the discharge/travel time pattern. Trends appear to be absent from annual data. Seascnallp divided data were no clearer except for the two uppermost reaches in autumn, where a teeuons, negative, linear rela tionshi F appears. Often, between
Hansard and Shelley, autumn peak differences are the louest, signif ying relatively smaller inputs downstrea m, The na ture of autumn precipitation allows vides~readrecript w ithin the basin. Theref ore, low peak differences my =Elect a thirsty groun dwater conditicn and in•’luent streams in the area contributing to the Praser River at Shelley. With the elimination of snbstantial input f rozi this area, the Hansasd peak can dominate and allow almost regular travel times on this reach. If the increases in discharge are expressed as ~ercentayes,the result is not imgroved. In a second atterart to reduce @#noiseq*,simple discharges ) were s~paratedinto twc groups according to the relative height of the preceeding peak; that is, higher or lower. This division should reduce problems created when seasured events occur too close together in time and the system is carrying previous
highwater conditions in its mnemoryfi. Again, typical broad
scatters ve re produced in most cases. A scattered, positive relationship between discharge and travel time is indicated on the lover tuo reack~swhen highflows are sraaller than their
predecessor. Because river velocities are a function of discharge, the asscciated maximu@ velocity for the preceeding
peak will also be high. Although velocity will decrease after
the first peak because of itlcreased baseflow, it Bay still be
relatively high uhen the second peak is generated, Therefore, velocity is already guite fast, Zt is unlikely that a small peak
preceded by a larger one will record a slow travel the,
regardless of the complexities of unsynchrcnised inputs from the suthasins, In the c~positecase where prior events are larger,
high discharges appear to be restricted to relatively fast
ve I cci tie s,
A final exasioation vas made of discharges and velocities
averag~dova the whole reach, instead of values from fixed
~ointswhich may not be representative. No relationships could be deterntined and the overall conclusion from this section is
that a siaple correlation between discharge and travel tim or
apprent velocity does not seem to exist on the Fraser River, --4, 4 ----Influence --of ~eteurolocric~Conditions
It is hypothesised that storns f ron different directions may conplica te the patterns due to contrasts in precipitation mechanislas, v clutaes prod wed and timing of runoff generation, Three iueteorological features were considered important in governing direction of storm movement, ria nely, f ronts, upper air flows and cold low centres, The predoininant frontal approach is from the northwest, but speed of gassage and upper air flows are variable for each stora. Upper air flows tend to steer stor~s and theref cre the Geostrophic winds are a use•’ul indicator for tracking (Gary Schaeffer, pers comm). In spring, warming upE;er air frola the southwest (Hawaii) leap be sore responsible for inducing soovraelt peaks. In winter, cold low centres are likely to dotainate over the Northeast
Pacific and may proceed northwards along the coast, allowing a series of fronts to pass over British Colurebia, Conversely, in summer the lows thetaselves are more likely to move over British Colas bia and produce instability showers. Therefore the cha nging relation between the Hawaiian High and the Yorth Pacific lows is very isportant in determining the spatial extent cf storm activity in British Ccluiabia, In the following analysis each flood peak was classified according to direction of pro tab1 e storm approach and upFer air features. Approximately one third of the spring peaks in the data set were associated with general instability and southwest upper air flcus, itaplying that snowmelt is important. Snowinelt produces an inconsiste~ltinput to the Praser River allowing the Ransard volume to dominate at Shelley. Further downstreata between Texas
Creek and Hope, snowmelt events exhibit much variation in the discharge/travel time relationship. In summer, the meteorological conditioas associa Ped with peaks are highly variable, Uftilo the vasiabilit y dce s not allow conclusions about the effects of meteorological conditions on the discharge/velocity relationship, it does explain the confused patterns exhibited by the data, In autumn, northwest fronts my cross Eritish Colulabia in nulti~les,creating no table flood peaks between Red Pass and Hansard. Por a series of storms, river inputs ccntinue to increase after the first "peakm, thereby extending the overall hydrogra ~h timebase, T he first stcrm my not producf the highest peak, and peaks at adjaceat stations may not be caused by the saae storla. The duration of each frontal passage does not appear to have a distinguishable effect.
T he fastest t ravel tines between Bansard and Shelley occur with a relatively low discharge produced by a front approaching from the northwest. This supports the idea that the time of peak at Shelley is inde~endentof the arrival of a flad wave from
Nansard. The slowest travel tirtles for this reach are associated with westerly fronts and my result from relatively late precipitation receipt in the basin above Hansard. This, allows a tine separation between the input from the area contributing more immediately to Shelley and the arrival of a flood wave from upstream, Theref ore, wslovm travel t irses ~cssiblyillustrate the time difference actually produced by 2lood wave rrovement. For all sections of the Praser River, the greatest range and variability of travel times is in sulemer. Additionally, travel times for each reach seem to behave without reference to neighbourin g sections,
Average values of both discharge and veloci tg were considered also for each reach, Results were inconclusi ve because responses were not differentiated by direction of either frontal approach or nppr air flow in any reach. Unstable conditions tend to be associated with higher discharges for a given velocity on the siddle sections. Possibly travel times during unstable conditions are more representative of real travel time because the whole basin slay not be contributing, Atteapts to model the direction of frontal approach proved unsuccessful because the time of passage is relatively short coapared to basin dimensions and surface processes. Therefore, the main benefit of a classification based on direction, is to distinguish stor&characteristics accrued fro^ the source a rea rather than time differences introduced by actual movement direction across the basin, The overall ccnclu~ionis therefore, that the *noiseM interfering with supposed generalised trends cannot be fully ex~lainedky large scale meteorological differences. The most
outstanding feature is the presence of unstable conditions and southwest upper air flows, enabling snoumelt in spring. Weather conditions associated with a peak in summer are more variable, im~lyingthat antecedent conditions exert an influence. Certain groups of mfteorological factors indicate tentative reasons for
erratic relationships between discha rge and travel time, hut not
general trends, Therefore a range of discharges can be associated uith aost travel times for the upstream reach.
Until this point, only positive travel times were analysed. Positive travel times are defined as events in which the
upstream peak occurs before its downstreaa counterpart. There
are a significant number of cases where the reverse Dccnrs,
itsplying that travel times are negative, Host negative travel
times were observed on the Hansard to Shelley section aad fewest between Shelley and Texas Creek. They exhibited no preference for season or meteorological conditions (see table 4.3) . This facilitates the conclusion that basin response, or the time of
concentration 2 for a subbasin, is dominating time-of-peak at a
station. Obviously in these instances, peak generation is a function of local basin factors and not wave progression! Time of concentration was examined briefly to assess the im~crtance------of subbasins in deteroining time-of-peak. In almost 2Tbe O,S, Departl~entof Agriculture defines ti~of concentration as "the time required for runoff to travel from the hydraulically most distant prt of the storm area to the watershed outlet or some otber poiat of reference" {Viessma~et al, 1977) unsta bl~ NE front N front NW front # front SW front total + ve/- ve
all cases of negative travel tiaes, upstream time of concentration is longer than that downstream, This allows the upstream peak to occur later, resulting in a negative travel tintew, Tiwe of concentration is highly variable between reaches and also k~tuesnevents over the whole system. The largest ti~e of concentration occurs in spriag due to increiaentaf increases from snow @elt ,
Cases where upstream tine cf concentration was longer than downstream can occur in each of the three seasons but mainly in sumner between Bed Pass and Iiansard. This suggests that localised storm effects are important. Often, lung upstreaa tie
of concentrations occur in conjunction vi th changing meteorclogical conditions, and sometines these cases were anomalous in the discharge/travel time relationships, Now, the
travel tine irregularities cn the section between Bansard and Shelley are well explained. In spring, des~itea range of travel
times and discharges, a long time of concentration upstrean predoainately accounts for very short travel times with low discharges. #any of tke first summer peaks also have a long upstream time of concentration, which again explains the majority of extranecus points. For example, a very high head with slow travel tiae, and the very fastest travel times occur under these conditions, Exceptional autumn cases are also attributed to time of concentration irregularities, While the effects are not so explicit between Shelley and Texas Creek, between Texas Creek and Hope a lcny time of concentration upstream is associated mith the faster travel times.
In conclusicn, an exaaination of time of concentration explains much abont apparently erratic trawl times, and in aany cases, time of concentration irregularities can be related to meteorological conditions. Once again the iaporta nce of subbasin contributions to time of peak at a station is highlighted, more specifically, the tiae taken fcr araximura runoff generation at a point, seems tc be of most significance in deter~iningtiltle of peak anywhere along the Fraser River. The translation of a flood wave appears to be of minor ir~ortancebecause, for the majority of events, a negative travel time is exhibited between cne or more stations, 4.5 Observed and model genera ted velocities ------u--
When the time differences between two peaks at neighbouring stations are ccnverted to the velocities that are necessary for the same flood wave to be present in both peaks, some unrealistic velocities are implicated. This section deals aore fully with real and apparent velocities from streamf low and model generated data.
It %as presupposed that a flood wave traversing the system produced one peak vhich was observed at each successive station.
Thus the tires between peaks, derived from strea laf low data, can be expressed as wave travel times (table 4.4. ) When compared to generated travel times (table 3.5) the real da ka suggest wave celerity is extremely high. This could be doe to a shortcoming of the model or a total disregard of flood wave translation in real peak timing. The dichotomy can be more easily resolved when ' actual vater relocities and prokahle wave celerities a re consi doced,
Observations suggest wave celerity to be 1.4 to 2.0 times greater than vater velocity (Linslep et al, 1949). Velocity and discharge data, seasured in the field three or four times per annum, were obtained for each station f roa Water Survey of
Canada mter notes and used to calculate an expected range for wave celerity (table 4.5). Quick and Pipes (1976a) suggest that the best estimate of wave celerity for the Fraser River is 7.5 Table 4.4. Travel time statistics. -- I------I__
Positive times Negative times Range # mean S. D. # mean S.D.
fP to B 69 38 16 5 39 24 -76 +76 H to S 70 11 8 28 12 9 -35 +38 S toTc 63 48 11 7 17 8 -27 +73 Tc to Ho 31 14 9 8 9 6 -19 +49
(time from correencement in hours)
Key: RP-Bed Pass, ff=Hansard, S=Shelley, Tc=Texas Creek and Ho=Hope
Ye loci ties Y eloc it ies frctn travel from field tises (m/s) data (1) (mjs)
#Inean 1 S, D. ( range [3) I I I
(1) Cerived from discharge-velccity curve at a station (2) Only calculated when travel tine more than zero hours, (3) After Linsley et a1 (1949) (4) After Quick and Pipes (1 97th)
time the gauging station weloci ties, Clearly, the velocities derived from travel times have averages gfeater than is normally observed for wave translation. In addit ion, the velocities implicated by the travel times for the upper-~osttwo reaches are higher than the expected range, The real velocity-discharge curves shov that significant cross-sectional changes did not occur either as discharge increases, or for the ten years of study, Therefore, the lack cf good relationships is not due to dundam ental channel changes.
The reach-hp reach analysis cf velocities was supplemented by a coatparison of velocities fro@travel times between adjacent reaches. Spearaaa* s 8*r*quas very low for all pairs, suggesting independence of travel times: a phenomenon that is physically inpossible, l4eteorological conditions typical of errati c velocities frcrm Red Pass through to Hope could not be discerned for these cases. Analysis of ad jaeent reaches is also hindered because few events #ere recorded at all stations. This Bay be due to data loss caused by problems at the gauging station, or simply no trace of a peak, The latter may he caused by attenuation or drowning" of relatively small tri butary inputs by larger Eraser Biver flows.
A11 the ccnclurions reached in this chapter ~ointto discrete responses of the river at each gauging station- Rather than providing evidence of OM? flood wave passing through the system, it appears that "travel time" is not an acceptable, descriptive term for the time differences between pea ks. Travel tise traditionally refers to the mximum peak, but the mdel generated hydroyra ~hssuggest most highf low events are aulti-peaked. Hydrographs for latf summer and autumn events were reconstructed frcaa ri,S.C. recorder chart data for the ten years of study. For this, the hourly data were invaluable, Hydrogra~h shape variations between staticns per event, and between storms, were readily apparent, The hydrographs were divided into three types, The first showed a regular progression of hydrogra ~h shape between all stations and ~ositivetravel times, The second group exhibited one or more "negativem travel times and the third exhibited changes in hydrcgraph shape, By comparing the changes in shape, volume and timing uith the model, it was possible to infer precipitation source areas or storm centres.
The Fraser Liver hydrcgra~hswere classified by the a ~~arentsource region of preci~itation. They were then checked with real precipitation distribution data which were available only on a daily basis, Precipitation will not commence everywhere at the same time in a basin as large as the Praser, but the time lag introduced by runoff genera tion nay be sufficient to ignore these aberrations (at this scale).
Theref ore, onl y the presence of ~recipitation was recorded, enabling an approximation of its spatial extent. Most classifications using hydrograph shape alone were success•’ul,
Although it is difficult to distinguish precipitation scurce areas precisely fro@ the sparse aetwork of meteorological supportive in 58% of the cases, Another 20% of the cases were
considered to be half correct. Hodel hydrographs will not
replicate Fraser ff iver hydrographs exactly, because the model represents just one case of each storm. However, general
hydrograph forrs does seem to be simulated well by the model. Promising associations between hydrogra ~h form and
precipitation distribution were found for the im jority of hydrographs. Hydrographs whose precipitation sources were
incorrectly located occurred mainly in suamer, lri th Arctic
fronts or high pressure conditions, These meteorological
conditions are associated with an uneven distribution of
- precipitation which may be causing the unpredictability. A ccmmon factor in extraneous autumn cases, uas upper air flow
from the southwest, This warm air flow possibly induces melt of
early snow at the higher elevations, disrupting regular precipitation patterns. Generally, the inclusion of frontal activity and upper air characteristics did not offer any further
explanations, Broad scale seteorological variables do not seem
to be sensitive enough to account for runoff variations in a basin with the diversity of the Fraser.
The shape cf the Fraser Biver hydrograph at Hansard may be
exhibited occasionally at af 1 stations downstream. This requires a limited duration, localised input in the north of the basin, Such a stor a often h rod aces a low, rounded hydrogra~hwhose peak
volume nay not be a noticeable addition to the flow at Hope, Exaut~lesare shown in figures 4.2~and 4.2d, and should be compared with figure 3 -6, The Hansard peak may not be apparent at Hope, as in thes~two exam~les,This may occur if water is influent to the groundwater systeDc in the middle Praser, neqating the increa~edvolume from upstream, or the wave bas attenuated completely. Voluree increases downstream are explained by baseflow coatritutions. Although basef lov is excluded from the model hydrcgraghs, flood peak volume changes are of the sarae order of magnitude as the model, The shape of the hydrograph at
Hansard may pass through the system with few alterations duriag the sumscar, when precipitation in arid areas laay not necessarily result in appreciable volumes of runoff, Storlas in the north have the same effect, They are associated with fronts f roa the north, northeast cr northwest, but the last also can be responsible for a range of spatial precipitation patterns,
An examination of shape changes in Fraser River hydrographs for events passing downstream revealed that pre-peak changes are ' more noticeable than changes after the peak, A rise or plateau on the hydrograph recession limb resulting from upper Praser flows was rarely visible, In•’act, attenuation is ~ossibly more prevalent t ban expressed in the model, The next peak f ollovs closely in ntany cases, obscuring the ~rofile cf the recession lirnk. Another facet of the systeru highlighted by examining real hydmgraphs, was the fairly even, less erratic shaped hydrographs of the Thontpson river at Spences Bridge compared with the Fraser river at Texas Creek, The smoother shape HANSARD SHELLEY TEXAS CREEK HOPE
0 100 200 0 100 200 0 100 200 0 100 200
Time (hours)
FIGURE 4.2 Fraser River hydrographs reflects the regulating effect of lake storage on discharge fluctuations, Mult i-peaked hydrcg ra phs are comaon for many events cn the Eraser River (figure 4-2a and 4.2b). This illustrates the need to identify past and future discharge changes above kaseflow, to assess which peaks are discrete. The Praser River hydrographs for precipitation over the uhole tasin shcwed good similari tes to the model hydrographs.
For example, the increased volume and broadening of the hydrcgraph shape f roat Hansard to Shelley If igure 4. 2a and 4,2b),
and the earlier tiae-of-peak in the latter case, The hydrograph
%or mode I at Texas Creek is very similar to that in figure
4.2a. ?he model suggests the first peak relates to Bridge river
flows, the seccnd ~eakto inputs along the middle Fraser River
and th~third blip to urper Fraser flous- The broadening of the
main peak at Hope is due to the Thorn~wnand the decreased slope of the upper Fraser flows due to attenuatio~(figure 4.2a). These three peaks are dlso visible at Hope in figure 4.2b. In
this case the Thompson input was ROE substantial as evidenced
by t be larger volurae increase,
Praser Biver hydrogra~hsf rola storeas ovEr the Cariboo
Plountains (figures 4,2e and 4.2f) also followed the model clcsely, For example at Texas Creek the voluae has increased but
the peak has experienced attenuation, 3 y Hope, the volune has increased and the shape is lacre ~~0notInCed,The differences between figures ir,2e and 4.2f are understandable since the extent of a Cariboo storm is difficult to determine and the degree of influence on the upper Praser and Thompson will produce different hydrographs, In all cases however, the model should only be consi.de red as relative,
Continuous discharge data allowed hydrograph shapes to be portrayed accurately, and a more precise evaluation of peak time. Many travel times beteen adjacent stations a re less than
24 hours and therefore daily data do not possess enough sensitivity to determine the tilae of =in peak, It is even more difficult to identify secondary peaks f rum daily data. Theref ore much information is lcst at the daily time scale,
---4.7, ----Discha~eLTravel Time y&aticmshi&s fqr selected pseci pitation source areas
After verifying the zone of precipitaticn, the basic relations between travel tiae and discharge were analysed again.
Wow that the data wese split acccrding to precipitation source regicn, the results were generally good, and implied faster travel titses with larger discharges, Often the trends exhibited the curvi-linear form predicted by Linsley, Kohler and Faulhus
(1 949) , For exaaple, the Hansard to Shelley reach and the Shelley to Texas Creek reach with storne centres over the Cariboo mountains and in the ncrth (figures 4.3,2a, 4- 3. 2h, 4-3.3a and
4,3.3b), This trend can also be seen for FIansard to Shelley with precipitation cver the whole or centre of the basin, and to some extent beween Texas Creek and Hope with the latter Whole Basin Precipitation
Legend X Shelley 9 rlansard
-20 -10 0 10 20 Travel Time in hours
Legend + Texas Creek x sh0ll.y
Travel Time in hours
5 10 15 Travel Time in hours FIGURE 4.3.1 Discharge- travel time relationsh ips by source region o precipitation Precipitation over Cariboo Mountains n \
Legend X Shelby 0 Hantard
I I I I I 0 5 10 15 20 Travel Time in hours
Travel Time in hours
3000
2500 - A A
2000 - + Legend 1500 - + A Hop + hxa8QWc innn
Travel Time in hours FIGURE 4.3.2 Discharge- travel time relationships by source region of precipitation 116 Preci~itationin the North of Basin
Legend x Shdky 0 Hanaard
0 20 40 60 80 100 Travel Time in hours
Travel Time in hours
FIGURE 4.3.3 Discharge- travel time relationships by source region of precipitation a) Precipitation in the Centre of the Basin
Legend X Shelley 3 Hanaard t -30 -20 -10 0 10 20 Travel Time in hours
Legend + 1ocorCm.k X Shrlky 0 20 40 60 80 Travel Time in hours
Legend A Hop. + ~o(CUcm* -60 -40 -20 0 20 Travel Time in hours FIGURE 4.34 Discharge - travel t ime relationships by source region of precipitation 118 precipitation distribution [figures 4.3, la, 4-3.4a and 4.3. Yc),
These trends however include "negativeit travel times and nay be purely coincidenta 1, When discharges at both upstrean and dohnstream stations on a reach are compared, there seems to be a negative relationship between travel time and the difference between the two discharges. That is, discharge volumes are nore likely to be si~ilarvolumes when the travel time is long, This is particularly noticeable on the Hansard to Shelley reach and the
Shelley and Texas Creek reach (figures 4, 3.2a, 4.3,3a, 4,3,4a). However, for pfecipitation in the centre of the basin, where this trend i+ most marked (figure 4,3.4a), the curvi-linear trend is also least apparent. Clearly the large additions betweea Hansard and Shelley allow "negati vew travel ti~esand disrupt the discharge/travel tiae relationship.
For cases where the negative curvi-linear trend is not apparent, the timearea model prcvides explanations, For example ' between Texas Creek and Hope with precipitation over the whole or centre of the basin (figure 4.3, Ic and 4.3.4~) , the relative iinportance of t he Thom~sonconfuses the pattern, "Wegat ive"
travel titties occur when the T hospson supplies a more important input than the fraser, Precipitation in the centre of the basin also confnses the discharge/travel tiae relationship between
Shelley and Texas Creek (figure 4.3.4b1, due to the relative
inpcrtance of several tributaries in this reach. It is
interesting also that basin-wide ~recipitationonly provided two travel times for the Shelley to Texas Creek reach (figure
4.3.lb). This again suggests travel time is inde~endentof discharge, The cases that do not fit the expected trend provide more evidence that wave progressi.cn is interupted when many tributaries are generating inputs, At these times, actual tributary input volume3 and the balance between tributaries a pear most important in deteraining absolute peak magnitude and timing. In contrast to the timing coaaplexities revealed in the original analysis, the most predictable reach is Hansard to
Shelley. After elisrinating the "ncisem created by different spatial distributions of precipitation, the relationship between travel time and discharge for Hansard and Shelley is improved.
This can possibly be attributed to both the shortness of the reach and the limited nuaber of tributary inputs, Predictability between Shelley and Texas Creek varies, with some evidence of negative trends between discharge and travel the when a storm - is resent in the Cariboo aountains or the north of the basin if igure 4.3-2b and 4.3.313). There are insufficient cases for the
Texas Creek to Hcpe reach to dram good conclusions, hut the additian of the Thompson river Frobably disturbs the shape of the Praser hydrograph and thus expected travel times,
Tbis section has demonstrated how the tinting of tributary contributions can conaplicate a a cverall trend between discharge and travel time. Similar mainstrean hydrographs are produced for each storm centered in a given area and a relations hi^ between travel tiae and discharge can be expected, except where substantial tributary inputs can alter the time of peak.
The model developed in chapter 3 is successful in allowing observed hydrograph changes to be interpreted in terms of ~recipi tation receipt/runoff scurce area, For certain precipitaticn source regions and reaches, trends between discharge and travel time can be shown to exist. While events with basin- vide precipitation do not readily conform to expected trends, the changes in hydrograph shape through the system allow an assessment of relative tributary inputs. In these cases, a more appropriate analysis would be that of highflow duration: a yara~eterof equivalent importance in flood damage calculations. V, Discussion
-5.1 JIjortagt cgntgog TAg of Peak
As discussed in chapter three, tiiae of peak is dependent mainly on the time taken by water frcaa the most productive basin zone to reach the main channel via the drainage net. Therefore, the governing factors can be split into two groups,
1, Eydraulics of overland flow.
2. Hydrologic and storm characteristics. The multitude cf interrelations between basin, storm and channel cbaracteriz tics allow aany per ruta ticns of the net effect,
Langbein et a1 (1947) made several significant observations in this regard. They surmised that river systems have differing efficiencies as agents for the ccllection and conduction of water. Further to this, that variations in the supply are more sensitively perceived in the aain channel as the hydrograph tiaekase diainishes.
The time taken for water tc reach the basin mouth will be influenced by drainag~density. Basins with a high drainage density can respond faster and attain greater flood peak voluraes than a basin of equivalent size but lower draiuage density,
Heerdegen (1973) found these features were exhibited in Unit
Hydrographs of contrasting Pennsylvania State rivers. He shoved that both high peak discharges and unit hydrographs with a short
basele ng th reflect basins with a combination of small area, short overland travel tiaes, low drainage density and reduced
channel sinuosity. Basin shape is inherent in all of these
ex fressions, Five groups of topcgraphical features which
influence the hydrograph were listed by Sherman (1932). Shape,
together with area and size, was in the primary grouping, After
an exasination of the silailarities between models and the real
world however, Black (1972) suggested that watershed
eccentricity, rather than sbape per se, was a nseful expressicn
of basin control on maximur peak flows and certain time
parameters of the hydrograpb.
- Unfortunately, the absolute size and diversity of the Fraser Basin hinders the prodaction of a siiple unit hydrogra~h.
For exaaple, the observed hydrograph at Hope is the sum of attenuated inputs frca &any tributaries and therefore, it is poorly represented by a si~~leUnit hydrograph of the whole
basin. However, unit hydrogra gh assumptions are more acceptable
for individual tributary subbasins. Here, it is feasible to
consider the charactefistics of the sukkasins as being honogeneons, especially as size decreases. In a small basin, a significant percentage of tbe time-to-peak is spent io overland
flow and it is therefore influenced by topographic features. Conversely channel runoff ~redo~inatesand streant hydraulic characteristics become sore prominent in large basins, At a large scale, studies id~ntifyinyspecific relationships between physiogra ~hiccharacterist ics and hydrolcgical parameters can only be fairly crude. For example,
Heerdegen and Reich (1973) stated: "time of peak and peak discharge are dependent on area and other associated
~hysiogra~hicparaa~ters'~. In crder to be more specific,
investiga ti cns aust be vler y small scale, The main reasons for these difficulties is the interdependence between variables,
Resnlt~from Langbein et a1 (1947) imply that none of the to~cgraphicparameters are unique in their inf hence on the hydrograph, and that each reflects a condition which also
influences the others, Some of this variability may be reduced by using hydrometeorological regions,
W it bin a givea hydrometeorological region, actual discharge is ~artlya function of basin size. Thereafter, the percentage
of precipitation producing runoff indicates the relative
importance of storage and pondage within the region, In arid zones with reduced slopes and strea~sinfluent to the grcunduater systertl, time to peak is relatively long and peak
discharge relatiwely low, Although great contrasts in climate
and to~ographyexist within the Fraser Basin, at the scale of a
tributary sobbasin, vegetation, cfiaate and physiography are Bore nnif ora,
T he very irregular shape of the Praser Basin a nd nuaerous
tributary inputs alcng the river, produce a coaplex hydrograph even before considering the spatial extent and characteristics of individual storms, The sheer size of the basin Confounds the possibility of precipitation beginning concurrently throughout and it is plausible that precipitation will not be received everywhere, especially in summer. Also the amounts received at any one place are extreltlely variable. Therefore, it is feasible for all tributaries to add to the mainstream only under special conditions and at these times, they may be operating on separate timebases. Storm duration also affects the sped of runoff,
Heylaan (1975) ~ostulated that the factors coatrolli ng infiltration are most noticeable for snall StOrlsS and that multiple rain periods pose extra corttplications,
Rustonen (1 9b6) cautioned that the yuantificat ion of climatic and basin characteristics only produces indices of the costbined effects of several physical factors and theref ore, it is potentially misleading to use complex statistics- Uhile this
is a justifiable assertion, quantitative models inevitably must be com~lexto allow reasonable results- The II-B-C- aodel of the *
Fraser is a gocd example of this. OvDonnell (1966) suggested
that ccmp~terscan assist in providing SO~U~~O~Sbut that the results are still limited by current kncvledge and the un derstanding of the processes si eulated,
Therefore, the model generated in this study was kept su ff ic iently simple to provide an approximtion of tittle-of- peak at each major tributary junction and other subsequent points along the Fraser, 'ihe use of a time-area rstethod for a precise
peak prediction is not advisable hcvever, because countless interactions and daily fluctuations in basin conditions affect
travel times az;d thezefore question rigid spacing of isochrones.
Alternative1y, a t ime-area model usefully provides an i mpressioa of basin responses, when the in herent raw assumptions are
appreciated, In flccd control it is also useful to be able to identify intividua 1 components of a h ydrograph (Clark, 1945) , Studies utilising flood routing techniques often produce an accurate predict icn of peak discharge but ignore hydrograph
shapf. The mathematical representation of peak time or peak
voluae by these nethods ma y hide significant secondary peaks
which can be important in determining total downstrea~
responses, The IPU lti~eakednature of the hydrogra phs ge nerd ted
for one event on the Praser River clearly shows the itsportance
of this omission. The highest nueber of peaks per event occur
when input fro@ the whole basin is luo~edto ~roducea
hydrograph at the lover Praser River gauging points. While real
hydrographs often exhibit gore than one peak, they do not show
the same number as in the model hydrographs described above. By
routing each tfibutary to its Praser River con•’hence and then
routing the summat ion d flows, a more realistic &ode1
hy d rograph is developed. C lark f 1945) acknowledged that his
basic method possitly exaggerats the in•’luence of basin shape
and the capacity of the basin to produce high peaks. Yith this
constraint in mind, the use of the study laudel can be evaluated. In the Fraser Easin time-area laodel developed for this study, each subbasin is treated separately but small changes within them do not appear to be visible in hydrographs at tiope,
The model a llovs the incorporation of a channel storage function and therefore includes attenuation. It also gives a reasonably realistic impression of how the tributary flows are synchronised in different circumstances. T he model provides a usef ul representation of time-of-peak and spatial variations in basin response.
It appears that fraser River peak flov times are independent of flood wave translation and are governed predoninately by the time taken for runoff to accumulate in the channel, Climatic and physiogra~hiccharacteristics are therefcre of priae importance, It follows from this that differences between time of peak at two adjacent stations is rarely eqnal tc flood wave velocity, Wave celerity is greater than water velocity (Linsley et a1,1958), but this cannd acceunt for the phenomenal velocities inaplicated in aany cases on the Fraser rive^.
Travel time in the winstream is related closely to the storage capacity of the open channel (Clark, 1945) contrasting to the hydrologic and tasin characteristics governing stater collection, The progression of a flood wave along the Fraser
River can fe okserved when limited duration storms are centered in the north of the basin. When the input is more complicated than this, flood wave ~rogressionis disturbed, This ex~lains the paucity of relaticnships found between travel time and discharge, even when classsif ifd by fronta 1 a~proachand upper air flow directicn.
Subbasin contributians may be either synchronised for one storm throughout the basin, or may act independently, The time of arrival of peak flow from each tribntary tnay os may not coincide uith the arrival of geaks froat the upstream Fraser
River. This depends upon stcr at extent and dnration. Variations in arrival times of peaks from a couple of tributaries can significantly alter the shape of the hydrograph at Hope, and consequently, instantaneous time of peak. Once again, the impostance of tributary flow interactions dolaina tes and completely @asks correlations which could enakle travel t ime
~redictions,
Sometimes, the estimation of travel tiws f fom real data is ' complicated by the absence of a peak at all stations, The time-area model enables several explanations: U~pr'fraser storms localised and effects attenuated at lower stations.
Lower localised storm, not experienced in the Upper Fraser,
Peak inputs delayed fro^ the source in some regions, e. g. altitude effects uFon snow retention.
Input froa one or more tribntaries synchronised with lover flows between peaks on the Fraser, may eliminate substantial ~eaksat downstream stations.
5. Several stcrtas over a feu days obscure the effects of one.
an d also, 5. Recorder out of operation,
During other events, apparent negative travel times occ ur when the dounstream peak is earlier than its upstream countesprt,
These negative travel times do nat appear to be correlated with either fast or slcu flows on the adjacent reaches. Eetween Texas Creek and Hope negative travel times agpear aore dependent on the relative dominance of the Fraser or Thompson, Because the reasan for a missing peak may not be clear, an examination of travel time irregularities using discharge data alone would be highly speculative, Theref ore, the tine-area model is an invaluable aid for the Praser Basin,
The aodel has shown the necessity of understandin9 the co~plexityof a river system and also dealing with continuous data, Borexaaaple, an apparent series of peakson the recorder - charts nay be coraponents of only one event, but distributed by tine-area inputs, familiarity wlth the @ode1 and real processes within the system allows an inter~retationof the effects of one storm, These interpretretations in turn, permit explanations of the observed travel time i rregufarities, L5 3 --Further --Plork
The model presented here assists an explanation of peak flow travel time irregularities and offers a better understanding cf the Praser Basin, Unfortunately, it cannot supply accurate predictions, The ti~e-areamodel could possibly be improved by considering slnall hut important variations. Examples of these include altefing channel storage relations in the Fr aser fiivfr to accoetodate backwater effects, especially at the Thompson confluence, and also the inclasian of lateral inflow and mincr tributaries. Field nonitoring would be necessary to obtaia a reasonable sirenlation, but the quality of the acquired data would then exceed that of the other inputs.
Further ref ineaents could assess the role of baseflow conaponents and suksurface flows, but the end result probably would not justify the extra time involved,
An interesting addition could study model sensitivity to changing inputs in terms of timing, voluae and extent of basin affect~d,especially with respect to Ransard and Shelley peak tinting, It may be possible to identify several key precipitation stations and relate rainfall characteristics to hydrographs.
The statistical properties of travel times could also be examined, Anderson (1972) proposed that the Erlang distribution gives a~proxinatepeak inter-arrival tigtes a t stations, and this could ke test~don a heteCrCg€?ri~tI~basin like the Fraser, Weymen
(1 975) questioned if velocities consistently increase downstream as discharge increases. An answer for this could be incorporated nsef ully in a time-area model.
Precise input-output analysis howe ve r, is confounded by insurmcuntable pro tleas of measuretaent: not only the deteriainat ion cf volumes in ungauged catchments, but also
precipitation characteristics such as intensity and duration,
Analysis of interrelationships between variables per se, is a thankless task and the results are unclear, Therefore, determining hydrologic resgonse from geoaorphic features is more a~~ropriate.Existing models are deficient due to their linear and/or static nature, The ultietate mdel would be a
process-based catchment atodel (Wepan, 1975) which would include
topographic variables, Before this is attempted however, it is
necessary to determine the most significant va riables, for example, drainage density, The relationship between drainage density and the time-area
concept needs more thorough investiga tion, Drain age densit y is
fundamental to the timing and magnitude of runoff, hence it is
relevant to time-a rea ideas. Sokolov (1969) recognised drainage
density as being the lacst itsportant factor characterising
conditicns of flood flow formation. Current studies eatphasise
the dfrnaraic nature of the stream network and its spatial
varia tions, Collection of data concerning the dyaamicit y of the network poses many problems, but renote sensing and i~agery
should provide a useful source. Not only is a knowledge of network con•’iguraticn ilspor tan t, but also t he channel carrying capacity, that is, the amount of water that can te removed in a
given time. This volume is depend~nton relief, channel size and resistance, netwcrk shape and integration, among others. Gregory
(1977) attempted to quantify these factors by producing an index
of channel network voluree, and subsequently (Gregory, 1979) an in dex embracing both channel velocity and basin relief, Velocity is related closely tc stream size and thus, a re1ati.cn to streare order can also be expected. Gnpta et af
(1980 ) cited itlathema tical evidence linking an output ftydrogra ~h with channel network geometry, 1 n a similar vein, Rogers (1972) proposed a new drainage basin parameter called Channel Length
Freguency Distribution [C,L,F,I).), that has a qualitative
relationship to the surface runoff hydrograph. C. L. P1D, is
determined by measuring the distances froa the head of each
first order channel1 to the basin outlet, Frequency histograms
of these distances show similarities to surf ace runoff
hydrogra phs of general storms that exhibited reasonable variations in ~reci~itationamount and intensity. Although
Bogers claimed that the correspondence between C, L, F. D, and hydrogra~hshape was too consistent to be coincidental, he
achieved ozly ~artialsuccess in quantifying the method, Nevertheless, similar studies could give nore insight into
rnechanisias controlling peak ti~ingand symchronisation of tributary inputs f roma contrasting hydroaeteorological a reas. The above studies make a first step to unify geomorphic principles with hydrologic response. In•’ormation relatiag these two continues to grow, It seems of particular advantage to pursue these studies in the Fraser Basin ard results pro~iseto be exciting. Preliminary studies to link the Instantaneous Unit
Hydrograph with geoaor~hicpraaeters of a basin are presented by Rodriguez-Iturbe and Valdes (1979) Valdes et a1 (1979) and
Bodriguez-Iturbe et a1 (1979)- This work is based on the premise that the form and shape of a drainage net is governed by geoinorphological laws The concept is extended, suggesting . hydrological resFonse is also governed by basic themes which can
he related back to gecmorphalogical laws, To do this, general equations expressing the Instantaneous Unit fiydrograph as a
function of Rortcnrs numbers* are derived, Tests of the model in a real world situation ~roducedvery good results especially with regard to estimation of peak discharge and time-of -peak. Gupta et a1 [1980) devdop~da model on similar fines to that of Rod riguez-Iturbe and Valdes. They achieved most success in tbe larger basins and sulcrsequently questioned the validity of assuning a Linear precipitation-runof f transf craation- It seems plausikle tc test this type of taodel on the Fraser Basin, A slightly less mathe~aticalroute similar to Boyd (1978) and Boyd et a1 l1979) may be just as useful. They developed a relationship b~tueenlag time and drain age basin geomorphologp ------using ~arameters ------originated by H orton a nd S trafiler to allocate ZHorton, 1932 and 1945 storages. This eliminates the assumption implicit in the time-area model, that all storage elements are equal. It also removes the ~rcbleIRof interpolating isochrones from limited data, When compared to the real world, the Boyd model allowed reasonable calculations of lag titre.
While these studies may at first appear somewhat removed from travel tifie deterinination, it is clear that basin gecmor~holcgyand its spatial variations can exert an itaportant control uFon time-of-peak and therefore apparent travel time, It is suggested tbat further studies should concentrate on a Beans of assessing the time distributions of discharge from all subbasins, including those that are ungauged. In particular, the role of drainage density should be assessed because of its direct influence on generation of discharge and peak flows. Drainage density can then be used as the basis for a routing ntodel, The develo~mentof predictive relationshi~sbetween geomorphic expressions, such as channel network geometry and hydrology are of fundataenta l significance for advancement in this field. A simple time-area model based on Clark (1945) has been used tc derive a series of bydrographs for the Fraser Basin. The model assuares peak flow to vary directly with maximum width of drainage area, The t ime-area values were then assigned weights which were derived from Daean annual precipitation data, This allowed a representation of the timing of suhbasin inputs, and the relative eolunes to be expected under ideal conditions, Each tributary input uas added to the Praser Piver flow, and routed downstream inccr~oratiagthe effects of attenuat ion and increased water velocity, The effects of timing and magnitude of tributary inputs relative to mainstream voluee, were shown to be critical in determining the time of absolute peak.
The importance of subbasin additions to time of peak on the
Fraser Biver is clear when peak times at two successive points axe compared. In many cases, the time difference between peaks at the two stations does not necessarily ref1ect flood wave travel time. Therefore in a heteorogeneous, irregular-shaped basin, travel times do not behave in a mnaer contingent upon discharge, The inclusion of broad scale meteorologica 1 conditions and directicn of stora approach do not clarify the situation, Ohen data concerning the pak alone are extracted from the records, much infornation concerning hydrograph shape is masked, It is ittl~ossibleto know if the peaks downstream correspond to peaks translated frola upstream, or to larqe and/or
unsync hroni sed inputs between the gauging .stations. To distinguish between these it is necessary either to analyse a
series of hydrographs for the same event at different gauging stations, or to determine the influence of storm extent upon
Praser River hydrographs,
The tiiae of arrival of a highflow peak and the actual
volume of flow received at this time are intrinsic in flood forecasting. Both variables are affected by the degree of syachrcnisa tion of subkasin inputs as shown by the present study, Because all the subbasins can be included, the model can he adapted to assess the effects of stream diversion projects such as the HcGregor diversion proposed by the Praser River
Board (1963)3. The loss of the HcGregor input would result in reduced flows in the Fraser River. Eeid, Crowther and Partners
(1978) estimated these reductions to be of the order of 28% at
Shelley, 13% at Texas Creek and 9% at Hope. Consequently, the
relative influence of the cther tributaries will be changed, Not
only would this affect peak tilning and volume, but also thermal regime and the river8s capacity to assimilate contaminants. The
tiae-area model can be readily applied to this proble~.
Phile the time-area method bas been criticised for its --time-consu ------r ------ing and laborious coraputations, it provides a useful JTbe diversion of the RcGregor river to the Arctic drainage was one of nine projects designated as System E by the Fraser River Board for f loud frotection and H ydro-electric production, Engineering studies cn the ~rojectwere suspended in 1978 by the B.C. Hydro and Power Authority. explanation cf travel time irregularities observed on the Fraser
River. The method is not readily adaptable to flood forecasting studies, but it has highlighted the importance of basin geomor~hologyin determining time of peak, and the need for studies to quaatif y the spatial distribution and speed of runoff genera tion within each subbasin. APPENDIX Red Pass to Ha ssard
Da te Time season TT Discharge ( m3 s") 1971 Sept 0700 S ~pt 1 SO0 Sept 1900 0 ct 1500 1973 Hay 0200 aY 1500 fray 1100 June 0200 J one 0400 J uly 0600 July 1500 Sept 1600 1974 May 2 100 June 0600 July 2200 A ug 2400 S ept 0800 Sept 0800 Oct 1% 0 Oc t 1200 0 ct l5OO 1975 May 1700 J me 0100 June 1300 J une 1.600 J uly 180 0 Aug 1800 Aug 180 0 A ug 0200 S ept 1400 Oct 0700 1976 Hay 100 0 a ay 1800 June 01 00 J une 0 100 J uly 1100 July 0800 J ulp 2 30 0 A u5J 1400 sug 2100 A ug 0000 Sept 1200 0 ct 1500 0 ct 0900 1977 Bay 1600 flay 1000 June 1500 Date season TT Disch acqe [u' s-I) J une J une June J uly July July A ug A ug S ept flay nay June June J uly July July J uly Aug Aug Sept Sept 0 ct J~Y 1975 Sep 1976 Iray 1978 Bps 1979 June J une
Hansard to Shelley
1973 June June J uly J uly Sept Oct 197Q flay July Sept Oct Oct 1975 June 3 uae June J une a ug Aug Sept Date Time season TT Discha rge (a' s") S ept 0300 0 ct 0900 Oc t 1700 1976 Hay 2 000 June 1100 J une 12ao 3 u ly 1100 July 0100 A ug 0 500 A 11g 2200 1977 May 0 90 0 fl dl' 2400 flay 190 0 June 2000 June 0700 J une 200 0 June 1800 Jul p 0400 J uly 1300 July 1600 S rpt 1000 Sept 1200 Oct 0000 1978 Hay 1400 J une 0600 J une 0600 July 1900 July 090 0 J uly 1300 July 1300 hug 1900 Sept 170 0 Oct 2200 oct 1200 1979 June 200 0 July 1100 * July 1700 Sept 0 $0 0 1980 Hay 2 100 J une 1200 June 0500 1972 June 0600 1973 ilpr 0500 may 1600 nay 1100 el' 2300 1974 June 0300 J une 1200 Oct 1000 1975 flay 2000 3 ay 1500 Dat e Time season TT Discharge (m3s") Jul y 0400 1976 nay 200 0 July 2200 a ug 1300 SeP 0 50 0 0 ct OUO 0 Oct 2000 1977 Aug 1300 1978 Aug 0100 S eP 1900 Oct 2200 1979 June 0 100 1980 Apr 1600 aY 1600 J uly 1100 July 1700 A "g 2 100 A ug 1300
Shelley to Texas Creek
1971 May 170 0 M aY 0000 June 1700 J one 0900 July 0 00 0 1973 Hay 1700 J une ow0 J une 130 0 Oct 2200 O ct 2200 1974 Hay 2 30 0 nay 1800 Jnne 0300 J uly 2 30 0 S eP 1500 0 ct 1800 1975 H ay 1500 J une 1800 June 2400 J me 1500 J uly 1500 sq 1800 SeP DUO0 Oct 0400 Oct 0800 1976 Hay 0100 nay 0 100 June 1TOO J nne 0 100 3 uly 0800 Dat e season TT Discharge (s's-' ) Jul y 4385 a ug 4722 A ug 4385 A ug 359 1 A ug 3840 See 1954 Oct 2251 1977 Play 3806 J une 3103 June 4 180 J une 4 225 J uly 3432 July 4078 A ug 2 230 SeP 1869 1978 flay 1900 June 3832 J me 2 956 July 2798 July 297 3 A ug 1999 Oct 1529 1979 Apr 38 2 3 * aY 3U70 3 une 3914 July 399 5 1980 Ray 3 176 J une 2478 June 380 3 O ct 3 145 1976 Aug 3591 1977 Hay 3375 1978 Nay 1455 1979 June 3 800 Aug 1340 1989 Bay 3 320 Texas Creek to Hope
1971 flay 1973 flay nay J une O ct 1974 Hay June 3 ul y 1975 Hay J une July 7976 May Date Time season TT Discharge (a's") May 1900 18 9073 J une 0700 July 000 0 lug 1700 A ug 1100 SeF' 0700 Oct 0500 Oct 0500 1977 Hay 0 100 June 1100 A ug 0400 Aug 2300 197b June 1300 1979 Hay 0700 Hay 1100 J uae 1800 197 3 June 1200 1974 flay 1800 1975 June 03 0 0 1976 Bay 2000 1977 June 1300 1978 June 0900 Jnl y 1200 1979 June 0500 July 0400
Key: season 1 = spring season 2 = STlPmer season 3 = autumn TT = travel time in hours BIBLIOGRAPHY
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