Precipitation

T. Giambelluca GEOG 405

University of Hawai‘i at Mānoa

Humidity Humidity = the water vapor content of the air

Water vapor content can be expressed in various ways:

•  Specific Humidity = mass of water vapor per mass of air (g/kg)

•  Absolute Humidity = mass of water vapor per volume of air (g/m3)

•  Mixing Ratio = mass of water vapor per mass of "dry air" (g/kg)

•  Vapor Pressure = partial pressure of water vapor (mb)

Relative Humidity

•  Relative Humidity = (actual water vapor content of air)/(maximum water vapor capacity of air)

•  RH = (VP/Saturation VP) * 100%

•  RH = e/esat * 100%

SATURATION: condition of equilibrium between liquid water and water vapor or between ice and water vapor

At the molecular level:

•  Liquid to Gas: Occurs when liquid water molecules hit the air-water interface with sufficient kinetic energy to overcome surface tension. Velocity (kinetic energy) of molecules can be observed as the temperature of the water. The warmer the water, the more frequently molecules will "escape" the liquid to become gas molecules.

•  Gas to Liquid: Gas molecules are also moving around, and those striking the liquid water surface will become liquid. The higher the the concentration of water vapor molecules (the higher the humidity), the more often water vapor molecules will strike the water surface and become liquid.

•  So, the transition from liquid to gas depends mostly on the water temperature and the transition from gas to liquid depends mostly on the humidity.

•  In the figure above, if the box is sealed and initially has no water vapor, the humidity will start to increase as liquid water molecules escape the surface tension. As the humidity increases, gas molecules hit the water surface more and more frequently. Eventually the humidity increases to a point where the rate of gas to liquid transitions is equal to the rate of liquid to gas transitions.

•  This is an equilibrium.

•  At this point, the humidity no longer increases and the air is said to be saturated.

•  The relative humidity is 100%.

Saturation Humidity e.g. Saturation Vapor Pressure The humidity at which the air becomes saturated depends on the temperature

The relationship between air temperature and saturation vapor pressure does not have an exact analytical solution. But, it can be approximately very closely using one of several expressions. Below is one such equation. In put temperature (T) in degrees Celsius to get the answer in hectoPascals (hPa).

Sample Problem

•  If the vapor pressure is 10 mb and the temperature is 20ºC, what is the relative humidity?

•  RH=100* e/esat

•  First, you have to get the saturation vapor pressure, which is a function of the temperature. From the table, we get esat = 23.4 mb.

•  RH = 100 * 10/23.4 =42.7%

T (ºC) esat (mb) T (ºC) esat (mb)

10 12.3 23 28.1

11 13.1 24 29.8

12 14.0 25 31.7

13 15.0 26 33.6

14 16.0 27 35.6

15 17.0 28 37.8

16 18.2 29 40.0

17 19.4 30 42.4

18 20.6 31 44.9

19 22.0 32 47.5

20 23.4 33 50.3

21 24.9 34 53.2

22 26.4 35 56.2

Dew Point Temperature

Example: •  Air with a vapor pressure of 20 mb, and a

temperature of 25ºC is unsaturated (because esat @ T = 25ºC is 31.7 mb). What is the dew point temperature.

•  Dew point temperature is strictly a function of the vapor pressure. Look at the table to find out the temperature at which 20 mb would be the saturation vapor pressure.

•  From the table, we see: •  esat @ T = 17ºC is 19.4 mb •  esat @ T = 18ºC is 20.6 mb •  By interpolation, we can get esat @ T = 17.5ºC is 20

mb •  Therefore, the dew point temperature is 17.5ºC. •  In other words, if this air were cooled from 25ºC

down to 17.5ºC, the air would become saturated.

T (ºC) esat (mb) T (ºC) esat (mb)

10 12.3 23 28.1

11 13.1 24 29.8

12 14.0 25 31.7

13 15.0 26 33.6

14 16.0 27 35.6

15 17.0 28 37.8

16 18.2 29 40.0

17 19.4 30 42.4

18 20.6 31 44.9

19 22.0 32 47.5

20 23.4 33 50.3

21 24.9 34 53.2

22 26.4 35 56.2

Unsaturated air, if cooled sufficiently, will eventually reach saturation. The temperature to which you would have to cool a parcel of air in order to saturate it is called the Dew Point Temperature.

LIFTING MECHANISMS

1. Orographic 2. Frontal 3. Convergence 4. Convection

Humidity Measurement Sling psychrometer

Chilled mirror hygrometer

Thin-film capacitance probe

Open-path infrared gas analyzer

Humidity Measurement

Mint Julep Hygrometer

Back to Precipitation: Thought Problem

Assignment: Go out and measure rainfall, and give me as much information about rainfall as possible. You have no access to specialized equipment. How would you make the measurements? What kinds of information would you try to provide?

Questions to Consider

•  Instrument? •  Interval? •  Units? •  Duration? •  Spatial coverage? •  Intensity? •  Purpose of data?

What about data quality? •  What are the sources of error?

–  Measurement error •  Evaporation •  Overflow •  Out of level •  Leaks •  Wind

–  Sampling error •  Representative time period? •  Representative location? •  Appropriate interval? •  Interval divides events?

–  Data transfer error •  Misreading instrument •  Copying error

Descriptive Statistics

•  Mean: Excel function: =average()

•  Standard Deviation: Excel function: =stdev()

•  Coefficient of Variation: Excel function: = stdev()/average()

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Double Mass Analysis: Checking Consistency

•  Network of stations whose precipitation is correlated

•  Check each station against series of aggregated values of the other stations

•  Use cummulative totals

Double Mass Analysis: Step-by-Step

1.  Identify the column for the station in question 2.  For each year calculate the average rainfall of all the

other stations 3.  Calculate the cummulative rainfall total for each year

for the station in question 4.  Calculate the cummulative rainfall total for each year

for the average of the other stations (from step 2) 5.  Plot a scattergram of the cummulative totals for the

station in question against the cummulative totals for the average of the other stations

6.  Examine the plot for changes in slope, which would indicate some kind of change in the location or exposure of the station

Missing Data Problem: Normal Ratio Method

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Areal Average Rainfall •  Arithmetic average •  Theissen polygon method

•  Isohyetal method

•  Interpolation to a grid