Runoff Prediction from Agricultural Lands Rabi H. Mohtar

Thought of the day: Most natural hydrologic phenomena are so complex that they are beyond comprehension, or exact laws governing such phenomena have not been fully discovered. Before such laws can ever be found, complicated hydrologic phenomena (the prototype) can only be approximated by modeling -- Ven Te Chow

Objectives The objective of this module is to predict peak runoff flow rate and total runoff volume over a small watershed (≤ 2000 acres) using the SCS soil-cover-complex method. The goal is to critically evaluate the runoff processes which influence the peak runoff rate and total runoff volume.

Material previously covered - Hydrologic cycle - Precipitation - Soil physical properties - Infiltration - Concept of a watershed

Material to be covered - Introduction to runoff, why we study it and what are the factors affecting it - Conceptual hydrograph - SCS curve number - Soil Cover-Complex Method for determining runoff volume and peak runoff rate - Example problem - Summary

Introduction When water entering an area is more than what can be transmitted or routed by established water courses, flood occurs. Generating hydrographs from big storms becomes the job of flood predictions. We use the word prediction because we still deal with probabilities of events.

Why do we study runoff? - To quantify volume and rate of water to be handled by water management facilities. - To predict soil erosion and transport of surface pollutants. - To identify critical non-point source pollution areas.

What are the factors that affect the runoff process? Watershed related - Slope - Vegetation cover - Length of slope - Soil characteristic Storm related - Rainfall intensity, duration, time, and spatial distribution CONCEPTUAL PRECIPITATION-RUNOFF PROCESS

Figure 1. Conceptual Hydrology Model - Peak runoff rate - Time of concentration - Volume of runoff

Figure 2. Hydrograph of streamflow in response to a rainstorm from a 100-square-kilometer basin. - Base flow - Rising limb - Recession limb - Time to rise - Lag to peak

Figure 3. Rainfall, runoff, infiltration, and surface storage Rainfall, runoff, infiltration, and surface storage during a natural rainstorm on a hillside plot. The shaded areas under the rainfall graph represent precipitation falling at a rate exceeding the infiltration rate. The dark gray area represents depression storage, which is filled before runoff occurs. Light gray shading represents overland flow. The initial infiltration rate is fo and ff is the final constant rate of infiltration approached in large storms. (Modified from Horton, 1940, Soil Science of America Proceedings, vol. 5, pp. 399-417, by permission of the Soil Science Society of America.)

Figure 4. Rainfall and runoff with assumptions.

Figure 5. Dimensionless curvilinear unit hydrograph arc equivalent triangle hydrographs.

The dimensionless curvilinear units hydrograph has 37.0% of the total volume in the rising site, which is represented by one unit of time and one unit of discharge. This dimensionless unit hydrograph also can be represented by an equivalent triangular hydrograph having the same units of size and discharge, thus having the same percent of volume in the rising side of the triangle. - Peak runoff rate - Time of the base Tb - Time to peak - Duration

Precipitation data

Figure 6. Log-probability plot of 30-min. rainfall depths - Probability of occurrence - Return period TIME OF CONCENTRATION

It is the time required for surface runoff water to travel from watershed’s most remote point to the point of interest. There are three methods to determine tc. 1) 0.77 -0.365tc=0.00718L S

2)

0.70.8

0.5

1000L 9CNtc

1140 S

⎛ ⎞−⎜ ⎟⎝ ⎠=

3) chart below

Figure 7. Watershed lag and time of concentration chart

EFFECTIVE RAINFALL It is the rainfall excess. Volume of effective rainfall is the volume of stormwater runoff. Rain=Effective Rain + Abstractions. All rain goes into infiltration until rainfall rate exceeds infiltration rate. At this point, surface storage begins to fill. As long as rain rate exceeds infiltration rate, surface storage continues to fill. Runoff begins when storage is filled. When rainfall is less than infiltration rate, ponds start to infiltrate and runoff stops. Calculations based on Green & Ampt Calculations based on CN Hydrograph Basic terminology Conceptual model Unit hydrograph Shape of unit hydrograph SCS dimensionless unit hydrograph

SOIL-COVER-COMPLEX METHOD

This method is based on the relationship existing between rainfall P, runoff Q, and the water retained on or in the soil during the storm:

aIPQ

SF

−= (1)

where F is the actual retention, S is the potential maximum retention, Ia is the initial abstraction, Q is the actual runoff, P is the potential runoff. The initial abstraction, Ia, is the depth of rain retained on vegetation, stored on the soil surface, or infiltrated prior to runoff. The retention, F, is the difference between effective precipitation (P- Ia) and runoff:

QaIPF −−= )( (2) Substituting (2) into (1), yield:

aIPQ

SQaIP

−=

−− )( (3)

Solving for Q:

)(

2)(

SaIPaIPQ+−

−=

(4)

If we assume, Ia = 0.2 S, then

SPSPQ8.0

2)2.0(+−

= (5)

Curve number is related to S by the relation:

101000+

=S

CN or 101000−=

CNS (6)

Figure 8. Graphical solution of runoff equation

CURVE NUMBER It is a measure of the percentage of precipitation, which is expected to runoff from the watershed and is a function of the soil, vegetative cover, and tillage method.

Table 1. Curve number for agricultural land - Cover type - Hydrologic condition - Hydrologic soil group (Taken from USDA-SCS, 1986).

Cover Hydrologic soil group

Land use Treatment Or Practice

Hydrologic Condition

A

B

C

D

Fallow Straight row ----- 77 86 91 94 Row crops “ Poor 72 81 88 91 “ Good 67 78 85 89 Contoured Poor 70 79 84 88 “ Good 65 75 92 96 “ and terraced Poor 66 74 80 82 “ “ “ Good 62 71 78 81 Small grain Straight row Poor 65 76 84 88 “ “ Good 63 75 83 87 Contoured Poor 63 74 82 85 “ Good 61 73 81 84

Hydrologic condition Degree of soil cover, ability of soil to infiltrate

“ and terraced Poor 61 72 79 82 “ “ Good 59 70 78 81 Close-seeded Straight row Poor 66 77 85 89 Legumes1 “ “ Good 58 72 81 85 or Contoured Poor 64 75 83 85 Rotation “ Good 55 L69 78 83 Meadow “ and terraced Poor 63 73 80 83 “ and terraced Good 51 67 76 80 Pasture Poor 68 79 86 84 Or range Fair 49 69 79 84 Good 39 61 74 80 Contoured Poor 47 67 81 88 “ Fair 25 59 75 83 Good 6 35 70 79 Meadow Good 30 58 71 78 Forest Poor 45 66 77 83 Fair 36 60 73 79 Good 25 55 70 77 Farmsteads 59 74 82 86 Road (dirt)2 ----- 72 82 87 89 (hard surface)2 ----- 74 84 90 92 Open spaces, lawns, parks, golf Courses, etc. Good condition: 75% grass cover

39

61

74

80

Fair condition: 50% to 75% grasscover 49 69 79 84 Commercial and Business Areas (85% impervious) 89 92 94 95 Industrial districts (72% imprvious) 81 88 91 93 Residential: Average lot

size Average % Impervious

1/8 acre or less 65 77 85 90 92 ¼ acre 38 61 75 83 87 1/3 acre 30 57 72 81 86 ½ acre 25 54 70 80 85 1 ACRE 20 51 68 79 84 Paved parking lots, roofs, driveways 98 98 98 98 Streets and roads: Paved with curbs and storm sewers 98 98 98 98 Gravel 76 85 89 91

Dirt 72 82 87 89 Construction site (denuded) 77 86 91 94

water Poor = high runoff Good = low runoff

Hydrologic soil group A D High poor infiltration

Table 2. Correction to antecedent conditions - CN 20 - CN 100, 1:1 relation

Curve Number for

Factor to Convert Curve Number for Condition II to

Condition II Condition 1 Condition III 10 0.40 2.22 20 0.45 1.85 30 0.50 1.67 40 0.55 1.50 50 0.62 1.40 60 0.67 1.30

70 0.73 1.21 80- 0.79 1.14 90 0.87 1.07

100 1.00 1.00 5-Day Antecedent

Rainfall (mm) Condition General Description Dormant

Season Growing Season

I Optimum soil condition from about lower plastic <13 <36 II Average value for annual floods 13-28 36-53 III Heavy rainfall or light rainfall and low temperatures

within 5 days prior to the given storm >28 <53

Runoff volume Runoff volume = Average runoff depth x watershed area

Figure 9. 10-year, 24 hrs rainfall depths

Peak runoff rate (SCS Complex Method)

AQpqpQ = (7)

where A is the area in acres, Q is the runoff depth in inches, qp is the unit peak discharge in cfs/acre inch from Figure 10. Peak flow rate calculations Using the Rational Method This rather simple "model" estimates peak runoff rates by the formula: q = CiA where: q = peak runoff rate, cfs; C = runoff coefficient; with duration equal to the time of concentration i = rainfall intensity, in/hr; and A = area, acres.

avgCiAiC for composite areas: CAi

∑=

∑

The "rationale" of this method is: (1) Units agree: 1 cfs = 1 in/hr x 1 acre, and (2) C (a dimensionless quantity) varies from 0 to 1 and can be thought of as the percent of rainfall that becomes runoff. Assumptions for the rational formula are related to the intensity term and to quantifying C. They include: Rainfall occurs uniformly over the entire watershed. - Rainfall occurs with a uniform intensity for a duration equal to the time of

concentration for the watershed. - The runoff coefficient, C, is dependent upon physical characteristics of the watershed,

e.g. soil type. - The formula is usable for watersheds or drainage areas smaller than 2000 acres. A table with limited C values is: Runoff Coefficients for Rational Equation* Hydrologic Soil Group Land Use, Crop, and Management A B C D CULTIVATED, with crop rotations

Row Crops, poor management .55 .65 .70 .75 Row Crops, conservation mgmt .50 .55 .65 .70 Small Grains, poor management .35 .40 .45 .50 Small Grains, conservation mgmt .20 .22 .25 .30 Meadow .30 .35 .40 .45

PASTURE, permanent w/moderate grazing .10 .20 .25 .30 WOODS, permanent, mature, no grazing .06 .13 .16 .20 Urban residential

30 percent of area impervious .30 .40 .45 .50 70 percent of area impervious .50 .60 .70 .80

Hydrologic Soil Group Descriptions: A -- Well-drained sand and gravel; high permeability. B -- Moderate to well-drained; moderately fine to moderately coarse texture; moderate permeability. C -- Poor to moderately well-drained; moderately fine to fine texture; slow permeability. D -- Poorly drained, clay soils with high swelling potential, permanent high water table, claypan, or shallow soils over nearly impervious layer(s).

Figure 10. Unit peak discharge chart, fixed I/P

Example problem A prosperous and expanding populace in a small upstate New York community is exerting tremendous development pressure upon the last rural watershed in the area. County planners are on the verge of enacting a zoning change that would allow virtually unlimited development in the area. Your task is to evaluate the runoff potential of the watershed under current conditions, and under conditions of uncontrolled development. The watershed now has the following land uses: - old growth forest in good conditions - 300 acres - corn, contoured, good condition - 275 acres - low density residential (1 acre lots) - 20 homes - alfalfa, contoured, good condition - 275 acres - meadows - 130 acres The entire watershed is composed of hydrologic group”C” soils. You have determined that the watershed now has a time of concentration of 60 min., but this would decrease to 30 min. if the area were totally developed. The 100-yr., 24 hrs. rainfall for the area is 5”. 1- Calculate the 100 yr. return period peak runoff at the stream outlet for current

conditions. 2- Calculate the 100 year peak runoff assuming that 1500 homes are built. Associated roads, schools, shopping centers, etc. that are built in the area contribute 0.03 acres of impervious area per home built. Proposed zoning requires 0.25 acre lots. Construction will occur in areas that currently corn, alfalfa and meadow.

Solution Curve number determination before the development:

Soil-Cover Complex Portion CN Portion x CN Forest, good, C soil 0.3 70 21.00 Corn, contour, good, C 0.27 82 22.55 Residential, 1 ac.lot, C 0.02 79 1.58 Alfalfa, contour, good, C 0.275 78 21.45 Meadow 0.13 71 9.23 Watershed weighted avg 75.8

Time of concentration (given): 60 min. 100 year, 24 hrs. rainfall: 5” Runoff depth (chart or equation 5): 2.5” Runoff volume: (2.5”)(1 ft/12”)(1000 acres)(43560 ft2/1 acre)=9,075,000 ft3 Looking at the chart (attached) for drainage area=1000 acres, CN=75, 24 hrs. rainfall = 5”, the peek discharge=400 cfs. CN after development

Soil-Cover Complex Portion CN Portion x CN

Residential, .4 ac. L0t, C 0.375 83 31.125 Impervious 0.045 100 4.5 Forest, good, C soil 0.16 70 11.20 Residential, 1 ac. Lot, C 0.02 79 1.58 Corn, contour, good, C 0.135 82 11.07 Alfalfa, contour, good, C 0.135 78 10.53 Meadow 0.13 71 9.23 Watershed weighted avg. 79.2

Rainfall = 5” Runoff (chart) = 2.9” Runoff volume = (2.9”)(1’/12”)(1000 acres)(43560 ft2/1 acre)= 10,527,000 ft3 Looking at the chart (attached) for drainage area=1000 acres, CN=80, 24 hrs. rainfall = 5”, the peak discharge=650 cfs.

References Dunne, T., and L.B. Leopold. 1978. Water in environmental planning. Freeman and Co.

San Francisco. Jarrett, A.R. 1995. Water management. Kendall/Hunt Publication Company, Dubuque,

IA. Schwab, G.O., D.D. Fangmeier, W.J. Elliot, and R.K. Frevert. 1993. Soil and water

conservation engineering. Fourth ed. John Wiley and Sons, Inc. New York NY. Soil conservation service (recently changed to NRCS). 1972. National Engineering

handbook, section 4, hydrology. SCS, USDA. Soil conservation service. 1986. Urban hydrology for small watersheds. Technical

release 55 (TR-55). SCS, USDA.