evapotranspiration Atmospheric Water.pptx

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1. CHAPTER THREE Atmospheric Water

2. Of the many meteorological processes occurring continuously within the atmosphere, the processes of precipitation and evaporation , in which the atmosphere interacts with surface water , are the most important for hydrology Much of the water precipitated on the land surface is derived from moisture evaporated from the oceans and transported long distances by atmospheric circulation The two basic driving forces of atmospheric circulation result from the rotation of the earth and the transfer of heat energy between the equator and the poles

3. Water Vapor Atmospheric water mostly exists as a gas, or vapor, but briefly and locally it becomes a liquid in rainfall and in water droplets in clouds, or it becomes a solid in snowfall, in hail, and in ice crystals in clouds. The amount of water vapor in the atmosphere is less than 1 part in 100,000 of all the waters of the earth, but it plays a vital role in the hydrologic cycle.

4. Vapor transport in air through a hydrologic system can be described by the Reynolds transport theorem(RTT) . Letting the extensive property B be the mass of water vapor . The intensive property ᵦ = dB / dm is the mass of water vapor per unit mass of moist air ; this is called the specific humidity qv , and equals the ratio of the densities of water vapor ( ρ v) and moist air ( ρ a):

5. By the law of conservation of mass, dBldt = mv , the rate at which water vapor is being added to the system + ve for evaporation and – ve for condensation The Reynolds transport equation for this system is the continuity equation for water vapor transport:

6. Vapor Pressure ( e ) Dalton's Law Of Partial Pressures states that the pressure exerted by a gas (its vapor pressure) is independent of the presence of other gases ; the vapor pressure e of the water vapor is given by the ideal gas law as where T is the absolute temperature in K, and Rv is the gas constant for water vapor. If the total pressure exerted by the moist air is P, then p — e is the partial pressure due to the dry air , and

7. where ρ d is the density of dry air and R d is the gas constant for dry air (287 J/kg-K). The density of moist air ρ a is the sum of the densities of dry air and water vapor , that is, ρ a = ρ d + ρ v and the gas constant for water vapor is Rv = Rd/0.622 , where 0.622 is the ratio of the molecular weight of water vapor to the average molecular weight of dry air . Combining (3.2.3) and (3.2.4) using the above definition gives

8. By taking the ratio of Eqs . (3.2.3) and (3.2.5), the specific humidity q v is approximated by Also, (3.2.5) can be rewritten in terms of the gas constant for moist air, Ra, as The relationship between the gas constants for moist air and dry air is given by:

9. Saturation Vapor Pressure For a given air temperature, there is a maximum moisture content the air can hold , and the corresponding vapor pressure is called the saturation vapor pressure e s . At this vapor pressure, the rates of evaporation and condensation are equal . Over a water surface the saturation vapor pressure is related to the air temperature as shown in Fig. 3.2.1; an approximate equation is:

10. where e s is in pascals (Pa = N/m2) and T is in degrees Celsius(°C) Gradient of Saturation Vapor The gradient ∆ = de s / dT of the saturated vapor pressure curve is found by differentiating (3.2.9): where  is the gradient in pascals per degree Celsius Relative Humidity The relative humidity R h is the ratio of the actual vapor pressure to its saturation value at a given air temperature (see Fig. 3.2.1):

11. The temperature at which air would just become saturated at a given specific humidity is its dew-point temperature T d .

12. Water Vapor In A Static Atmospheric Column Three laws govern the properties of water vapor in a static column: i ) the ideal gas law ii) the hydrostatic pressure law

13. iii) the variation of air temperature with altitude is described by where α is the lapse rate Lapse rate   is the rate at which Earth's atmospheric temperature decreases with an increase in altitude, or increases with the decrease in altitude.

14. As shown in Fig. 3.2.2, A linear temperature variation combined with the two physical laws yields a nonlinear variation of pressure with altitude . Density and specific humidity also vary nonlinearly with altitude. From (3.2.12), ρ a = p/ RaT , and substituting this into (3.2.13) yields:

15. Substituting and integrating both sides between two levels 1 and 2 in the atmosphere gives From (3.2.14) the temperature variation between altitudes z 1 and z 2 is

16. Precipitable Water The amount of moisture in an atmospheric column is called its precipitable water . Consider an element of height dz in a column of horizontal cross-sectional area A (Fig. 3.2.2). The mass of air in the element is paAdz and the mass of water contained in the air is qvpaA dz . The total mass of precipitable water in the column between elevations z1 and z2 is:

17. The integral (3.2.17) is calculated using intervals of height  z, each with an incremental mass of precipitable water where qv and  a are the average values of specific humidity and air density over the interval. The mass increments are summed over the column to give the total precipitable water.

18. 3.3 Precipitation Precipitation includes rainfall, snowfall, and other processes by which water falls to the land surface, such as hail and sleet. The formation of precipitation requires the lifting of an air mass in the atmosphere so that it cools and some of its moisture condenses. The three main mechanisms of air mass lifting are: Frontal lifting , where warm air is lifted over cooler air by frontal passage; Orographic lifting , in which an air mass rises to pass over a mountain range ; and convective lifting , where air is drawn upwards by convective action, such as in the center of a thunderstorm cell.

19. The formation of precipitation in clouds is illustrated in Fig. 3.3.1

20. Cloud seeding is a process of artificially nucleating clouds to induce precipitation. Silver iodide is a common nucleating agent and is spread from aircraft in which a silver iodide solution is evaporated with a propane flame to produce particles. While there have been many experiments wherein cloud seeding was considered to have induced precipitation, the great variability of meteorological processes involved in producing precipitation make it difficult to achieve consistent results.

21. Terminal Velocity Three forces act on a falling raindrop (Fig. 3.3.2): a gravity force Fg due to its weight, a buoyancy force Fb due to the displacement of air by the drop, and a drag force Fd due to friction between the drop and the surrounding air. If the drop is a sphere of diameter D, its volume is (  /6)D3 so the weight force is:

22. and the buoyancy force is Where pw and pa and are the densities of water and air, respectively

23. The friction drag force is given by where Cd is a dimensionless drag coefficient A = (  /4)D 2 is the cross-sectional area of the drop, and V is the fall velocity.

24. If the drop is released from rest , it will accelerate until it reaches its terminal velocity Vt , at which the three forces are balanced. In this condition , which, solved for Vt , is:

25. The assumption of a spherical raindrop shape is valid for drops up to 1 mm in diameter . Beyond this size, the drops become flattened on the bottom and more oval in cross section; then they are characterized by the equivalent diameter of a spherical raindrop having the same volume as the actual drop ( Pruppacher and Klett , 1978). Raindrops can range up to 6 mm in diameter, but drops larger than 3 mm are unusual, especially in low-intensity rainfall .

26. Variability of Precipitation Precipitation varies in space and time according to the general pattern of atmospheric circulation and according to local factors. The average over a number of years of observations of a weather variable is called its normal value. Total JJAS rainfall (mm/day) climatology over Ethiopia. ** Kiremt  is the main rainy season, occurring from June to September. During this season, the Inter-Tropical Convergence Zone (ITCZ) and the moist southwesterly monsoon flow from the southern hemisphere are the main rain producing structure. The onset and spatial distribution of rainfall are also found to follow the oscillation of the ITCZ and the intensity of the southern hemispheric anticyclones**

27. Total FMAM rainfall (mm/day) climatology over Ethiopia. Note: October to January is called bega season in Ethiopia cool and dry

28. The El Niño - Southern Oscillation (ENSO) phenomenon is a global event arising from large-scale interactions between the ocean and the atmosphere in the tropical Pacific Ocean . Much has been established about ENSO and its impacts, as well documented ( Zebiak and Cane 1987; Mason et al. 1999). Regarding ENSO and Belg rainfall relationship previous studies have had little to say about ENSO and the Ethiopian Belg rainfall, and those that have addressed this relationship have concluded that an ENSO- Belg signal is weak. Nonetheless, this study suggests a clear link between ENSO and Belg rainfall. The linkage can be illustrated using CCA, whose dominant loading pattern depicts an ENSO versus FMAM rainfall relationship in which In La Niña state the main recipients of Belg rainfall experience deficient rainfall, while in El Niño situation most of the Belg rainfall-benefitting areas experience enhanced rainfall (Fig.5).

29. 3.4 Rainfall Rainstorms vary greatly in space and time. They can be represented by isohyetal maps; an isohyet is a contour of constant rainfall. Isohyetal maps are prepared by interpolating rainfall data recorded at gaged points. A rain gage record consists of a set of rainfall depths recorded for successive increments in time.

30. A Rainfall Hyetograph is a plot of rainfall depth or intensity as a function of time

31. By summing the rainfall increments through time, a cumulative rainfall hyetograph, or rainfall mass curve, is produced ,

32. The maximum rainfall depth, or intensity , (depth/time) recorded in a given time interval in a storm is found by computing a series of running totals of rainfall depth for that time interval starting at various points in the storm, then selecting the maximum value of this series.

33. For example, for a 30-minute time interval, Table 3.4.1 shows running totals beginning with 1.17 inches recorded in the first 30 minutes, 1.65 inches from 5 min to 35 min, 1.81 inches from 10 min to 40 min, and so on. The maximum 30 minute recorded depth is 3.07 inches recorded between 55 min and 85 min, corresponding to an average intensity of 3.07 in/0.5h = 6.14 in/h over this interval. Table 3.4.1 shows similarly computed maximum depths and intensities for one and two-hour intervals. It can be seen that as the time period increases, the average intensity sustained by the storm decreases (5.56 in/h for one hour, 4.10 in/h for two hours), just as the average intensity over an area decreases as the area increases.

34. Computations of maximum rainfall depth and intensity performed in this way give an index of how severe a particular storm is, compared to other storms recorded at the same location, and They provide useful data for design of flow control structures. An important fact to be determined from historical rainfall records is the average depth of rainfall over an area such as a watershed .

35. 2.5 Mean Precipitation over an area Rain gauges rainfall represent only point sampling of the areal distribution of a storm The important rainfall for hydrological analysis is a rainfall over an area, such as over the catchment To convert the point rainfall values at various stations to in to average value over a catchment, the following methods are used: arithmetic mean the method of the Thiessen polygons the isohyets method

36. Arithmetic Mean Method When the area is physically and climatically homogenous and the required accuracy is small, the average rainfall ( ) for a basin can be obtained as the arithmetic mean of the h i values recorded at various stations. Applicable rarely for practical purpose

37. Method of Thiessen polygons EXAM CALCULATION The method of Thiessen polygons consists of attributing to each station an influence zone in which it is considered that the rainfall is equivalent to that of the station. The influence zones are represented by convex polygons. These polygons are obtained using the mediators of the segments which link each station to the closest neighbouring stations

38. Generally for M station The ratio called the weightage factor of station i

39. Isohyetal Method

40. P 1 , P 2 , P 3 , …. , P n – the values of the isohytes a 1 , a 2 , a 3 , …., a 4 – are the inter isohytes area respectively A – the total catchment area - the mean precipitation over the catchment Isohyetal Method The isohyet method is superior to the other two methods especially when the stations are large in number. NOTE

41. 2.6 Intensity – Duration – Frequency (IDF) Relationship Mass Curve of Rainfall 1 st storm, 16 mm 2 nd storm, 16 mm

42. IDF …. Hyetograph is a plot of the accumulated precipitation against time, plotted in chronological order Total depth = 10.6 cm Duration = 46 hr

43. In many design problems related to watershed such as runoff disposal, erosion control, highway construction, culvert design, it is necessary to know the rainfall intensities of different durations and different return periods. The curve that shows the inter-dependency between i (cm/ hr ), D (hour) and T (year) is called IDF curve. The relation can be expressed in general form as: IDF …. i – Intensity (cm/ hr ) D – Duration (hours) K, x, a, n – are constant for a given catchment

44. 35 MEAN PRECIPITATION OVER AN AREA 2. Thiessen-Mean Method    

45. 36 MEAN PRECIPITATION OVER AN AREA 3. Isohyetal Method