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C H A P T E R

9

Fundamentals of Surface-Water Hydrology I: Rainfall and Abstractions 9.1 Introduction Surface-water hydrology is the science that encompasses the distribution, movement, and properties of natural water above the surface of the earth. Applications of surface-water hydrology in engineering practice are mostly encompassed within the field of engineering hydrology, which includes modeling rainfall events and predicting the quantity and quality of the resulting surface runoff. Designing systems to control the quantity and quality of surface runoff is the responsibility of a water-resources engineer. The land area that can contribute surface runoff to any particular location is determined by the shape and topography of the land area surrounding the given location. The potential contributing area is called the watershed, and the area within a watershed over which any particular rainfall event occurs is called the catchment area. In most engineering applications, the watershed and catchment area are taken to be the same, and are sometimes referred to as the drainage basin or the drainage area. The runoff from a watershed or catchment is concentrated at the catchment outlet, which is sometimes called the pour point of the catchment. The characteristics of the catchment determine the quantity, quality, and timing of the surface runoff for a given rainfall event. The types of pollutants contained in surface runoff generally depend on the land uses within the catchment area, and pollutants in surface-water runoff that are typically of concern include suspended solids, heavy metals, nutrients, organics, oxygen-demanding substances, and pathogenic microorganisms. These pollutants may be in solution, in suspension, or attached to particles of sediment. To facilitate water management in the United States, the country is divided into a hierarchy of watersheds called hydrologic units with the following four levels: region, subregion, accounting unit, and cataloging unit. Regions represent the largest scale of watershed and are shown in Figure 9.1, and these 21 regions are further divided by lower-level topography into 222 subregions, 352 accounting units, and 2262 cataloging units. Hydrologic unit codes are used to identify hydrologic units, with regions identified by a 2-digit code, subregions by a 4-digit code, accounting units by a 6-digit code, and cataloging units by an 8-digit code. As an example, Lake Winnebago (Wisconsin) is located within region 04, subregion 0403, accounting unit 040302, and cataloging unit 04030204; note the hierarchy embedded in the numbering system. In engineering practice, it is common to refer to the cataloging unit by its “HUC8” number (referring to the 8-digit hydrologic unit code), which for the Lake Winnebago watershed is 04030204. 9.2 Rainfall The precipitation of water vapor from the atmosphere occurs in many forms, the most important of which are rain and snow. Hail and sleet are less-frequent forms of precipitation. Engineered drainage systems in most urban communities are designed primarily to control the runoff from rainfall. The formation of precipitation usually results from the lifting of moist air masses within the atmosphere, which results in the cooling of the air mass and condensation of moisture. The four conditions that must be present for the production of precipitation are: (1) cooling of the air mass, (2) condensation of water droplets onto nuclei, (3) growth of water droplets, and (4) mechanisms to cause a sufficient density of the droplets for the precipitation to fall to the ground. 401

Fundamentals of Surface-Water Hydrology I: Rainfall and Abstractions

FIGURE 9.1: Hydrologic regions in the United States

(01) (01)

NO OR TTHH W (17) (17) WEE STT

(09)

UPPER MISSISSIPPI

(10)

GRR EAA TT LLA KKEESS (04)

(07) U UPPPPEE COLO RR RADO (14) (14)

(02) OHIO OHIO (05) (05)

(18)

DE RA N RII O G

LLO OW WEERR C CO OLLO ORRAA D DO O (15) (15)

(13)

AARRR D D KKAA NNSSAAS––-W HI T I EE–-–RREED (11)

TTEE XXAA S–-–G ULL F (12) (12)

EE SEE (06) NEES TTENNN

GU LLF

R NIA FO R CALI

M MIID––AT -A LA NT ICC

MISSOURI MISSOURI GRR EAATT BBAASSIN N (16) (16)

NE W E NGL AAND

PA

SO UR I S-R ED -R AI N YA

CCI FI IC

Source: Seaber et al. (1987).

IS SI S S IP P I

Chapter 9

LO WE RM

402

–-– ICC NTT LAA AATTL T H T H U OU SO (03) (03)

(02) Water ces Water Resources Resources Resour Regions Regions

(08) (08)

0

400 MILES

ALASKA ALASKA (19) Kauai Oahu Oahu

CARIBBEAN CARIBBEAN (21) (21) (21)

(20) Molokai Molokai Maui Moui

HAW HAWAII AII HAWAII 00

400 MILES MILES 400

00

Hawaii 150 MILES MILES 150

Puerto Rico PuertoRico Rico Puerto

00

80 MILES MILES 80

Cloud droplets generally form on condensation nuclei, which are usually less than 1 µm in diameter and typically consist of sea salts, dust, or combustion by-products. These particles are called atmospheric aerosols, which also play an important role in regulating the amount of solar radiation that reaches the surface of the earth (Hendriks, 2010). In pure air, condensation of water vapor to form liquid water droplets occurs only when the air is supersaturated with water molecules. In cold clouds, where the temperature is below freezing, water droplets and ice crystals are both formed and the greater saturation vapor pressure over water compared to over ice causes the growth of ice crystals at the expense of water droplets. This is called the Bergeron–Findeisen process or ice-crystal process. In warm clouds, the primary mechanism for the growth of water droplets is collision and coalescence of water droplets. When the moisture droplets and/or ice crystals are large enough, the precipitation falls to the ground. Moisture droplets larger than about 0.1 mm are large enough to fall, and these droplets grow as they collide and coalesce to form larger droplets. Rain drops falling to the ground are typically in the size range of 0.5–3 mm. Drizzle is a subcategory of rain with droplet sizes less than 0.5 mm. Most of the clouds and atmospheric moisture are contained within 5500 m (18,000 ft) of the surface of the earth. The main mechanisms of air-mass lifting are frontal lifting, orographic lifting, and convective lifting. In frontal lifting, warm air is lifted over cooler air by frontal passage. The resulting precipitation events are called cyclonic or frontal storms, and the zone where the warm and cold air masses meet is called a front. Frontal precipitation is the dominant type of precipitation in the north-central United States and other continental areas (Elliot, 1995). In a warm front, warm air advances over a colder air mass with a relatively slow rate of ascent (0.3%–1% slope) causing a large area of precipitation in advance of the front, typically 300–500 km (200–300 mi) ahead of the front. In a cold front, warm air is pushed upward at a relatively steep slope (0.7%–2%) by advancing cold air, leading to smaller precipitation areas

Section 9.2

Rainfall

403

in advance of the cold front. Precipitation rates are generally higher in advance of cold fronts than in advance of warm fronts. In orographic lifting, warm air rises as it flows over hills or mountains, and the resulting precipitation events are called orographic storms. An example of the orographic effect can be seen in the northwestern United States, where the westerly airflow results in higher precipitation and cooler temperatures to the west of the Cascade mountains (e.g., Seattle, Washington) than to the east (e.g., Boise, Idaho). Orographic precipitation is a major factor in most mountainous areas, and the amount of precipitation typically shows a strong correlation with elevation (e.g., Naoum and Tsanis, 2003). The lee side of mountainous areas is usually dry, since most of the moisture is precipitated on the windward side, and this is sometimes called the rain shadow effect (Davie, 2008). In convective lifting, air rises by virtue of being warmer and less dense than the surrounding air, and the resulting precipitation events are called convective storms or, more commonly, thunderstorms. A typical thunderstorm is illustrated in Figure 9.2, where the localized nature of such storms is clearly apparent. Convective precipitation is common during the summer months in the central United States and other continental climates with moist summers. Convective storms are typically of short duration, and usually occur on hot midsummer days as late-afternoon storms. 9.2.1 Measurement of Rainfall Records of rainfall have been collected for more than 2000 years (Ward and Robinson, 1999). Rainfall is typically measured using rain gages operated by government agencies such as the National Weather Service and local drainage districts. Rainfall amounts are described by the volume of rain falling per unit area and are given as a depth of water. Gages for measuring rainfall are categorized as either nonrecording (manual) or recording. In the United States, most of the rainfall data reported by the National Weather Service (NWS) are collected manually using a standard rain gage consisting of a 20.3-cm (8-in.) diameter funnel that passes water into a cylindrical measuring tube, the whole assembly being placed within an overflow can. The measuring tube has a cross-sectional area one-tenth that of the collector funnel; therefore, a 2.5-mm (0.1-in.) rainfall will occupy a depth of 25 mm (1 in.) in the collector tube. The capacity of the standard collector tube is 50 mm (2 in.), and rainfall in excess of this amount collects in the overflow can. The manual NWS gage is primarily used for collecting daily rainfall amounts. Automatic-recording gages are usually used for measuring rainfall at intervals less than one day, and for collecting data in remote locations. Recording gages use either a tipping bucket, weighing mechanism, or float device. The original tipping-bucket rain gage was invented by Sir Christopher Wren in about 1662, and accounts for nearly half of all recording rain gages worldwide (Upton and Rahimi, 2003). A typical tipping-bucket rain gage is FIGURE 9.2: Typical thunderstorm

404

Chapter 9

Fundamentals of Surface-Water Hydrology I: Rainfall and Abstractions

FIGURE 9.3: Tipping-bucket rain gage

(a) Rain gage

(b) Support structure

shown in Figure 9.3, where Figure 9.3(a) shows a close-up top view of the rain gage with projections that help prevent the splattering of incident rainfall. The structure that usually supports the rain gage is shown in Figure 9.3(b), where a solar panel (front) provides power for the data recorder (back), and the rain gage is on top of the structure. The tipping-bucket gage is based on funneling the collected rain to a small bucket that tilts and empties each time it fills, generating an electronic pulse with each tilt. The number of bucket-tilts per time interval provides a basis for determining the precipitation depth over time. Typical problems with tipping-bucket rain gages include blockages, wetting and evaporation losses of typically 0.05 mm (0.002 in.) per rainfall event (Niemczynowicz, 1986), rain missed during the tipping process which typically takes about half a second (Marsalek, 1981), wind effects, position, shelter, and dynamic rainfall effects (Habib et al., 2008). A weighing-type gage is based on continuously recording the weight of the accumulated precipitation, and float-type recording gages operate by catching rainfall in a tube containing a float whose rise is recorded with time. Older weighing-type gages are mechanical-weighing and analog-recording devices, while modern weighing-type gages are electronic-weighing and digital-recording devices; significant discrepancies in measured rainfall intensities between analog and digital gages have been found for rainfall durations less than 5 min (Keefer et al., 2008). The accuracy of both manual and automatic-recording rain gages is typically on the order of 0.25 mm (0.01 in.) per rainfall event. Rain-gage measurements are point measurements of rainfall and are only representative of a small area surrounding the rain gage. Areas on the order of 25 km2 (10 mi2 ) have been taken as characteristic of rain-gage measurements (Gupta, 1989; Ponce, 1989), although considerably smaller characteristic areas can be expected in regions where convection storms are common. In the United States, the National Weather Service makes extensive use of Weather Surveillance Radar 1988 Doppler (WSR-88D), commonly known as next-generation weather radar (NEXRAD). A typical WSR-88D tower is shown in Figure 9.4, and each WSR-88D station measures weather activity over a 230-km (143-mi) radius area with a 10-cm (3.9-in) wavelength signal. This radar system provides estimates of hourly rainfall from the reflectivity of the S-band signal (1.55–3.9 GHz) within cells that are approximately 4 km * 4 km (2.5 mi * 2.5 mi). Since radar systems measure only the droplet size and movement of water in the atmosphere, and not the volume of water falling to the ground, radar-estimated rainfall should generally be corrected to correlate with field measurements of rainfall on the ground. Comparisons of rainfall predictions using WSR-88D with rainfall measurements using dense networks of rain gages have shown that WSR-88D estimates tend to be about 5%–10% lower than long-term rain-gage measurements (Johnson et al., 1999), and comparisons of WSR-88D with daily rain-gage measurements have shown significant spatial variability in radar accuracy, with typical annual bias on the order of −15%, correlation between radar

Section 9.2

Rainfall

405

FIGURE 9.4: Weather radar station (WSR-88D) Source of close-up view: NOAA (2012a).

(a) Far view

(b) Near view

and rain-gage measurements on the order of 0.7, and typical agreement in detecting the occurrence of rainfall on the order of 85% (Young and Brunsell, 2008). Errors in WSR88D estimates of rainfall have been shown to depend on the type of rainfall, with opposite biases for frontal and convective rainfall (Skinner et al., 2009). In spite of measurement inaccuracies, radar provides the advantage of covering large areas with high spatial and temporal resolution. Spatially distributed rainfall measurements provided by NEXRAD and other high-resolution weather radar systems have been incorporated directly into rainfallrunoff models to provide improved estimates of runoff distribution (e.g., Gires et al., 2012, Vieux et al., 2009). For example, real-time high-resolution NEXRAD measurements within 1 km * 1 km (0.6 mi * 0.6 mi) cells have been combined with hydrologic models to provide near-real-time flood alerts in the Brays Bayou Watershed in Houston, Texas (Fang et al., 2008). Care must be taken in using radar measurements to estimate short-term (e.g., 10-min) rainfall, since radars sample precipitation aloft and by the time the precipitation reaches the ground, wind-induced drift may have caused a horizontal shift of several kilometers (Islam and Rasmussen, 2008). Such conditions occur during intense convective storms, which typically have strong spatial and temporal gradients of intensity. Errors in short-term radar-measured rainfall can sometimes be reduced by increased spatial or temporal averaging (e.g., Knox and Anagnostou, 2009). 9.2.2 Statistics of Rainfall Data Rainfall measurements are seldom used directly in engineering design, but rather the statistics of rainfall measurements are typically used. Rainfall statistics are most commonly presented in the form of intensity-duration-frequency (IDF) curves, which express the relationship between the average intensity in a rainstorm and the averaging time (= duration), with the average intensity having a given probability of occurrence. Such curves are also called intensity-frequency duration (IFD) curves (e.g., Gyasi-Agyei, 2005). A typical IDF curve (for Miami, Florida) for return periods ranging from 2 to 100 years is shown in Figure 9.5. To fully understand the meaning and application of the IDF (or IFD) curve, it is best to review how this curve is derived from rainfall measurements. The data required to calculate the IDF curve are a record of rainfall measurements in the form of the depth of rainfall during fixed intervals of time, t, typically on the order of 5 min. For a rainfall record containing several years of data, the following computations lead to the IDF curve:

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Chapter 9

Fundamentals of Surface-Water Hydrology I: Rainfall and Abstractions

FIGURE 9.5: Intensityduration-frequency (IDF) curve

15

Rainfall intensity in inches per hour

Source: Florida Department of Transportation (2000).

15

10 9 8 7 6 5

10 9 8 7 6 5

2 Years 3 Years 5 Years 10 Years 25 Years 50 Years 100 Years

4 3

4 3

2

2

1.0 0.9 0.8 0.7 0.6 0.5

1.0 0.9 0.8 0.7 0.6 0.5

Miami, FL Zone 10

0.4

0.4

0.3 0.2 0.8 10

0.3

15

20 Min

30

40 50 60

2

3

4

5

10

15

20 24

0.2

H Duration

Step 1: For a given duration of time (= averaging period), starting with t, determine the annual-maximum rainfall (AMR) for this duration in each year. Step 2: The AMR values, one for each year, are rank-ordered, and the return period, T, for each AMR value is estimated using the Weibull formula T=

n + 1 m

(9.1)

where n is the number of years of data and m is the rank of the data corresponding to the event with return period T. As an alternative to using Equation 9.1 to estimate the return periods of the AMR values, an extreme-value distribution (typically Type I or Type II) may be fitted to the AMR values for the given duration, t (e.g., Koutsoyiannis et al., 1998). Step 3: Steps 1 and 2 are repeated, with the duration increased by t. An upper-limit duration of interest needs to be specified, and for urban-drainage applications the upper-limit duration of interest is typically on the order of 1–2 h. Step 4: For each return period, T, the AMR versus duration can be plotted, and this relationship is called the depth-duration-frequency curve. Dividing each AMR value by the corresponding duration yields the average intensity, which is plotted versus the duration, for each return period, to yield the IDF curve. This procedure is illustrated in the following example.

Section 9.2

Rainfall

407

EXAMPLE 9.1 A rainfall record contains 32 years of rainfall measurements at 5-min intervals. The annual-maximum rainfall amounts for intervals of 5 min, 10 min, 15 min, 20 min, 25 min, and 30 min have been calculated and ranked. The top three annual-maximum rainfall amounts, in millimeters, for each time increment are given in the following table:

Rank

5

10

1 2 3

12.1 11.0 10.7

18.5 17.9 17.5

t in min 15 20 24.2 22.1 21.9

28.3 26.0 25.2

25

30

29.5 28.4 27.6

31.5 30.2 29.9

Calculate the IDF curve for a return period of 20 years. Solution For each time interval, t, there are n = 32 ranked rainfall amounts of annual maxima. The relationship between the rank, m, and the return period, T, is given by Equation 9.1 as

T=

n + 1 32 +...