Peak runoff simulation in a subarctic region

NOTES

Un modkle mathematique de prediction du debit de pointe le long du trace de la future route de la vallee du Mackenzie a ete etabli pour la region comprise entre Fort Good Hope et la route Dempster.

Les rCsultats montrent que la fonte de neige de fin mai ou dCbut juin engendre le debit de pointe annuel.

On a etendu la portee des donnees hydrographiques existantes par la methode de I'hydrogramme unite. Un ensemble de quatre stations de jaugeage de conditions hydrologiques similaires a celles de la rCgion d'etude a etC utilisC. La dimension de leurs bassins versants varie entre 250 et 8200 mi2 (648 a 25000 km2). On a ainsi engendre un total de 46 debits de pointe annuels.

En utilisant les paramktres hydrographiques et meteorologiques, on a ensuite etabli une correlation mathematique. Les resultats montrent que les facteurs de corrClation les plus impor- tants sont la taille des bassins versants, le pourcentage de lacs dans chaque bassin, la quantite d'eau Cquivalente B la neige au sol au debut de la periode de fonte et la duree de la fonte de la neige. Le modkle a Cte calibre pour des bassins versants de taille comprise entre 100 e t 10000 mi2 (250 a 25 000 km2).

[Traduit par la revue] Can. J. Civ. Eng., 3, 555 (1976)

Peak runoff simulation in a subarctic region

J. PENEL A N D T. KUNG Fenco Consrrl/un/s Ltd., 1116, Liberty Building, Edmonton, Altu., Canrida T5J2W9

Received February 6, 1975

Accepted August 4, 1976

Due to the lack of stream guaging stations, a peak flow simulation based on physical and meteorological parameters was established for the area along the proposed Mackenzie Valley Highway between Fort Good Hope and the Dempster Highway.

Calculations based on snowmelt and rain-on-snow runoff were developed, as it was found that the snowmelt of May or early June gave the yearly spring peak discharge.

Due to the gap in existing flow data, a unit hydrograph method was developed to generate additional yearly spring peak discharges. Altogether, hydrographs from four gauged watersheds of similar physical conditions with size ranging from 250 to 8200 mi2 (648 to 21 240 km2) were used. In total, 46 yearly peak flows were generated.

A regression equation ofpeak discharge computation was derived, usingdifferent hydrological and meteorological parameters. It was found that the most significant factors were the drainage basin area, the lake areas in the drainage basin, the water equivalent of the snow on the ground prior to melt, the rainfall in the period close to peak discharges, and the duration of snowmelt.

The simulation was calibrated for drainage basins between 100 and 10000 mi2 (250 to 25000 km2).

Objective of the Work The purpose of the study was to determine

the peak flow of rivers and streams for a given return period in order to obtain the bridge opening and culvert sizes along the proposed Mackenzie Valley Highway between Fort Good Hope and the Dempster Highway in the North- west Territories, latitude 66" 16' to latitude 68" 18'. The design return period was 50 years, as required for the type of highway under consideration.

Due to the complete lack of gauging stations on the streams under study, a snowmelt and

rain-on-snow runoff simulation of peak flow computation was established for the area along the proposed Mackenzie Valley Highway between Fort Good Hope and the Dempster Highway. In a first step the unit hydrograph method was used to extend the existing data and finally a computer correlation was established between the various physical and meteorological parameters. Figure 1 shows the various phases of the study.

Brief Description of the Study Area The region east of the Mackenzie River is

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CAN. J. CIV. ENG. VOL. 3, 1976

b e o f records of a 9 9 T o t o f record 17 years

Unit Hydrograph Method (snovmelt + r a i n f a l l )

I 1 I

Number of years generated

Regression Equation

Q = f ( A , AL V

each p a s t Year pe& flow can be generated fo r ungnuged r i v e r between 100 and 10 OD0 mi2 ( 2 5 0 t o 2 5 0 0 0 km2).

FIG. 1. Study summary chart.

one of moderate relief, rising from approxi- mately 100 ft (30 m) above sea level at the Mackenzie River to over 1200 ft (365 m) in the headwaters. A continuous cover of vegeta- tion is composed of spruce trees with open spaces of muskeg and swamp. Numerous small lakes are found that cover up to 33% of the watershed area. In some cases major lakes are found slightly upstream of the proposed highway crossing.

Unit Hydrograph Method Due to the complete lack of gauging stations

in the study area at the time of the study, records from four outside watersheds with similar hydrological conditions were used:

Willowlake River (area of 8200 mi2 (21 240 km", with 4 years of complete record)

Ross River (2800 mi"7250 km2), 1 1 years of record)

Martin River (665 mi2 (1722 km'), 1 year of record)

Caribou Creek (250 mi"648 km') , 1 year of record).

Locations of these basins are shown on Fig. 2. A total of 17 years of data were available to use hindcasting techniques. This amount of data was insufficient to perform a rigorous statistical analysis.

The analysis of the hydrological and meteorological data shows that the main peak discharge in that area is due to snowmelt during May or early June. There is a possibility of some rainfall in addition to the snowmelt as shown on Fig. 3. For the small watershed used in the study (Caribou Creek and Martin River), the graphs show an extremely sharp peak for maximum flow during spring. Later June rainfall is represented by a negligible peak which is due to melting of the active layer of the permafrost, and to the high water storage capacity resulting from this condition.

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DRAINAGE B A S I N S U S E D I N R E G R E S S I O N A N A L Y S I S

FIG. 2. Locations of outside watersheds.

At the time of peak flow in early spring, the form than rainfall, and would make application runoff coefficient is high and remains constant of the unit hydrograph method easier. for the duration of the peak flow; unit hydrographs can therefore be developed with a Snowmelt Computation reasonable degree of confidence. The variation of the degree-day factor has

For large watersheds, peak flow is caused been considered on an annual basis since the mainly by snowmelt, in which case snowmelt actual yearly snowmelt period is computed ac- across a large watershed would be more uni- cording to temperature. Using the water equiva-

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Willow lake River 1972

---- snowmelt E E

- rainfall - 1 0

- 5

I I, 1 1 1 1 : I I . , I

I

I 15 3 1 15 30 15 31 15 3 1 15 30

MAY JUNE JULY AUG SEPT

FIG. 3. Hydrograph showing snowmelt causing peak discharge of Willowlake River in 1972.

lent of snow on the ground, measured several 111 M,i,,, = 0.039 ( T , - 32) times during spring by the Atmospheric En- vironment Service at various locations along with T , mean daily air temperature in OF. the Mackenzie Valley, an equation of daily The snowmelt calculation at Fort Simpson is snowmelt was developed as a function of the given as one example (see Fig. 4). It was mean daily air temperature. Snowmelt in inches found that the duration of snowmelt in that of water is as follows: part of the country was between six days and

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. c ~ m p u t a d v e l u a

F a r To > 3 2 ' F

Sno .m.11 Y l i n . 1 : 0 . 0 3 9 ( T a - 3 2 1

0 1 0.1 I

FIG. 4. Snowmelt computation-Fort Simpson 1966.

one month, with an average of 10 to 12 days. Actual water equivalent of snow on the ground was calculated in a similar manner for each year of available record.

To extend the length of peak flow records, a unit hydrograph was developed for each of the four watersheds. Each recorded hydrograph was broken into snowmelt and rainfall runoff using the procedure shown on Fig. 5 . The runoff coefficient was assumed to be constant for snowmelt and rainfall at the time of peak flow. This allowed the development of separate snowmelt and rainfall unit hydrographs for each of Willowlake River, Ross River, Martin River, and Caribou Creek watersheds. During early spring flow, the soil is frozen and the groundwater flow is extremely low, accounting for low base flow.

To develop a unit hydrograph, an S curve was constructed for various snowmelt ~er iods . Peak flow records were then extended for all years of meteorological and 'snow on the ground' data as calculated previously. Records were extended to an average of 11-12 years for each watershed. A total 46 yearly peak

flows was generated. Willowlake River was one of the watershed areas used in the study for which documentation was the most adequate, with 7 years of records and 4 years of complete peak records. The unit hydrograph was developed for 1 year and checked against the other 3 years of record. Results of the analysis are shown on Figure 6. The close agreement give confidence in the use of the unit hydrograph method for this specific area. The method can be used for watersheds as large as 8200 mi"21 240 kmy. An identical technique was applied for Ross River to generate 11 years of record.

Regression Analysis The following hydrological and rneteorologi-

cal parameters were tried by computer to cor- relate the annual maximum discharge:

A = area of drainage basin in square miles AT, = area of lakes and ponds in the drain-

age basin in square miles V , = water equivalent of snow on the

ground at the beginning of the melt period in inches

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1:

IMAY 51 T l m a , day

FIG. 5. Procedures to generate hydrographs of Willowlake River in 1972.

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NOTES 561

M o x i r n u r n a n n u a l d ~ r c h o r g e r e c o r d e d

FIG. 6. Comparison between recorded and generated discharges.

R = rainfall in the period close to the peak discharge in inches

d,, = duration of snowmelt in days d, = duration of rainfall in days S:, = average river slope The average river slope did not give reliable

correlation and therefore was deleted from the analysis. The measurement of rainfall duration (d,.) was very questionable as there could be several small rainfalls during peak flow. This is especially true for large watersheds like Willowlake. As (d,.) did not improve the correlation coefficient. it was also deleted. Numer- ous runs of the computer correlation were tried. The most significant parameters were found to be: A, A , , V,, R , and d,.. A and AI, were combined into one parameter in order to decrease the number of independent variables in the correlation. Such a combination makes it possible, up to a certain point, to account for the effect of the lakes, which are extremely numerous in that part of the country and as in the case of the Willowlake watershed, cover up to 22% of the area.

The regression equation used was of the form :

Using spring peak discharges generated by the unit hydrograph method for basins of Willowlake River, Ross River, Martin River, and Caribou Creek with their corresponding historical meteorological data and the measured values of A and AL, the constants C1, k,, k,, and k, were determined to be as follows:

Cl = 2.65

k3 = -0.1 The variables A and AI, used in this analysis

were measured from topographic maps published by the Department of Energy, Mines, and Resources of Canada. The meteorological data used were adapted from Monthly Records and Snow Cover Data published by the De- partment of Environment of Canada. Thus, the equation used to estimate the yearly peak flood discharge was found to be:

X (V, + R)O." d,.-O.l

In metric units results become:

with Q,,, in m3/s, A and Ar, in km" V e and R in mm, and d , in days.

The multiple correlation coefficient of this regression equation is 0.95. Considering the lack of field data in northern Canada, this correlation can be considered as good. Equa- tion [4] was used in our case to generate the yearly peak flow for each highway crossing under study for the year of meteorological data available (1 1 years of data available). A fre- quency analysis was then undertaken and peak discharge was extended to the design return period of 50 years.

Discussion of Results

[2] ell, = Cl (A - A,,)"I (V, + R)li2dv1;3 As expected, [4] shows clearly that the drainage area and the amount of snowmelt are

u

where Q,,, = annual peak discharge in cubic governing factors determining peak discharge. feet per second; C1 = a coefficient; and, kl, k,, Snowmelt duration (degree-day factor) ap- k, = constant exponents determined by apply- pears to be of less importance as seen by the ing statistical principles. power of d, coefficient equal to 0.1. The

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562 CAN. J. CIV. EN(

; , - 2 0 0 0 0

Rapresaion Equation 1 ~ . , o ~ ~ ~ Q , , , = 2.65 ( ~ - ~ , ? ~ ~ ( ~ a . ~ p ( d y j O '

: 2 - . 5 0 0 0

: lo" 1 - - 2 000

: a . . 1 0 0 0

0 0

FIG. 7. Comparison between values of Q ,,,,. and Q. , . c . .

equation was developed for watersheds with scattered lakes covering up to 30% of the total drainage basin.

The comparison between peak discharge generated by the unit hydrograph method (Q,,,.K.) and the peak discharge calculated by the regression equation (Q,,,.,.) is shown as Fig. 7.

We realize 11 years of developed records is extremely small for a projection to a 50 year return. A reliable indication of flood magnitude on a statistical basis is given by the equation developed. It is suggested that this is the most accurate equation to predict peak flows in the study area.

Extensive field work was undertaken in the area under study; highwater marks, slopes, and levels were recorded, and peak discharges were estimated based on the slope-area method. Good agreement was found between field work

3. VOL. 3, 1976

results and the simulation model. This was a reliable check. As in all hydrological runoff relationships, it should not be used where watershed conditions are substantially different from those assumed in the study.

Acknowledgment This paper presents some of the results of a

study carried out by Fenco for the Depart- ment of Public Works of Canada under the title "Hydrology study-Mackenzie Highway - Fort Good Hope to Dempster Highway".

ANDERSON, J. C. and MACKAY, D. K. 1973n. Preliminary results from Boot Creek and Peter Lake Watersheds, Mackenzie DeltaRegion. N.W.T. Tech. Rep. 2.Glaciol. Div.. Water Resour. Branch, Dep. Environ. Ottawa. Can.

19730. Preliminary study of the seasonal distribu- tion of flow in the MackenzieDelta. N.W.T. Tech. Rep. 3 , Glaciol. Div., Water Resour. Branch, Dep. Environ. Ottawa, Can.

CHOW, V . T . 1964. Handbook of applied hydrology. McGraw-Hill Book Co. , New York, N.Y.

DEPARTMENT OF ENVIRONMENT. 1973. Hydrology as- pects of northern pipeline development. Task Force on North. Oil Dev., Rep. No. 73-3, Ottawa, Can.

1963-1973. Snow cover data in Canada. Dep. Envi- ron. Toronto, Ont.

DEPAR~TMENTOF TRANSPORT. 1963-1973. Monthly record, meteorological obser-vations in Canada. Dep. Transp., Toronto, Ont.

GRAY, D. M. 1970. Handbook on the principles of hydrology. Can. Nat. Comm. for the Intelnational Hydrologi- cal Decade, Ottawa, Can.

LINSLEY, R. K. , KOHLER, M. A., and PAULHUS, J. L. H. 1958. Hydrology f o ~ engineers. McGraw-Hill Book Co., New York, N.Y.

NEVILLE, A . M., and KENNEDY, J. B. 1968. Basic statistical methods for engineers and scientists. International Textbook Co., Scranton, Pa.

SELLARS. C. D. 1973. Hydrology studies a t culvert sites on the Mackenzie Highway. Hydraul. Des. Assess. Comm., Environ. Work. Group, Dep. Environ., Ot- tawa. Can.

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Documents

Peak runoff simulation in a subarctic region