2.1 The The HydroloHydrologic gic CycleCycle
The wor ld’s supply of fresh wate r is quite small comp ared to the enormous volumes of salt water in the oceans. Fortunately the freshwater supply is renewed by the hydrologic cycle, which is an immense solar distillation system. Water evaporated from the oceans is transported over the continents by moving air masses. When this moisture-bearing air is cooled to its dewpoint temperature, the vapor con denses into water droplets forming fog or cloud. The cooling occurs when the moist air is lifted to higher elevations. Since air pressure decreases with elevation (Table A-3), the air expands as it is lifted and cooled in accordance with the Ideal Gas Law
p V /T =
const (2.1)
Lifting occurs in three ways. Orographic lifting occurs when the air is forced up over the underlying terrane. Frontal lifting occurs when the air mass is pushed up by a cooler air mass. The boundary between the two air masses is called a frontal
surface. Finally, the moist air may be heated from below as it passes over a warmer
1 “Hy drology is the science tha t treats of the waters of the Earth, their occurrence, circulati on, and distribution, their chemical and physical properties, and their reaction with their environment, including their relation to living things.” (From “Scientific Hydrology,” U.S. Federal Council for Science and Technology, June 1962.)
9 9
10 WATER-RESOURCES ENGINEERING
FIGURE 2.1
Schematic diagram of the hydrologic cycle.
surface, causing convective lifting, which may result in a convective thunderstorm. Often two or more of these mechanisms may take place together.
About two-thirds of the precipitation that reaches the land surface is returned to the atmosphere by evaporation from water surfaces, soil, and vegetation and through plant transpiration. The remaining third of the precipitation returns ultimately to the ocean through surface or underground channels. The large percentage of precipitation that is evaporated has often led to the belief that
increasing this evaporation by construction of reservoirs or planting of trees will increase the moisture available in the atmosphere for precipitation. Actually only a small portion of the moisture (usually much less than 10 percent) that passes over any given poin t on the ea rth ’s surface is pre cipitate d.1 Hence, moisture evaporated from the land surfaces is a minor part of the total atmospheric moisture.12
The hydrologic cycle is depicted diagramfnatically in Fig. 2.1. No simple figure can do justice to the complexities of the cycle ass it occurs in nature. The science of hydrolog y is devoted to a study of the rate of exchange of water between phases of the cycle and in particular to the variations in this rate with time and
1G. S. Benton, R. T. Blackburn, and V. O. Snead, The Role of the Atmosphere in the Hydrologic Cycle, Trans. Am. Geophys. Union, Vol. 31, pp. 61-73, February 1950.
2 F. A. Huff and G. E. Stout, A Preliminary Study of Atmospheric-moistur e-precipitation Relationships over Illinois, Bull. Am. Meteorol. Soc., Vol. 32, pp. 295-297, 1951.
DESCRIPTIVE HYDROLOGY 11
place. This information provides the da ta necessary for the hydraulic design of physical works to control and utilize natural water.
2.2
2.2 The The River River BasBasinin
A river basin (catchm ent)1 is the area tri butary to a given point on a stream and is separated from adjacent basins by a divide, or ridge, that can be traced on topographic maps. All surface water srcinating in the area enclosed by the divide is discharged through the lowest point in the divide through which the main stream of the catchment passes, it is commonly assumed that the movement of ground- water conforms to the surface divides, but this assumption is not always correct, and large quantities of water may be transported from one catchment to another as groundwater.
PRECIPITATION PRECIPITATION 2.
2.3 3 Types Types of of PrecipitationPrecipitation
Precipitation includes all water that falls from the atmosphere to the earth’s surface. Precipitation occurs in a variety of forms that are of interest to the meteorologist, but the hydrologist is interested in distinguishing only between liquid precipitation (rainfall) and frozen precipitation (snow, hail, sleet, and freezing rain). Rainfall runs off to the streams soon after it reaches the ground and is the cause of most floods. Froz en precipita tion may r emain where it falls for a long time before it melts. Melting snow is rarely the cause of major floods although, in
combination with rainfall, it may contribute to major floods such as that on the upper Mississippi River in 1969. Mountain snowpacks are often important sources of water for irrigation and other purposes. The snowfields serve as vast reservoirs that store water precipitation until spring thaws release it near the time it is required for irrigation. ^
2.4
2.4 FoFo g g Drip Drip anand d DewDew
•
Fog consists of water droplets so small that their fall velocities are negligible. Fog particles that contact vegetation may adhere, coalesce with other droplets, and eventually form a drop large enough to fall to the ground. Fog drip is an important source of water for native vegetation during the rainless summers of the Pacific Coast of North America.
On clear nights the loss of heat by radiation from the soil causes cooling of the ground surface and of the air immediately above it. Condensation of the water vapor present in the air results in a deposit of dew. The small quantities of dew
1The words river basin, drainage basin, watershed , and catchment are used interchangeably. A subbasin is a tributary basin of a larger drainage basin.
1
122 WATER-RESOURCES ENGINEERING
FIGURE 2.2
Standard 8-in. nonrecording precipitation gage. ( U.S . National Weather Service)
and fog drip deposited in any day do not contribute to streamflow or groundwater. They do, however, offer a source of water that may be exploited locally. Research in Israel1 has shown that br oad-lea ved crops such as cabbage may be efficient dew collectors that can be grown in an arid region with little or no irrigation.
2.5
2.5 Precipitation Precipitation MeaMea suremsurem ent—ent—
Amount of precipitation is expressed as the depth in inches or millimeters that falls on a level surface. This may be measured as the depth of water deposited in an open, straight-sided container. The standard gage1 2 used in the United States (Fig. 2.2) consists of a funnel 8 in. (20.32 cm) in diameter discharging into a tube 2.53 in. (6.43 cm) in diameter. The area of the inner tube is 0.1 that of the funnel, and a stick graduated in inches and tenths can be used to measure precipitation to the nearest 0.01 in. (0.25 mm). Precipitation in excess of 2 in. (50 mm) overtops the inner tube and collects in the overflow can. By removing the funnel and inner
1D. Ashbel, Frequency and Distribution of Dew in Palestine, Geogr. Rev., Vol. 39, pp. 291-297, April 1949.
2 Worldwide, a variety of different types of gages are used. Practically, there is little difference in accuracy in measuring rain, but smaller gages are not suitable for snowfall.
DESCRIPTIVE HYDROLOGY 13
tube from the gage, the 8-in.-diameter overflow can may be used to collect snowfall, which is melted and measured in the inner tube. Large storage gages are used in remote areas to catch and store precipitation for periods of 30 days or more. If snowfall is expected, an initial charge of calcium chloride brine is placed in the gage to melt the snow and to prevent the freezing of the liquid in the gage. A thin film of oil is used to prevent evaporation from the gage between observations.
Wind sets up air currents around precipitation gages that usually cause the gages to catch less prec ipita tion th an they sh ould.1 The low fall velocity of snowflakes makes this effect even more marked for snowfall than for rain. The deficiency in catch may vary from 0 to 50 percent or more depending on the type of gage, wind velocity, and local terrane. The U.S. National Weather Service1 2 uses an Alter shield consisting of a series of metal slats pivoted about a circular ring near the top of the gage and joined by a chain at the bottom. The tops of the slats are about 2 in. (5 cm) above the top of the gage. The flexible construction is intended to permit wind to move the slats and minimize the accumulation of snow on the shield.
In order to determine rates of rainfall over short periods of time, recording rain gages are used. The weighing rain gage has a bucket supported by a spring or lever balance. Movement of the bucket is transmitted to a pen that traces a record of the increasing weight of the bucket and its contents on a clock-driven chart or punched paper tape. The tipping-bucket gage consists of a pair of buckets pivoted under a funnel in such a way that when one bucket receives 0.01 in.
(0.25 mm) of precipitation, it tips, discharging its contents into a reservoir and bringing the other bucket under the funnel. A recording mechanism indicates the
time of occurrence of each tip. The tipping-bucket gage is well adapted to the measurement of rainfall intensity for short periods, but the more rugged construc tion of the weighing-type gage and its ability to record snowfall as well as rain make it preferable for many purposes.Subsequent to the development of radar in World War II it was found that microwave ra da r (1 to 20 bm wavelength) would indicate the presence of rain3 within its scanning area. The amount of reflected energy is dependent on the raindrop size and the distance from the transmitter. Drop size is roughly correlated with rain intensity, and the image on the radar screen (isoecho map) can be interpreted as an approximate indication of rainfall intensity. A calibration may also be determined from actual rain-gage measurements in the area scanned by the radar. Radar offers a means of obtaining information on a real rainfall distribution, which would be only roughly defined by the usual network of rain gages.
1C. C. Warnick, Experiments with Windshields for Precipitation Gages, Trans. Am. Geophys. Union, Vol. 34, pp. 379-388, June 1953.
2 The U. S. Weather Bureau was changed to the National Weather Service in 1970.
3 L. J. Battan, “ Rada r O bserva tion of the A tmosp here,” University of Chicago Press, Chicago, 1973.
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144 WATER-RESOLJRCF.S ENGINEERING
2.6
2.6 Computation Computation oof f Average Average PrecipitationPrecipitation
Large differences in precipitation are observed within short distances in mountain ous terrane or during showery precipitation in level country. The average density of rain gages in the United States is about one per 250 mi2 (700 km2), and the data so obtained represent only a scattered sample of precipitation over large areas. It is sometimes necessary to estimate the average precipitation over a given area. The simplest method of doing this is to compute the arithmetic average of the recorded precipitation values at stations in or near the area. If the precipitation is nonuniform and the stations unevenly distributed within the area, the arithmetic average may be incorrect. To overcome this error, the precipitation at each station may be weighted in proportion to the area the station is assumed to represent.
A common method of determining weighting factors is the Thiessen network (Fig. 2.3). A Thiessen network is constructed by connecting adjacent Stations on a map by straight lines and erecting perpendicular bisectors to each connecting line. The polygon formed by the perpendicular bisectors around a station encloses an area that is everywhere closer to that station than to any other station. This area is assumed to be best represented by the precipitation at the enclosed station. This is often a reasonable assumption but may not always be correct. To compute the average rainfall, the area represented by each station is expressed as a percentage of the total area. The average rainfall is the sum of the individual station amounts, each multiplied by its percentage of area. An alternative method is shown in Fig. 2.3. If the stations are uniformly distributed in the area, the Thiessen areas will be equal and the computed average rainfall will equal the arithmetic average.
The basis for the Thiessen method is the assumption that a station best represents the area that is closest to it. If precipitation is controlled by topography or results from intense convection, this assumption may not be valid. An isohyetal map (Fig. 2.4) showing contours of equal precipitation may be drawn to conform to other pertinent information in , addition to the precipitation data and thus present a more accurate picture of the rainfall distribution. Since precipitation
FIGURE 2.3 Thiessen network.
DESCRIPTIVE HYDROLOGY 1155 Isohyets Isohyets Area between Area between isohyets. isohyets. m m ii2 Average Average precipitation, precipitation, in. in. Product Product m m ii2 in .in . 3 3 .0.0 3 3 .5.5 1 1 99 3.453.45 66 66 4 4 .0.0 1 1 00 66 3.753.75 33 99 88 4 4 .5.5 1 1 00 22 4.254.25 44 33 44 5 5 .0.0 66 0 0 44 .. 77 55 22 88 55 5 5 .5.5 1 1 55 00 5.255.25 77 88 88 6 6 .0.0 8 8 44 55 .. 77 5 5 44 88 33 6 6 .5.5 4 4 77 6.206.20 22 99 11 Total Total 55 66 88 —— 27452745 FIGURE 2.4 \\ ee isohyetal map.
usually increases with elevation, the isohyets may be made to conform approx- imately with the contours of elevation.
To compute average precipitation from an isohyetal map, the areas enclosed between successive isohyets are measured and multiplied by the average precipita-
tion between the isohyets. The sum of these products divided by the total area is the average precipitation. If the isohyets are interpolated linearly between stations, the computed average precipitation will not differ appreciably from that computed with a Thiessen network.
2.7 Snow 2.7 Snow
The measurement of snowfall has been discussed in Sec. 2.5. Snow on the ground is measured in terms of its depth (in inches or centimeters). Shallow depths are measured with any convenient scale, while large depths are measured on a snow stake, a graduated post permanently installed at the desired site. Because of variations in snow density, a depth measurement is not sufficient to tell how much water is contained in the snow pack. The water equivalent , or depth of water that would result from melting a column of snow, is measured by forcing a small tube into the snow, withdrawing it, and weighing the tube to determine the weight of the snow core removed. There are a number of types of snow samplers, but the most common type is the Mt. Rose pattern with an internal diameter of 1.485 in. (3.772 cm) so th at each ounce of snow in the core represents 1 in. (25 mm) of water equivalent. The specific gravity of freshly fallen snow is usually about 0.1. Thus, its water equivalent is 0.1 in. for each inch of snow depth. The specific gravity increases with time as the snow remains on the ground and may reach a maximum of abou t 0.5 in heavy mountain snowpacks.1 The term density of snow is often
16
16 WATER-RESOURCES ENGINEERING
used synonymously with specific gravity, although this usage is not in accord with the common meanings of the two terms.
The area covered by snow may be mapped from aircraft or by satellite. The water equivalent of snowpacks in relatively flat areas has also been mapped from an aircraft flying at about 500 ft (150 m) altitude with a gamma ray c ounter.1 The natural gamma emission from the soil is attenuated by the water in the snow so that flights with and without snow permit estimating snow water equivalents up to a maximum of about 12 in. (300 mm) with accuracy on the order of 0.5 in. (12 mm).
2.8
2.8 Variations Variations in in PrecipitationPrecipitation
The complex pattern of precipitation in the United States (Fig. 2.5) reflects several interacting influences. In general, precipitation decreases with increasing latitude because decreasing tem peratures reduce atmospheric moisture. A more important
control in the United States is distance from a moisture source, as evidenced by the concentration of precipitation along the coasts and to some extent to the leeward of the Great Lakes. The importance of mountains as a factor in the production of precipitation by orographic lifting is evident in the isohyetal pattern
in the Wester n states and a long the Appalachian M ountains. Heavier precipitation normally occurs along the windward slope of a mounain range with a rain shadow on the leeward slope.
From the engineering viewpoint, time variations in precipitation may be more important than regional variations. The most marked of these variations is the annual precipitation cycle shown for selected stations in Fig. 2.6. In the Far West precipitation is at a minimum during the summer because a large high- pressure area in the Pacific blocks the path of storms. In contrast, a summer
maximum of precipitation is observed in the Great Plains, where the cold continental high-pressure center recedes northward during the summer. An essenti ally uniform distribuion of precipitation prevails in the Eastern states. The dry summers of the West make irrigation a necessity for many crops and emphasize the importance of storage reservoirs.
Variations in precipitation from year to year make it important to design reservoirs that are adequate during years of low rainfall. In some cases reservoirs must carry water in storage for a period of several years. Over 100 different cycles in precipitation with periods up to 700 yr in length have been reported by various investigators. Sunspots and planetary configurations have been among the factors suggested as controlling these cycles. No one has been successful, however, in
1E. L. Peck and V. C. Bissell, Aerial Measurement of Snow Water Equivalent by Terrestrial Gamma Radiation Survey, Bull Int. Assoc. Hydrol. Sel, Vol. 18., No. 1, pp. 47-62, 1973.
m manan
FIGURE 2.5 , b ,
18 WATER-RESOURCES ENGINEERING
FIGURE 2.6
Typical monthly distributions of precipitation (in inches) in various climatic regimes in the United States.
employing cycles for forecasting precipitation several years in advance. The best evidence now available suggests that the occurrence of a series of wet or dry years is purely rand om, such as might be expected by succes sive tosses of a coin. Accurate precipitation records are too short for a really satisfactory analysis of cyclic
variation, which, if it does occur, must be a complex variation consisting of several superimposed cycles of differing period.
E
FIGURE 2.7
DESCRIPTIVE HYDROLOGY 1919
table 2.1
M
M aximaxim um um recorded point recorded point rainfall rainfall (i(i n in i nches)nches)
Scatioii Duration Min hr 5 15 30 60 6 24 ^■xiiand, Oreg. 0.40 0.83 1.10 1.31 — 7.66 8/8/00 8/8/00 8/8/00 6/7/27 — 12/12/82
i_.:** Angeles, Calif. 0.44 1.05 1.51 1.87 3.37 7.36
1/14/08 11/19/67 11/19/67 11/19/67 3/2/38 12/31/33 Idaho 0.34 0.59 0.67 0.98 — 2.46 5/22/42 8/9/63 5/18/21 7/30/12 — 3/28/04 PV'enix, Ariz 0.68 1.14 1.27 1.72 2.41 4.98 9/16/69 9/16/69 9/16/69 8/18/66 9/4/39 7/1/11 Gaiteston, Tex. 0.85 1.94 3.06 5.31 11.79 14.35 4/13/29 4/13/29 10/6/10 10/22/13 10/8/01 7/13/00 York, N.Y. 0.75 1.63 2.34 2.97 4.44 9.55 8/12/26 7/10/05 8/12/26 8/26/47 10/1/13 10/8/03 Pittsburgh, Pa. 0.72 1.23 ■ 1.46 2.00 2.53 4.08 6/26/31 6/26/31 7/4/03 7/27/43 7/27/43 9/17/76 Msimi, Fla. 0.71 1.89 2.92 4.53 10.64 15.10 6/14/33 10/11/47 10/11/47 6/14/33 11/30/25 11/29/25
Figure 2.7 shows the w orld’s record rai nfalls for various du ratio ns .1 Most of the observations are derived from cooperative and unofficial stations. A similar pk>t for record rainfalls at U.S. First Order stations would fall at ab out one-third
i#e magnitudes shown in Fig. 2.7. This difference reflects the more effective sampling of the large num ber of cooperative and unofficial statio ns and emphasizes the importance of a careful search for data when a study requires information on rainfall Intensities. Table 2.1 presents maximum observed intensities for various durations a t a nu mber of geographic ally distributed stations in the U nited States.
STREAMFLOW STREAMFLOW
In the streamflow phase of the hydrologic cycle, the water from a given catchment
e usually concentrated in a single channel, and it is possible to measure the entire
quantity of water in this phase of the cycle as it leaves the area.
1
1 9 9 Measurement Measurement of of StreaStrea mflomfloww
A continuous record of streamflow requires the establishment of a relation between rate of flow and water level in a channel. In small channels this may sometimes
1 J. L, H. Pa'ilh us, Indi an Ocean and Ta iwan Rainfalls Se t New Records, Monthly Weather Rev., Vol.