2.19 Remote Sensing Of Hydrologic Data _: 3 0 Water-resources Engineering

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WATER-RESOURCES ENGINEERING

urbanization, other major changes in land use, or forest fires may be significant. A change in station location may also cause an inhomogeneity in ?the record. Corrections for changes should be made before the record is used; or alternatively, the analysis can be limited to the portion of the record before or after the change. The problem of representivity in areal sampling is primarily encountered in dealing with precipitation data. The data must adequately represent the true precipitation over the watershed. If a water balance (i.e„ continuity analysis) is to be made, the data should be true values. On the other hand, if a regression analysis is contemplated, the data need only be in fixed ratio to the true precipitation. Since the “true” precipitation is rarely known, precise confirmation of represeotativity is difficult. A successful relation between precipitation and streamflow is a pragmatic test. If a good relation capable of accurately reconstructing historic flows is derived, the precipitation is clearly representative. Since most hydrologic problems require an estimate of the probability of streamflow^ ability to reproduce historic probability characteristics will often be the best test.1 Much can be learned before analysis. Short and fragmented records can be adjusted to longer time periods and used to construct a mean annual (or seasonal) precipitation map that will show the effect of topography. Many short records can be found in most catchments by a careful search. Analysis of the climatology of the catchment is also helpful. If convective storms are important, the required density of stations will be higher than if frontal storms are the primary source of rain. ' \ 4 v: :.■ ' / " ' ""w': ■ ’ ' ' , :1' :I;;

2.19

Remote Sensing of Hydrologic Data

_

Sensors carried on aircraft or satellites can map many ground-surface characteris­ tics that may be helpful to hydrologists. Among these are Soil moisture,2 condition of vegetation, stage of agricultural operations, surface temperature, extent of snow cover, and location of flood water. By studying the type and extent of cloud cover, estimates of annual precipitation3 in remote areas may be possible. The presence of sediment, algae, and some pollutants in streams or lakes can be detected from photographs. Infrared photographs can indicate thermal differences in water bodies such as might result from submerged springs or inflow of hot cooling water. Precise quantitative evaluation of precipitation, streamflow, snow cover, or other hydrologic factors is not possible, observations generally being too in­ frequent (and uncertain because of cloud cover). Remotely sensed data are generally not a substitute for conventional data collection, but they can be an increasingly useful supplement to conventional data.

1 R. C. Johanson, Precipitation Network Requirements for Streamflow Estimation, Technical Report 147, Department of Civil Engineering, Stanford University, August 1971. 2 T. J. Schmugge, J. M. Meneely, A. Rango, and R. Neff, Satellite Microwave Observations of Spil Mpisture Variations, Water Resour. Bully pp. 265-281; April 1977. 3 D. W. Martin and W. D. Scherer, Review of Satellite Rainfall Estimation Methods^ Bull Am. Meteorol Soc„ Vol. 54, pp. 661-674, 1973.

DESCRIPTIVE HYDROLOGY

37

PROBLEMS 2.1. Using a topographic map provided by your instructor, delineate the catchment area for a point on a stream,by tracing the location of the divide. Determine the size of the area. i.-; .;p V-. 2.2. Determine from published data the mean annual precipitation at all available stations within a river basin assigned by your instructor. Using these data, find the average annual precipitation over the basin by the arithmetic average, Thiessen network, and isohyetal map. Compare your results by the three methods with the class average. 2.3. Repeat Prob. 2.2 using precipitation during a specified storm. 2.4. What should be the internal diameter of a snow sampler so that each 0,1 N of snow in the sampler represents 1.00 cm of water equivalent? 2.5. Plot the annual precipitation at some selected station as a time series. Are any regular cycles evident? It may help to plot the mass curve of departure from average precipitation or to plot curves of 5- or 10-yr running averages. Five-year running averages are computed by averaging the annual precipitation values in overlapping 5-yr periods. The average value is usually plotted at the middle year of the period; 2.6. Prepare a scatter plot of the annual precipitation data for station B of Prob. 2.10 by plotting each annual value against the value for the preceding year. Does your plot suggest that there are patterns of year-to-year variation in annual precipitation for this station or do the data suggest that annual variation is random? 2.7. Compute the streamflow for the following measurement data: Distance from bank, ft Total depth, d, ft Velocity, ft/sec 0.2d from surface 0.8d from surface .

o 0

2 0.8

4 2.7

6 6.4

8 8.5

10 7.2

12 5.7

14 3.2

o 0

1:0 0.8

4.7 1.4

2.6 2.1

2.9 2.3

2.7 2,2

2.4 2.0

2.3 1.9

16 3.3

18 2.1

2.3 1.8 2.0 ; 1.5

22 0 .t 1.5 ,0.. 1,2 0

20 i.l ’l "■.

Express your answer in cubic feet per second and in cubic meters per second. 2.8. At what distance from the bank should a surface float be placed in the stream of Prob. 2.7 so that 0.85 times the float velocity will equal the mean velocity in the stream? Assume the velocity varies parabolically with depth according to the relation’ .. V = V0(z;za)Vm where V is the velocity at a distance z above the streambed, V0 is the velocity at a distance z0 above the bed, and m is a constant. 2.9. What tracer dose concentration would you reedntmend for a tracer flow rate measure­ ment in a stream whose flow rate is in the range of 30 to 40 cfs if the dose ráte is 0.05 cfs, the detection limit of the tracer measurement device is 0.1 mg/L, and the background concentration of the tracer in the stream is below the detection limit? 2*10. Annual precipitation data at four weather stations in the vicinity of Salt Lake City, Utah, are as indicated in what follows. Analyze the data for homogeneity. That is, de­ termine whether or not any of the stations had been moved and in what year the move was made. Homogeneity may be checked by examining ratios of precipita­ tion at pairs of stations or by plotting a double mass curve, i.e; plotting X precipitation at station A versus X precipitation at station B, etc. Adjust the data to make them homogeneous with respect to the present

38

WATKR-KKSOUROiS HNCJINHHRINÍi

location of the stations. Also estimate the annual precipitation at station A in 1961 and 1962. Finally, estimate the mean annual precipitation of one of the moved stations in terms of its present location for the years 1950 to 1958, 1955 to 1964, and 1950 to 1967. Note that one item of data is incorrect. Which one is it? What do you think its true value may have been? Year 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 196? 1963 1964 1965 1966 1967

Station A

Station B

21.0 37.0 19.8 24.6 22.8 16.9 23.8 22.4 23.1 25.0 . 27.7, ■C v T ~ ■

-

^

\ y: ...

24.3 27.4 26.2 21.0 25.1

.

.

.

32.5 37.7 29.8 37.1 34.8 25.5 32.1 31.4 31.0 33.4 37.5 34.2 42.3 33.8 36.1 35.5 28.4 34.0

Station C 23.9 27.7 22.6 28.1 26.2 , 19.2 24.5 t 23.1 23.8 ' 25.5 28.2 25.7 31.8 24.8 27.8 26.9 21.4 25.6

Station D 29.1 33.3 27,6 34.6 / 31.5 23.4 29.9 27.8 29.4 30.5 32.4 . 27.8 34.4 27.4 30.1 29.2 23.5 27.8.;

2.11. Tabulated in whdt follows are measured discharges and stages at a gaging station and stages at an auxiliary station 2000 ft downstream from the main gage. Develop a slope-stage-discharge relation from these data. Determine the exponent n [Eq. (2.2)] by plotting Q JQ q versus Aza/Az0 on logarithmic paper. The slope of the line is the exponent n. Find the discharge for a stage of 19.85 ft and a fall of 1,17 ft. Note that it is convenient to take Az0 = 1 ft. Stage, ft Measured Qy cfs

\ Main gage

93,900 80,000 242,000 27,000 553,000 417,200 560,000 421,000 241,000 112,700 365,000 702,000 570,000 297,600

11.71 9.73 16.11 6.00 24.95 21.02 2175 23.51 14.48 10.75 18:30 27.22 26.45 21.60

Auxiliary gage 10.81 8.73 15.10 4.99 23.97 19.99 20.19 ‘ 22.77 13.02 9.53 17.00 26.07 , 25.58 20.98

DESCRIPTIVE HYDROLOGY,

JV

2.12. Listed in what follows is a series of discharge measurements with correspond­ ing stages at the gaging station and at an auxiliary gage 8400 ft downstream. Construct a slope-stage-discharge relation from these data. Use Áz0 = 1 ft: Calculate the discharge for a stage of 35.0 ft at the base gage and stages of 33.5, 34.0, and 34.5 ft at the auxiliary gage. If the stage at the base gage is 26.0 ft and the fall 0.8 ft, what is the discharge? Stage, ft Discharge, 1 0 0 0 cfs 12.3 170.0 72.0 43.1 23.9 16.0 157.0 51.5 * 111 38.4 115.5 102.5 76.3 40.4 16.1

Base gage

Auxiliary gage

14.89 42.60 30.16 27.60 22.70. 16.35 40.40 24.30

13.94 41.78 29.26 27.00 2 2 .2 0

v

2 1 .0 0

23.10 36.32 33.60 25.20 31.00

15.35 39.40 22.94 20.25

■

2 2 .1 0

7

2 0 .1 0

35.45 32.58 ' 23.20 30.69 19.65

2.13. With a stage of 7 m and a water-surface slope of 0.85 m/km, the flow rate in a river is 2500 m3/s. Approximately what would the flow rate be if the stage were 7 m and the water-surface slope 0.56 m/km? 2.14. On a river the following data were obtained by stream gaging: Main staff, ft

Auxiliary staff, ft

Flow rate, cfs

30.0 30.0

29.0 27.6

250 390

/,

\7

Estimate as accurately as possible the flow rate when the main staff* reads 30.0 ft and the auxiliary staff* reads 28.3 ft. • ; 2.15. Lake Mead behind Hoover Dam has a capacity of approximately 3.69 x lO10 m3. For how many years could this water supjply a city with a population of 920,000 if the average daily consumption is 410 L per person? Neglect the effect of evaporation. 2.16. A reservoir serving a population of 420,000 contains 67,000 acre-ft of water. The forecasted net inflow (streamflow plus precipitation minus evaporation) for the next year is 12,000 acre-ft. If it is desired to maintain no less than 30,000 acre-ft in the reservoir for the following year’s use/what is the average per capita use that must be achieved? Express your result in gallons per capita pér day^ ^ 2.17. A certain Asiatic city with a population of 510,000 uses 41 x 106 m3 of water per year. What is the mean consumption (a) in cubic meters per capita per day and (b) in gallons pereapita per day?