À . Bhatnagar

Determination of storm runoffby the use of infi ltration index

À . Bhatnagar , M inistry of R ailways,L ucknow, I ndia

SUMMARY: Storm runoff can be estimated quite accurately by an estimate of interception, retentionand an infi ltration index which includes other minor losses âèñÜ as evaporation, transpiration, etc.

Hydrological data of 17 representative catchments in Central India have been analysed toestimate initial losses and infi ltration indices occurring during storms. À ñî -axial relation betweeninfi ltration index (f ), the antecedent precipitation index (API), storm rainfall and storm durationhas also been evolved for the region.

I f storm duration, storm rainfall and antecedent precipitation conditions are known, theinfi ltration index during à storm on à catchment in this region can be determined. Storm ãèï î ããcan then be estimated by subtracting initial loss and infi ltration index from storm rainfall rates.

àéâî é : Üà th6orie de Ãø é1ããàã1î ï pr6sente la mhthode la plus pratique pour dbterminer lespertes par infi ltration qui constituent une partie considbrable des pertes totales pendant Ãà÷åãâå.L 'åñî è1åø åï ã ñÃà÷åãâåâ (åñî è1åø åï ã direct) peut Èãå dbterminb ñÃèï å ø àï 1åãå suffi samment

ðãåñ1âå åï å÷à1èàï ã les ðåããåâ |ï |ã|à1åâ sous la forme de Ã|ï ãåãñåðã1î ï , de la retention et de la perteinit iale par infi ltration et en introduisant Ãí è)|ñå d'infi ltration qui tient compte de Ãø é1ããàã|î ï et

des pertes moins importantes comme Ãå÷àðî ãàã1î ï , la transpiration etc.Les éî ï ï ååâ hydrologiques de 17 bassins reprbsentatifs en Inde Centrale sont àï à1óâáåâ pour

dbterminer les pertes init iales et Ãø é ñå ãÃãï é11ãàã|î ï pendant les averses.L es graphiques rbgionaux de relation entre Ãèüé ñå ñÃø é1ããàã1î ï (f ), Ãø é ñå des prbcipitations

prbcbdentes, les prbcipitations de Ãà÷åãâå et la äèãåå de Ãà÷åãâå ont åãå 6galement envisag6s.Si on connait la äèãåå de Ãà÷åãçå, les prbcipitations de Ãà÷åãçå et les condit ions des prbcipita-

tions prbcbdentes Ãø é ñå ãÃø é1ããàã1î ï pendant une averse ðî èã le bassin de cette region peut etreä@åãø |ï 6. On peut done å÷à1èåã Ãåñî è1åø åï ã direct si on soustrait de la valeur des prbcipitationsde 1'averse la perte initiale et Ãø é ñå d 'infi ltration.

I N T R O D U C T I O N

H ydrological studies often require an est imate of r unoff l ikely to resul t from à designstorm . Eff ect ive rainfal l (rainfall pr oducing runoff ) in successive smal l unit per iods mayfur ther be required for use in unit hydrograph appl icat ions. The infi l trat ion theory withcer tain appr oximat ions, off er s à pr actical method of estimat ing total stor m runoff andnet r ainfalls in unit per iods from à design storm . The use of infi l trat ion indices withini t ial loss allowance has fur ther simpl ifi ed the procedure (without sacr ifi cing the àññè-

r acy) . H ydrological data collected at 15 sites in Centr al I ndia region have been analysedto provide à method of determin ing infi l tr at ion indices and in it ial loss estimates. Theresul ts of the analysis are presented in this paper . A l l values given in th is paper havebeen conver ted fr om fps units.

R U N O F F A N D I N F I L T R A T I O N

R unoff is the residual of rainfal l that runs off fr om land af ter var ious losses have beenmet . À method of estimat ing sur face runoff from rainfall has to consider var ious typesof losses such as in terception and transpirat ion by trees and plants, retention , detent ion ,infi l tr at ion into soil , evaporation, stor age if any , etc., the infi ltration losses generallyp laying à very signifi cant and controll ing r ole. Once the infi l trat ion losses are determined

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D e t er m i n a t i o n î / ' s t o r m ã è è î ô Üó t h e t ts e î / ' i np l t r a t i o n i n d ex

and if other losses can be assessed separately or neglected, the surface runoff can beworked out. The usual procedure for determining runoff by the use of standard infi ltrat ioncapacity curves consists of drawing the standard infi ltration capacity curve upon anintensity-time graph of the rain and estimating the area between the two curves.

Complicated procedures have also been evolved for evaluating detention and retentionlosses. Infi ltration capacity of à soil is normally highest at the beginning of à rainfallwhile rainfall generally begins at moderate rates and à substantial period may elapsebefore rainfall intensity exceeds infi ltration to start runoff . The rainfall also occursintermittently and not always at rates greater than infi ltration capacity. The procedureis also not capable of accounting for any interfl ow, i .e. part of infi ltration which subse-quently appears in channels without reaching the ground water table. The use of standardinfi ltration capaci ty curves for estimating runoff , therefore, has à very limited application.À semi-empirical approach using infi ltration 1ï é ñåû ç more practical and probably moreaccurate. This approach assumes that after the " init ial loss" comprising initial moisture

defi ciency, interception loss, retention loss etc. have been catered for, any rainfall øexcess of the " infi ltration index " produces surface runoff ; The amount of precipitation

that can occur without producing runoff is therefore called initial loss. The average rateof loss, after the initial losses have been met, rainfall in excess of which will equal surfacerunoff , is defi ned as the infi ltration index (f ), (rainfall rates less than the infi ltrationindex being absorbed without producing surface runoff ). The infi ltration index, deter-mined from observed hydrological data thus includes infi ltration, evaporation, trans-piration and that part of detention losses wich percolates into soil after rainfall ends.The infi ltration index does not represent the true infi ltration rate but should be regardedonly as an index. But since they are derived from observed rainfall-ãëóï î (Ò data, theyare considered superior to infi ltration capacity curves for predicting storm ãø þ é'.

Ð À ÒÀ U SED A N D D ESCR I PT ION OF R EG I ON

The drainage areas of catchments studied vary from 12.5 to 362 sq. km and the hydro-logical data used consisted of hourly gauge and frequent discharge observations (using

T A B L E 1 . D e t a i l s o f B r i d g e s U s e d i n S t u d y

St r eam N o . L o c at i o n o f g au g in g si t eM i l e a g e R a i l w a y S e c t i o n N o . î Ã C a t c h m e n t a r e a r a i n g a u g e s V e a r s d a t a u s e d

( s q . k m ) i n c a t c h m e n t

1

2

3

4

5

6

7

8

9

1 0

1 1

1 2

1 3

1 4

1 5 1 0 0 / 2

1 8 5 / 2 3

3 9 4 / 7

6 0 4 / 2 1

5 6 6 / 2 1

4 5 4 / 7

5 1 7 / 1

5 5 7 / 1 5

7 7 / 9

2 1 8 / 2 5

1 / 1 5

1 / 9

2 5 3 / 1

3 6 5 / Î

70 / 6 B o m b a y - D e l h i

B o m b a y - N a g p u r

I t a r s i - N a g p u r

B o m b a y - D e l h i

B o m b a y - A I I a h a b a d

M a n m a d - S e c u n d e r a b a d

P a r b h a n i - P u r l i

M u k h e d - A d i l a b a d

K h u r d w a d i - M i r a j

B o m b a y - M a d r a s

B o m b a y - S e c u n d e r a b a d 2 5 .5 12 . 5 349 .0 362 .0 137 .0 1 16 .0 55 .5 342 .0 9 3 . 5 3 1.4 50 .7 79 .0 114 .0 1 18 . 57 1 . 5 2 1 6 6 3 4 2 5 4 3 3 2 3 3 3 1 9 6 2 - 1 9 6 4 1 9 6 3 1 9 6 1 - 1 9 6 4 1 9 6 1 - 1 9 6 4 1 9 6 4 1 9 6 1 - 1 9 6 4 1 9 6 3 1 9 6 4 1 9 6 1 - 1 9 6 4 1 9 6 4 1 9 6 4 1 9 6 4 1 9 6 4 1 9 6 4 1 9 6 2 - 1 9 6 4

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D eter mi nati on of ì î òò r unog by the use of i nf t l t r ati on i ndex

Initial loss was then determined for each storm by the following procedure:

1. The time of concentration of the catchment (Ò,) is roughly ascertained.2. Approximate length of main stream from site to extremity of catchment (L) and

approximate distances of each rain gauge stat ion along the stream (li , ls, etc.) aremeasured from à catchment plan.

3. Approximate times of travel of water from each zone controlled by the rain gaugestation to the site are calculated as equal to (l i Ò,)/~É = ti etc.

4. From the observed data, time the fl ood started at site (Ò) is obtained. Amounts ofrainfal l at each rain gauge station prior to this time minus the travel time from raingauge to site (Ò — ti ) etc. are determined.

5. The maximum of these fi gures is regarded as the approximate initial loss, since anyeff ective rainfall prior to (Ò — ti ) would have caused an earlier fl ood at site.

Infiltration index for each fl ood was determined by the following procedure:

1. From the discharge data of the fl ood, ground water fl ow is separated and the surfacerunoff in ò ò . is determined. Straight line base fl ow separation is adopted for the study.

2. The area controlled by each rain gauge in catchment is obtained by the TheissenPolygon Method.

3. Successive hourly rainfalls observed by each rain gauge in the drainage area is ta-bulated.

4. Value of initial loss as estimated ø previous para is noted against each rain gaugeand deducted from rainfall .

5. À trial value of infi ltration index (f ) ø ò ò /h. is calculated by dividing the totalinfi ltration losses by the approximate duration of storm in hours. The infi ltrationlosses can be obtained by subtracting the total of surface runoff and initial loss fromrainfall .

6. At each rain gauge station, hourly runofl ' is obtained by deducting f from successive

hourly rainfal l amounts, after the initial losses have been met with.7. The runoff values are added for each rain gauge zone. The weighted runoff from the

whole catchment is next obtained.8. The value of runoff obtained above is compared with observed runoff. In case of

variation between the two values, the trial value is modifi ed as required and freshtrials made ti ll the calculated runoff is equal to the observed runoff .

This method takes into consideration the var iation of intensity and aer ial distr ibutionof rainfall . I f the catchment has materially diff erent hydrological areas, diff erent valuesof / can be adopted for the corresponding areas.

R E SU L T S

Data of 52 moderate and heavy fl oods caused by fairly heavy storms in this area wereanalysed by the method outl ined in para 5, and values of initial losses and f were obtai-ned. The values of initial losses varied from 2.5 mm to 25 mm and the infi ltration indexvaried from 7.5 mm to 0.75 mm/h. The storms had produced rainfalls from 27.5 ò ò to277 mm and their duration varied from 3 to 64 hours.

Infi ltration capaci ty of à soil is not constant . I t not only changes during the fl ood, butthe minimum capacity changes appreciably from fl ood to fl ood. The âàò å applies toinfi l tration index. The factors aff ecting infiltration index (also infi ltration capacity) arenumerous, the important ones being :

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À . B hatnagar

9. Compute weighted hourly runoff if there more than one rain gauge.10. Add the weighted hourly runofF to get storm runoff , if required.

For determining maximum discharges, it is customary to use the lowest value of indexwhich will occur under the worst combination of factors. For such cases, à minimumvalue of 0.75 mm/h for infi ltration index may be used. À reasonably 1î ÷ value of ILwill be 2.5 mm. The method of determining storm ãï ï î é is the same as pointed out above.

Though the infi ltration and 1L values have been obtained for watersheds up to 362 sq.km in area, yet these values can be applied to much larger areas without introducing anyappreciable error. I f à large portion of catchment is hil ly, it is advisable to use à é éåãåï 1infi ltration index for the hilly portion.

S U M M A R Y

Determination of storm ãï ï î é' is required in all engineering studies. The infi ltration

index approach provides à practical method of estimating losses, and runofF. The practiceassumes that surface ãï ï î é' approximately equals the difference between the rainfall and

infi ltration and other recurring losses during the period of rainfall excess. Losses occur-ring after the cessation of rainfall are either ignored or accounted for by the infi ltrationindex. The semi-empirical method requires subtracting an infi ltration index from hourlyrainfall amounts after the initial moisture defi ciency, interception, retention and surfacestorage accounted by an Initial Loss Value have been met with. Similarly the infi ltrationindex covers infi ltration losses, evaporation, detention, transpiration etc., the infi ltrationlosses forming à maj or part of the total recurring losses.

Hydrological data of 15 catchments with drainage areas from 12.5 to 362 sq. km havebeen analysed to determine initial loss and infi ltration indices occurring during thestorms. À graphical ñî axial correlation has been indicated between antecedent precipi-tation index, storm duration and storm rainfall . An approximate relation has also beenindicated between API and initial loss. With the help of these two curves, storm ãï ï î éand hourly runoff amounts from à design storm can be determined.

R E F E R E N C E S

1. B HATNAGAR, À . S . ( 19 64) : " I n fi l t r at i o n I n d i ces f o r C en t r a l I n d i a C at ch m en t s " , C en t r a l B oar d

of I rrigation and Power Journal, vol . 21. No. 4.2. BHATNAGAR, À .S. (1966): " Infi ltration Index and the A PI for Central India Catchments" ,

I ndi an Êàéøàó Techni cal Bulleti n, vol . ÕÕØ , N o. 162.3 . Ñ ß ÅÀÎ ÅÊ, W . P ., Jv sTIN , J . D . an d Í í î â, J . ( 19 57) : " E n g in eer in g f o r Ð àï è " , v o l . 1. C h ap m an

& H all L td., London.4. " Hydrology H andbook " (1957): Ameri can Society î~ Ñò î Engi neers, Manuals î ( Engineering

Practice, N o. 28.

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