HYDROLOGY II CHAPTER 2 (2) - ROBERSON ET AL, WITH ADDITIONS SCS (NRCS) PRACTICE SURFACE RUNOFF: SURFACE RUNOFF IS IMPORTANT BECAUSE IT PRODUCES FLOODS. COMMON CALCULATION: ESTIMATION OF PEAK FLOODS DURING FLOODING. PEAK FLOODS ARE USED IN DESIGNING STORM DRAINS, FLOOD-CONTROL LEVEES, SPILLWAYS, AND BRIDGE OPENINGS. INFILTRATION: COMPLEX PROCESS THAT DEPENDS ON SOIL TYPE, SOIL GRAIN SIZE, LAND USE, AND SOIL COVER. CONDITION OF THE SOIL SURFACE IS IMPORTANT. ACTUAL INFILTRATION RATE OFTEN DECREASES WITH TIME. TRANSMISSION OF WATER THROUGH THE SOIL DEPENDS ON SOIL SIZE, SHAPE, AND PERCENT OF VOIDS IN THE SOIL. THIS IS THE SOIL'S PERMEABILITY. PERMEABILITY IS OFTEN AFFECTED BY ROOTS AND ROOT DECAY (VEGETATION). VEGETATION INCREASES TOTAL INFILTRATION BECAUSE IT PROTECTS CONDITION OF THE SOIL SURFACE, FAVORING THE PASSAGE OF WATER. HORTON FORMULA: f = fc + (fo - fc ) e-kt VALUES OF CONSTANTS ARE NOT EASILY DETERMINED. MINIMUM INFILTRATION RATES (fc) HAVE BEEN EVALUATED BY SCS, AND CLASSIFIED INTO SOIL GROUPS. IN LIEU OF HORTON'S INFILTRATION, AN AVERAGE INFILTRATION CAPACITY φ-INDEX HAS BEEN USED BECAUSE OF ITS SIMPLICITY. DURING FLOODS, A φ-INDEX IS A GOOD REPRESENTATION. EVAPORATION AND EVAPOTRANSPIRATION EVAPORATION FROM WATER (Ew) AND SOIL SURFACES (En) AND TRANSPIRATION THROUGH PLANTS (T) CAN ACCOUNT FOR SIGNIFICANT VOLUMES OF WATER. EVAPORATION IS THE PROCESS BY WHICH WATER TRANSFORMS INTO VAPOR. EVAPORATION FROM A WATER BODY IS A FUNCTION OF AIR AND WATER TEMPERATURES, THE MOISTURE GRADIENT AT THE WATER SURFACE, AND THE WIND SPEED. DALTON FORMULA (GENERIC): E = (es - ea) f(u) es = saturation vapor pressure at the water surface temperature ea = vapor pressure of the overlying air eo = saturation vapor pressure at the air temperature ea = eo (RH%) /100 f(u) = wind function MEYER EQUATION: E = C (eo - ea) [ 1 + (W/10)] E = EVAPORATION, IN IN/MONTH C = COEFFICIENT VARYING FROM 11 (LAKES AND RESERVOIRS) TO 15 (SMALL PONDS) . eo = SATURATION VAPOR PRESSURE OF THE AIR AT THE MEAN MONTHLY AIR TEMPERATURE, IN INCHES OF MERCURY. W = MEAN MONTHLY WIND SPEED AT 25-FT HEIGHT, IN MILES/HR. EVAPORATION RATES VARY FROM AS MUCH AS 86 IN PER YEAR IN SOUTHEAST CALIFORNIA TO 20 IN PER YEAR IN NORTHERN MAINE. THE STANDARD CLASS A PAN IS USED TO MEASURE EVAPORATION. EVAPOTRANSPIRATION IS THE TOTAL MOISTURE THAT LEAVES THE AREA. IT CONSISTS OF EVAPORATION AND EVAPOTRANSPIRATION. THERE IS EVAPORATION FROM WATER BODIES. THERE IS EVAPOTRANSPIRATION FROM ECOSYSTEMS, INCLUDING LAND AND WATER. CONVENTIONAL WISDOM STATES THAT IN TEMPERATE REGIONS, EVAPORATION AND EVAPOTRANSPIRATION ARE ROUGHLY THE SAME. PENMAN SUGGESTED THAT EVAPOTRANSPIRATION IS 60% OF EVAPORATION IN THE WINTER, AND 80% DURING THE SUMMER. ONLINE CALCULATION OF EVAPORATION/EVAPOTRANSPIRATION: ONLINEHYDRO. RAINFALL-RUNOFF RELATIONS TIME OF CONCENTRATION: THE TIME REQUIRED FROM A DROP OF WATER TO TRAVEL ON THE LAND SURFACE, FROM THE MOST DISTANT POINT IN THE WATERSHED/BASIN TO THE OUTLET. THE CONTINUOUS RECORD OF FLOW AT A STATION IS CALLED STREAM HYDROGRAPH. THE SHAPE OF THE HYDROGRAPH REFLECTS PHYSICAL CHARACTERISTICS OF THE DRAINAGE BASIN, AS WELL AS THAT OF THE STORM PRODUCING THE HYDROGRAPH. PEAKED HYDROGRAPHS SHOW LITTLE DIFFUSION: SMALL MOUNTAINOUS BASINS. SMOOTH HYDROGRAPHS SHOW GREAT DIFFUSION: LARGE BASINS OF MILD OVERALL SLOPE. STEEP SLOPES WILL PRODUCE MORE RUNOFF THAT FLAT SLOPES? VEGETATED DRAINAGE AREAS WILL PRODUCE LESS RUNOFF THAN BARE AREAS? Tesechoacan river at Azueta, Mexico, year 1972. QUANTITY OF RUNOFF DEPENDS ON WHETHER IT IS SHORT TERM OR LONG-TERM. WHETHER THE RUNOFF COMES FROM SURFACE S OR SUBSURFACE U. WE HAVE TO DISTINGUISH BETWEEN PEAK AND VOLUME. PEAK IS SHORT-TERM; VOLUME IS LONG-TERM. THE SAME CHARACTERISTICS THAT WILL DECREASE SHORT-TERM RESPONSE WILL INCREASE LONG-TERM RESPONSE. RATIONAL EQUATION IS THE CLASSICAL SHORT-TERM RESPONSE MODEL. IT FOCUSES ONLY ON THE PEAK DISCHARGE. THE VOLUME CAN ALSO BE CALCULATED, BUT IT IS NOT THE MAIN FOCUS. Qp = CIA THIS EQUATION HAS BEEN WIDELY USED IN THE DESIGN OF SMALL DRAINAGE SYSTEMS, SUCH AS AIRPORT AND URBAN DRAINAGE. THE RUNOFF COEFFICIENT VARIES FROM 0 TO 1; IN PRACTICE, RANGE OF 0.05-0.95. RATIONAL EQUATION IS DIMENSIONALLY HOMOGENEOUS. IT IS RATIONAL BECAUSE IT IS BASED ON THE RUNOFF CONCENTRATION PRINCIPLE. IT JUST SAYS THAT PEAK DISCHARGE WILL BE A PERCENTAGE OF THE MAXIMUM POSSIBLE, WITH THE PERCENTAGE DETERMINED EMPIRICALLY. THE MAXIMUM POSSIBLE DISCHARGE IS RATIONAL. RAINFALL DURATION IS EQUAL TO THE TIME OF CONCENTRATION. KIRPICH FORMULA: tc = (0.0000335L3/h) 0.385 tc = time of concentration, minutes L = stream length, feet h = maximum difference in elevation in drainage basin, feet HATHAWAY FORMULA: tc = {2Ln / [3(S)0.5]} 0.47 tc = time of concentration, minutes L = stream length, feet S = mean slope of the basin n = Manning's roughness coefficient. SIMPLICITY OF THE RATIONAL METHOD IS MISLEADING. THE RUNOFF COEFFICIENT FOUND IN TABLES IS FOR 5 AND 10 YR FREQUENCY. FOR LONGER FREQUENCIES, GREATER VALUES ARE JUSTIFIED. FREQUENCY OF RAINFALL EQUAL TO FREQUENCY OF RUNOFF? EXAMPLE 2-11 USE THE RATIONAL METHOD TO FIND THE 10-YR PEAK RATE OF RUNOFF FOR THE TWO AREAS, AND FOR THE CHANNEL AT POINT b. ALL FLOW FROM AREA A1 ENTERS THE CHANNEL AT POINT a. ALL FLOW FROM AREA A2 ENTERS THE CHANNEL AT POINT b. ASSUME IDF OF FIG 2-16 IS APPLICABLE. TIME OF FLOW FROM a TO b IS 8 MINUTES. SOLUTION: FOR A DURATION OF 20 MINUTES, FIG. 2-16 SHOWS I = 1.2 IN/HR THE PEAK RATE OF FLOW AT a IS: Qp = CIA = 0.6 × 1.2 × 6 = 4.3 CFS. THE PEAK RATE OF FLOW AT b, WITHOUT AREA A1, IS: Qp = CIA = 0.8 × 2.3 × 4 = 7.4 CFS. TO FIND THE PEAK RATE OF FLOW AT b, WE MUST CONSIDER BOTH AREAS SIMULTANEOUSLY. THE TIME OF CONCENTRATION AT b IS 20 + 8 = 28 min. THE PEAK RATE OF FLOW AT b, WITH AREA A1, IS: Qp = ∑ CIA = (0.6 × 1.0 × 6) + (0.8 × 1.0 × 4) = 6.8 CFS. THIS ASSUMES ONLY ONE STORM. NEGLECTS TRANSPORT IN THE CHANNEL. STORAGE IN CHANNEL IS NEGLECTED BY RATIONAL METHOD. BOOK ASSUMES TWO STORMS, AND INCLUDES TRANSPORT IN THE CHANNEL. IN THIS CASE: Qp = ∑ CIA = (0.6 × 1.2 × 6) + (0.8 × 1.0 × 4) = 7.5 CFS. SEE HOW DIFFERENT ASSUMPTIONS ABOUT STORMS CAN MAKE THE ANALYSIS COMPLEX. SOIL-COVER COMPLEX METHOD CURVE NUMBER METHOD: USED WHERE RUNOFF RECORDS ARE NOT AVAILABLE. RUNOFF CAN BE DETERMINED IN TERMS OF A SINGLE PARAMETER CN. CN VALUES WERE DEVELOPED EMPIRICALLY BASED ON DATA ON RAINFALL, SOIL TYPES, COVER, LAND USE, SOIL CONDITION, AND ANTECEDENT MOISTURE. CN SHOWN IN TABLES ARE FOR AMC II [NORMAL MOISTURE], WHICH HAS BEEN FOUND TO FREQUENTLY PRECEDE THE OCCURRENCE OF ANNUAL FLOODS. DEVELOPMENT OF CURVE NUMBER METHOD IS CONCEPTUAL/EMPIRICAL. THE MAIN CONCEPT OF CN METHOD IS THAT RETENTION ACHIEVES A MAXIMUM VALUE, KNOWN AS POTENTIAL RETENTION. INFILTRATION RATE ULTIMATELY BECOMES ZERO. THIS ASSUMPTION IS GOOD FOR FLOODS, BECAUSE SOIL PROFILES CAN BE COMPLETELY FILLED; THEY ARE NOT INFINITELY LEAKING. RUNOFF CURVE NUMBER EQUATION:   PROPORTIONALITY BETWEEN RETENTION AND RUNOFF: (P - Q) / S = Q /P THE RATIO OF ACTUAL RETENTION (P - Q) TO POTENTIAL RETENTION S, IS EQUAL TO THE RATIO OF ACTUAL RUNOFF Q TO POTENTIAL RUNOFF P. IN PRACTICE, AN INITIAL ABSTRACTION IS INCLUDED BECAUSE EXPERIENCE SHOWS THAT RUNOFF DOES NOT BEGIN IMMEDIATELY AFTER RAINFALL BEGINS. (P - Ia - Q) / S = Q /(P - Ia) Ia = 0.2 S Q = (P - 0.2 S)2 /(P + 0.8 S) SINCE S VARIES WITHIN A RELATIVELY LARGE RANGE (ZERO TO INFINITY), A MAPPING PARAMETER CN IS INTRODUCED, SUCH THAT CN = 100 FOR S = 0; AND CN = 1 FOR S = 990 IN. NOTE THAT THE TRANSFORMATION IS ARBITRARY. CN IS A SURROGATE FOR S. TABLE CN IS FOR AMCII. DRIER CONDITIONS (AMC I) WILL PRODUCE LESS RUNOFF; WETTER CONDITIONS (AMC III ) WILL PRODUCE MORE RUNOFF. MOCKUS INTERVIEW. PROCEDURE FOR USING CN METHOD -- STUDY THE SOIL TYPE, LAND USE AND COVER, HYDROLOGIC CONDITION, AND AMC OF DRAIN AGE AREA. SELECT A PROPER HYDROLOGIC SOIL GROUP. MAY NEED AERIAL WEIGHING. -- SELECT CN FOR PROPER HYDROLOGIC CONDITION: POOR, FAIR, GOOD. -- SPATIALLY WEIGH CN VALUES. -- FIND ACCUMULATED PRECIPITATION, IN. -- ESTIMATE RUNOFF USING P AND CN. Deforestation in Loja, Ecuador. EXAMPLE 2-12: DETERMINE 2-HR INCREMENTS OF RUNOFF FOR THE 100-YR, 24-HR STORM OF TABLE 2-6 FOR A 100-ACRE DRAINAGE AREA IN GOOD HYDROLOGIC CONDITION, WITH THE FOLLOWING CHARACTERISTICS: 25 ACRES IS COMPOSED OF PASTURELAND HAVING A SHALLOW SANDY-LOAM SOIL, AND 75 ACRES IS FOREST LAND WITH A CLAY LOAM SOIL. ASSUME CONSIDERABLE RAIN HAS PRECEDED THE STORM TO BE ANALYZED. SOLUTION: 25-ACRE SUBAREA: SOIL GROUP C, CN = 74 (PASTURE) 75-ACRE SUBAREA: SOIL GROUP C, CN = 70 (WOODS) CN (AVERAGE) = [(74 X 25) + (70 X 75)]/100 = 71 ASSUME WET CONDITION. FROM TABLE 72: CN = 88 DEVELOP TABLE OF ACCUMULATED PRECIPITATION IN TWO-HOUR INCREMENTS. FOR EACH PRECIPITATION, FIND Q FOR CN= 88. THE TOTAL RUNOFF IS 6.1 IN, THE TOTAL PRECIPITATION IS 7.5 IN. 1.4 IN WERE LOST TO INFILTRATION. METHOD QUESTIONABLE FOR AREAS GREATER THAN 5 TO 10 SQUARE MILES? TR-55 METHOD. MORE ON THE SCS METHOD. STREAMFLOW DETERMINATION OF PEAK STREAMFLOW THAT WILL BE EQUALED OR EXCEEDED ON THE AVERAGE ONCE IN A SPECIFIED NUMBER OF YEARS. PEAK FLOW CAN BE DETERMINED THROUGH STATISTICAL MEANS. WHEN Q RECORDS ARE NOT AVAILABLE, BUT P RECORDS ARE AVAILABLE, USE UNIT HYDROGRAPH FOR MIDSIZE BASINS. THE HYDROGRAPH: IT IS DIVIDED INTO -- BASEFLOW, -- RISING LIMB, -- PEAK SEGMENT, -- FALLING LIMB. RECESSION CURVE IS DUE TO FLOW OF GROUNDWATER. TIME-TO-PEAK IS IMPORTANT. BANK STORAGE IS ALSO IMPORTANT. STREAMFLOW HYDROGRAPH INTEGRATES ALL THE PHYSICAL PROPERTIES OF THE BASIN. UNIT HYDROGRAPH BUILDING BLOCK TO BUILD THE STORM OR FLOOD HYDROGRAPH. UNIT HYDROGRAPH: HYDROGRAPH FOR 1 UNIT OF EFFECTIVE RAIN FOR A GIVEN DURATION AND DRAINAGE AREA. LINEARITY AND SUPERPOSITION ARE THE PRINCIPLES OF THE UNIT GRAPH. TWO TYPES OF UNIT HYDROGRAPHS: -- MEASURED -- SYNTHETIC SYNTHETIC UNIT HYDROGRAPHS WHEN DATA IS NOT AVAILABLE. SNYDER AND SCS METHODS. THEY ARE BASED ON TIME LAG (TIME TO PEAK), PEAK FLOW FORMULA, AND TIME BASE FORMULA. SNYDER METHOD PROVIDES A REASONABLE ESTIMATE FOR LARGE BASINS (MORE THAN 400 MI2) . SCS METHOD IS MORE APPROPRIATE FOR SMALLER BASINS (LESS THAN 400 MI2). FOR SMALL WATERSHEDS, THE TIME BASE IS APPROXIMATELY 4-5 TIMES THE TIME TO PEAK. STORM DURATION SHOULD NOT EXCEED 20 PERCENT OF THE TIME OF CONCENTRATION. CONVOLUTION:   COMPOSITE FLOOD HYDROGRAPHS. 071214