GEOG415 Mid-term Exam 110 minute February 27, 2003 1 Name: ID: 1. The graph shows the relationship between air temperature and saturation vapor pressure. (a) Estimate the relative humidity of an air parcel having a temperature of 17.5 C and a dew point of 11 C. (3 pts) 13 / 20 100 = 65 % (b) Calculate the vapor pressure deficit of this air parcel. (2 pts) 20 mb 13 mb = 7 mb saturation vapor pressure (mb) 24 20 16 12 8 5 10 15 20 temperature (C) 2. Answer the following questions of interception. (a) Briefly describe gross precipitation. (1 pt) Amount of precipitation reaching the canopy top. (b) Briefly describe throughfall. (1 pt) Amount of precipitation that penetrates the canopy directly through spaces between leaves, or by dripping from leaves, twigs, and branches. (c) Briefly describe stemflow. (1 pt) Amount of precipitation that reaches the ground by running down stems and trunks. (d) What is an expected percentage of interception to total snowfall by coniferous trees during the mid to late winter in the boreal forests of the Prairie Provinces? (1 pt) 40-50 % (30-60 % is acceptable)
3. The table lists the annual-maximum series of 60-minute rainfall recorded at a weather station. (a) What is the annual-maximum series of 60-minute rainfall? Briefly explain how it is constructed from rainfall data. (2 pts) 2 Sample of the population of all 60-minute annual extreme rainfall at a station. It is constructed by 1) estimate maximum 60-min rainfall for all storms in a given year, 2) select the storm with the highest 60-min rainfall, and 3) repeat the procedure for all years. (b) Prepare a table of recurrence interval T = (n + 1)/m, where n is the number of samples and m is the rank. (2 pts) (c) Plot a graph of rain against T on the Gumbel paper provided. (2 pts) (d) From the Gumbel plot, estimate the amount of 60-minute rainfall with an exceedence probability of 0.1. (2 pts) 60 mm (e) Next page Year Rain (mm) 1991 26.4 1992 41.7 1993 21.5 1994 37.5 1995 38.5 1996 45.5 1997 36.5 1998 30.6 1999 53.2 2000 30.9 2001 61.8 rainfall exceedence probability.99.91.50.20.10.05.02.01 70 60 50 40 30 20 1.01 1.1 1.5 2 3 4 5 10 20 30 50 100 recurrence interval (yr) Rank Rain T (mm) (yr) 1 61.8 12 2 53.2 6 3 45.5 4 4 41.7 3 5 38.5 2.4 6 37.5 2 7 36.5 1.71 8 30.9 1.5 9 30.6 1.33 10 26.4 1.2 11 21.5 1.09
Question 3, continued from the last page. (e) Is it acceptable to use the 60-minute rainfall with 10-yr recurrence interval you just calculated as a representative of basin-average rainfall in the mapped area? Provide a brief explanation. (2 pts) 3 No. High-intensity, short-duration storms are usually very localized. A storm that drops 20 mm in 10 minutes at a particular station is unlikely to cover the entire basin. 4. Consider a small lake that has no surface inflow or outflow of water. (a) The graph shows the relation between the rate of water loss from the lake and the product of wind speed measured 2-m above the lake surface (u 2 ) and the difference between the saturation vapor pressure on the water surface (e s ) and the vapor pressure in the overlying air (e a ). Assume that the lake evaporation rate E 0 (cm d -1 ) is given by the mass transfer equation: E 0 = Nu 2 (e s e a ) Estimate the mass transfer coefficient N and report it with the appropriate unit. (3 pts) Water loss (cm d -1 ) 1 0.8 0.6 0.4 0.2 0 800 0.75 0 200 400 600 800 1000 u 2 (e s - e a ) (km d -1 mb) N = (0.75 cm d -1 ) / (800 km d -1 mb) = 9.4 10-4 cm d -1 / (km d -1 mb) (b) Next page
Question 4, continued from the last page. (b) Using the mass transfer coefficient, predict the evaporation (cm d -1 ) from this lake under the following condition. Air temperature = 15 ºC Relative humidity = 75 % Water surface temperature = 12 ºC Wind speed at 2 m = 1.5 m s -1 (3 pts) 4 u 2 = 130 km d -1 e s = 14 mb (from the diagram for Question #1) e a = 17 mb 0.75 = 12.8 mb E 0 = 9.4 10-4 cm d -1 / (km d -1 mb) 130 km d -1 (14-12.8) mb = 0.15 cm d -1 (c) The lake has an area of 0.12 km 2. Convert your answer in (b) to the volumetric rate (m 3 d -1 ) of total evaporation loss from the lake. (2 pts) 0.0015 m d -1 0.12 10 6 m 2 = 180 m 3 d -1 5. Answer the following questions about radiation and energy balance. (a) List at least three major components of net radiation, and briefly explain each component. (3 pts) Shortwave incoming: Sum of direct and diffuse solar radiation Shortwave outgoing: Reflected shortwave radiation (Albedo itself is not a component of radiation. Albedo is accepted as an answer only when it is used as an substitute for the reflected shortwave radiation.) Longwave incoming: Radiation emitted by the atmosphere and clouds Longwave outgoing: Radiation emitted by the surface (Net longwave radiation is also an acceptable answer) (b) Next page
Question 5, continued from the last page. (b) Consider a vegetated surface that receives net radiation. When the storage of heat is negligible, the net radiation input is balanced by the energy loss related to two important energy transfer processes. List the two processes and briefly explain them. (3 pts) Sensible heat transfer: Exchange of energy between the surface and the atmosphere due to conduction and convection by turbulent air flow. Latent heat transfer: Transfer of the latent heat of vaporization from the surface to the atmosphere by evaporation and transpiration. 5 (c) Consider a net radiation input of 200 W m -2. If all of this radiation is used to evaporate water, what is the expected rate of evaporation? Report the answer it in mm d -1. The density of water is 1000 kg m -3, and the latent heat of vaporization is 2460 J g -1. (3 pts) 200 J s -1 / (1000 kg m -3 2460 10 3 J kg -1 ) = 8.1 10-8 m s -1 = 7.0 10-3 m d -1 = 7.0 mm d -1 6. The field capacity of soil under an irrigated field is 0.22 in terms of volumetric water content. The wilting point of the same soil is 0.05. The field is planted with wheat having a rooting depth of 60 cm. (a) Calculate the available water capacity (AWC, mm) of this soil for wheat. (2 pts) (0.22-0.05) 600 mm = 102 mm (b) Next page
Question 6, continued from the last page. (b) A sample of soil was collected a few days after the field was irrigated. The total volume of soil was 120 cm 3, of which 13 cm 3 was water. Calculate the volumetric water content of the soil. Calculate also the available water (AW, mm) of this soil for wheat. (2 pts) 6 (13/120-0.05) 600 mm = 35 mm (c) The relationship between actual ET (AET) and potential ET (PET) is given by the following: AET/PET = f(aw/awc) where the form of the function f( ) is shown in the diagram below. If PET = 4.0 mm d -1, what is the expected AET for this soil? (2 pts) 1 AW/AWC = 35 mm/102 mm = 0.34 AET/PET = 0.80 AET = 4.0 mm d -1 0.80 = 3.2 mm d -1 AET/PET 0.8 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 AW/AWC #1 #2 #3 #4 #5 #6 Total /5 /4 /10 /8 /9 /6 /42