CE 394K.2 Hydrology, Lecture 2

CE 394K.2 Hydrology, Lecture 2

Precipitation Precipitation: water falling from the atmosphere to the earth. Rainfall Snowfall Hail, sleet Requires lifting of air mass so that it cools and condenses. Mechanisms for air lifting 1. Frontal lifting 2. Orographic lifting 3. Convective lifting Definitions Air mass : A large body of air with similar temperature and moisture characteristics over its horizontal extent. Front: Boundary between contrasting air masses. Cold front: Leading edge of the cold air when it is advancing towards warm air. Warm front: leading edge of the warm air when advancing towards cold air.

Frontal Lifting Boundary between air masses with different properties is called a front Cold front occurs when cold air advances towards warm air Warm front occurs when warm air overrides cold air Cold front (produces cumulus cloud) Cold front (produces stratus cloud) Orographic lifting Orographic uplift occurs when air is forced to rise because of the physical presence of elevated land. Convective lifting Convective precipitation occurs when the air near the ground is heated by the earths warm surface. This warm air rises, cools and creates precipitation. Hot earth surface Condensation Condensation is the change of water vapor into

a liquid. For condensation to occur, the air must be at or near saturation in the presence of condensation nuclei. Condensation nuclei are small particles or aerosol upon which water vapor attaches to initiate condensation. Dust particulates, sea salt, sulfur and nitrogen oxide aerosols serve as common condensation nuclei. Size of aerosols range from 10-3 to 10 m. Precipitation formation Lifting cools air masses so moisture condenses Condensation nuclei Aerosols water molecules attach Rising & growing 0.5 cm/s sufficient to carry 10 m droplet Critical size (~0.1 mm) Gravity overcomes and drop falls Forces acting on rain drop

Three forces acting on rain drop Gravity force due to weight Buoyancy force due to displacement of air Drag force due to friction with surrounding air Fg w g 3 D 6 Fb a g 2 V2 2 V Fd Cd a A Cd a D 2 4 2 3 D 6

D Fb Fd Fd Fg Volume D 3 6 Area D 2 4 Terminal Velocity Terminal velocity: velocity at which the forces acting on the raindrop are in equilibrium. If released from rest, the raindrop will accelerate until it reaches its terminal velocity Fvert 0 FB FD W

D 3 2V2 a g D Cd a D w g D3 6 4 2 6 FD FB W 2 V Cd a D 2 t a g D 3 w g D 3 4 2 6 6 Vt

4 gD w 1 3C d a Fd At standard atmospheric pressure (101.3 kpa) and temperature (20oC), w = 998 kg/m3 and a = 1.20 kg/ m3 Fb Fd Fg V Raindrops are spherical up to a diameter of 1 mm For tiny drops up to 0.1 mm diameter, the drag force is specified by Stokes law Cd 24

Re Re aVD a Precipitation Variation Influenced by Atmospheric circulation and local factors Higher near coastlines Seasonal variation annual oscillations in some places Variables in mountainous areas Increases in plains areas More uniform in Eastern US than in West Rainfall patterns in the US Global precipitation pattern Spatial Representation Isohyet contour of constant rainfall Isohyetal maps are prepared by interpolating rainfall data at gaged points.

Austin, May 1981 Wellsboro, PA 1889 Texas Rainfall Maps Temporal Representation Rainfall hyetograph plot of rainfall depth or intensity as a function of time Cumulative rainfall hyetograph or rainfall mass curve plot of summation of rainfall increments as a function of time Rainfall intensity depth of rainfall per unit time Rainfall Depth and Intensity Time (min) Rainfall (in) 0 5 10 15 20 25

30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 Max. Depth

Max. Intensity 0.02 0.34 0.1 0.04 0.19 0.48 0.5 0.5 0.51 0.16 0.31 0.66 0.36 0.39 0.36 0.54 0.76 0.51 0.44 0.25 0.25 0.22 0.15 0.09

0.09 0.12 0.03 0.01 0.02 0.01 0.76 9.12364946 Cumulative Rainfall (in) 0 0.02 0.36 0.46 0.5 0.69 1.17 1.67 2.17 2.68 2.84 3.15 3.81 4.17 4.56

4.92 5.46 6.22 6.73 7.17 7.42 7.67 7.89 8.04 8.13 8.22 8.34 8.37 8.38 8.4 8.41 Running Totals 30 min 1h 2h 1.17 1.65 1.81 2.22

2.34 2.46 2.64 2.5 2.39 2.24 2.62 3.07 2.92 3 2.86 2.75 2.43 1.82 1.4 1.05 0.92 0.7 0.49 0.36 0.28 3.07 6.14 3.81 4.15

4.2 4.46 4.96 5.53 5.56 5.5 5.25 4.99 5.05 4.89 4.32 4.05 3.78 3.45 2.92 2.18 1.68 5.56 5.56 8.13 8.2 7.98 7.91 7.88 7.71

7.24 8.2 4.1 Incremental Rainfall 0.8 Incremental Rainfall (in per 5 min) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 5

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 Time (min) Rainfall Hyetograph Cumulative Rainfall 10 9 Cumulative Rainfall (in.) 8 7 6 5 3.07 in 4 8.2 in 30 min 3

5.56 in 2 1 hr 1 2 hr 0 0 30 60 90 Time (min.) Rainfall Mass Curve 120 150 Arithmetic Mean Method

Simplest method for determining areal average P1 = 10 mm P1 P2 = 20 mm P2 N 1 P = 30 3 P mm N i 1 P i 10 20 30

P 20 mm 3 Gages must be uniformly distributed Gage measurements should not vary greatly about the mean P3 Thiessen polygon method Any point in the watershed receives the same amount of rainfall as that at the nearest gage Rainfall recorded at a gage can be applied to any point at a distance halfway to the next station in any direction Steps in Thiessen polygon method 1. Draw lines joining adjacent gages 2. Draw perpendicular bisectors to the lines created in step 1 3. Extend the lines created in step 2 in both directions to form representative areas for gages 4. Compute representative area for each gage

5. Compute the areal average using the following formula 1 N P Ai Pi A i 1 12 10 15 20 20 30 P 20.7 mm 47 P1 A1 P2 A2 P3 A3 P1 = 10 mm, A1 = 12 Km2 P2 = 20 mm, A2 = 15 Km2 P3 = 30 mm, A3 = 20 Isohyetal method

Steps Construct isohyets (rainfall contours) Compute area between each pair of adjacent isohyets (Ai) Compute average precipitation for each pair of adjacent isohyets (pi) Compute areal average using the following formula 1M N PP P Ai pA i i i A i 1 i 1 P 5 5 18 15 12 25 12 35 21.6 mm 47 10 20

P1 A1=5 , p1 = 5 A2=18 , p2 = P2 15 A3=12 , p3 = 25 30 P3 A4=12 , p3 = 35 Inverse distance weighting Prediction at a point is more influenced by nearby measurements than that by distant measurements The prediction at an ungaged point is inversely proportional to the distance to

the measurement points Steps P1=1 0 P2= 20 Compute distance (di) from ungaged point to all measurement points. d1=25 d2=15 p Compute the precipitation at the ungaged point using the following formula 2 2 d12 x1 x2 y1 y2 N Pi 2

i 1 d i P N 1 2 i 1 d i P3=3 0 d3=10 10 20 30 2 2 2 P 25 15 10 25.24 mm 1 1 1 25 2 152 10 2

Rainfall interpolation in GIS Data are generally available as points with precipitation stored in attribute table. Rainfall maps in GIS Nearest Neighbor Thiessen Polygon Interpolation Spline Interpolation NEXRAD NEXt generation RADar: is a doppler radar used for obtaining weather information A signal is emitted from the radar which returns after striking a rainfall drop Returned signals from the radar are analyzed to compute the rainfall intensity and integrated over time to get the precipitation NEXRAD Tower Working of NEXRAD

NEXRAD data NCDC data (JAVA viewer) http://www.ncdc.noaa.gov/oa/radar/jnx/ West Gulf River Forecast Center http://www.srh.noaa.gov/wgrfc/ National Weather Service Animation http://weather.noaa.gov/radar/mosaic.loop/DS.p19r0/ar.us.conus.shtml

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