Meteo 300 Final

When a Cartesian coordinate system is placed on the globe, the negative x-axis always points to the west.

true

Consider matter that has an emissivity of 0.9 and is at a temperature of 368 K. What is the peak wavelength of the irradiance (micrometers, 3 decimal places).

7.85

An air parcel has the following characteristics: p = 925 hPa; T = 17 oC; w = 4 g kg-1. What is the pressure at the Lifting Condensation Level, pLCL (in hPa, 0 decimal places)?

710 (Two quantities are conserved with vertical ascent below cloud base: w and potential temperature. Go up the dry adiabat and the constant w lines until they intersect. The pressure at that point will be the LCL pressure.)

Consider a water drop growing by vapor deposition. If the drop is 2.0 μm in radius after growing 1.0 minutes by vapor deposition, what is the radius in μm (1 decimal place) after growing 23 minutes by vapor deposition?

9.6 (Use Equation 5.15 for both times and combine to eliminate the constant C) rd = (Ct)1/2

The supersaturation is -0.08. What is the relative humidity (%, 0 decimal places)?

92

Consider the fluctuations in the wind velocity (𝑈→U→ ) and the temperature T in the equation for advection: 𝑎𝑑𝑣=−𝑈→⋅∇→𝑇adv=−U→⋅∇→T Write 𝑈→U→ in its mean and perturbed parts and T in its mean and perturbed parts, take the Reynolds average and then write down an equation for the mean advection, 𝑎𝑑𝑣⎯⎯⎯⎯⎯⎯=−?adv¯=−? In the answers below, we will use < > to indicate the average instead of the overbar and will not have arrows over U and , but they are vectors. Which of the following terms survive?

<U' * DELTA (T)'> and -<<U><T>>

Stratospheric ozone is made by the reaction sequence:

O2+UV→O+O; O+O2+N2→O3+N2

For the following case, match "up" or "down" with each energy term in the energy budget for that case.

Qs: net radiation = Earth's IR (up) - (solar + atmospheric IR) (down) QH: sensible heat flux (up or down) QE: latent heat flux (up or down) QG: surface heating (up or down) ΔQs: surface energy storage in trees, buildings, etc.

When a Cartesian coordinate system is placed on the globe, the positive y-axis always points toward the North Pole.

True

The water vapor flux is usually interpreted as an energy flux for the atmosphere because water vapor is less dense than dry air and is thus more buoyant.

false

There is no boundary layer on a mountain top if it is 3000 m high.

false

When a Cartesian coordinate system is placed on the globe, the x-axis goes along a constant longitude line.

false

Consider an air parcel with a virtual temperature of 25 oC in an environment with a virtual temperature of 26.0 oC and at a pressure 913 hPa. What will be the air parcel's vertical velocity (m s-1, one decimal place) after one minute if the buoyancy does not change?

-2

Ozone has an absorption cross section of 1.0 x 10-23 m2 at a wavelength of 310 nm. If the average ozone concentration in the ozone layer is 2 x 1018 molecules m-3 and the thickness of the ozone layer is 25 km, what is the fraction of ultraviolet radiation that gets through when the solar zenith angle, SZA = 75.7o, 2 decimal places?

.13

In a cloud of volume 904084 m3,if the mean cloud drop diameter is 10 um (i.e., 10-6 m) and the mean number per volume is 658 cm-3, what is the liquid water mass (in metric tons (1 tonne=1000 kg), to two decimal places)?

.31

If the mean cloud drop diameter is 11 um (i.e., 10-6 m) and the mean number per volume is 640 cm-3, what is the liquid water content, LWC (in g m-3, to two decimal places)?

.45

Ozone has an absorption cross section of 1.0 x 10-23 m2 at a wavelength of 310 nm. If the average ozone concentration in the ozone layer is 2 x 1018 molecules m-3 and the thickness of the ozone layer is 25 km, what is the fraction of ultraviolet radiation that gets through when the solar zenith angle, SZA = 16.2o, 2 decimal places?

.59

Consider a beam of radiation passing through a uniform gas that has a cross section σ = 48 x 10-23 m2 and a number density, n = 7 x 1017 molecules m-3. What fraction of the irradiance remains after it travels 1051 m through the gas, to two decimal places? (hint: use Equation 6.10)

.7

Suppose that two things have the same total irradiance but the ratio of thing 1's to thing 2's emissivity is 2 (i.e., emissivity (thing 1)/emissivity (thing 2)). What is the ratio of the temperatures of thing 1 to thing 2 to two decimal places (i.e., T(thing 1)/T(thing 2))?

.84

Consider an air parcel with a virtual temperature of 25 oC in an environment with a virtual temperature of 25 oC and at a pressure 937 hPa. What is the acceleration of the air parcel due to buoyancy (m s-2) to three decimal places?

0

Consider two air parcels: parcel 1 with pressure 288 hPa and temperature 224 K and parcel 2 with pressure 940 hPa and temperature 310 K. Which parcel has the greater potential temperature? Type the number 1 for parcel 1 and type the number 2 for parcel 2.

1 Calculate the two potential temperatures and then compare them.

There are two things: thing 1 and thing 2. The ratio of the peak wavelength for thing 1's Planck distribution function spectral irradiance to thing 2's is 0.98. What is the ratio of temperatures of thing 1 to thing 2 to 2 decimal places(i.e., T(thing 1)/T(thing 2))?

1.02

Density Calculation Consider a parcel with the following variables... Pressure: 916 hPa Temperature: 15 C Specific Humidity: 5 g/kg Calculate the density in kg m-3 (2 decimal places). Use 273 K as the equivalent to 0oC.

1.1 (The best way to get the density from the given data is to first calculate virtual temperature and then use the Ideal Gas Law for dry air to calculate the density.) First calculate the virtual temperature. Be sure to get specific humidity in units of kg/kg. Then use the Ideal Gas Law in the form ρ=pRdT Remember that p must be in Pascals and T must be in Kelvin.

Frequency

1/s Hz

Consider a beam of radiation passing through a uniform gas that has a cross section, LaTeX: \sigmaσ = 79 x 10-23 m2 and pathlength of 438 m. The fraction that remains is measured to be 0.54. What is the number density, n, of the absorbing molecules, in units of 1017 molecules m-3 (0 decimal places)?

18

Consider an idealized vertical temperature profile that is the constant temperature of 300 K over the entire boundary layer (from 0 to 1000 m height) and then jumps to 309 K just above 1000 m in the free troposphere and then falls off with the dry adiabatic lapse rate. Assume that the pressure is constant at 960 hPa for this entire height. If the boundary layer is well mixed and the surface heating rate is 334 Watts m2 starting at 10 am, when will the troposphere become unstable? Use a 24-hour clock and keep the fraction of an hour (e.g., time 16.5, which is 4:30 pm). (hint: calculate the density and volume of a column of air 1000x1x1 m3.) Use the heating rate equation and use the temperature difference between the boundary layer and the free troposphere just above it to calculate the time it will take for instability to set in. Draw the profile if it would help you visualize what is happening.

18.4 (Use the heating rate equation and use the temperature difference between the boundary layer and the free troposphere just above it to calculate the time it will take for instability to set in. Draw the profile if it would help you visualize what is happening.)

Earth's average surface temperature in 2013 was 14.6 oC, or 287.7 K. This temperature is about 1 K higher than the 20th century average. Suppose that policymakers decided that Earth's average surface temperature should be 1.9 K lower than the 2013 temperature in order to have a stable climate. Engineers tell them that they can put reflectors in space to block some of the sun, and thus reduce the surface temperature. What percentage of the solar radiation must be blocked by the space reflectors in order to reduce Earth's temperature by the desired amount (to one decimal place)? Assume that the Earth's average surface temperature is proportional to the 1/4 power of the incoming solar radiation at the top of the Earth's atmosphere (Equation 7-3).

2.6

The O-O chemical bond can be broken with 495 kJ/mol. Find the wavelength of a photon that is energetic enough to break the bond (0 decimal places). =

240

Consider a volume of dry air (296 m3) that has a pressure of 964 hPA and temperature 27 oC. This air is cooled at a rate (Q) of -102 Watts (J/s) for 2 hours. What is the final temperature of this air parcel in oC to one decimal place?

25 Tfinal = (heating rate*time)/(cp*mass) + Tinitial. Use the Ideal Gas Law with Rd to find the mass.

Suppose that the 500 mb surface is at 542 dam (decameters, 10's of meters) and the 1000 mb surface is at 3 dm. What is the average temperature (in Kelvin, 0 decimal places) of the layer between 1000 mb and 500 mb?

266 Use equation: z2−z1= (Rd/g)*ln(p1p2)*T

For a constant pressure, which temperature gives you the greatest height?

270 K (higher temperature = greater height)

For a constant altitude, which temperature gives you the greatest pressure?

270 K (higher temperature = higher pressure)

For a dry air parcel with a temperature 17 oC and a pressure 619 hPa, what is the potential temperature in Kelvin?

333 (Use the equation for potential temperature. Be sure to convert temperature to Kelvin before using the equation.)

In the text, I used a two-layer atmospheric model to illustrate how Earth's surface temperature increases when there are atmospheric layers that strongly absorb infrared radiation. Suppose that we use instead a model with 6 layers. Calculate the surface temperature (K, 0 decimal places) that would result using the same thinking that is used in the text for the two-layer model. Assume all the other properties that were assumed in the text for the two-layer model. Use 1361 W m-2 for the solar constant, 0.294 for the albedo, and 5.67 x 10-8 W m-2 K-4 for the Stefan-Boltzmann constant

415

The Cl-Cl chemical bond can be broken with 239 kJ/mol. Find the wavelength of a photon that is energetic enough to break the bond (0 decimal places).

500

Consider a layer of air that is 921 meters thick with a pressure of 858 hPa and temperature of 286 K. Assume an area of 1 square meter. the air in a column 921 tall and 1 square meter in area experiences a heating rate Q of 355 Watts m2 for 5 hours at constant pressure. How much does the air temperature change, in oC to one decimal place? Calculate the density of the column of air using the Ideal Gas Law, then multiply by the volume (height times area). The heating rate times the time is then divided by the specific heat capacity, constant pressure, times the mass to give the temperature change in Kelvin, or oC, which are of course the same for a temperature change.

6.6 Calculate the density of the column of air using the Ideal Gas Law, then multiply by the volume (height times area). The heating rate times the time is then divided by the specific heat capacity, constant pressure, times the mass to give the temperature change in Kelvin, or oC, which are of course the same for a temperature change.

2b. If we assume that the average temperature in equation 2.19 is 242, then the scale height, H, in units of km to 1 decimal place is

7.1

Consider a water drop growing by vapor deposition. If the drop is 2.0 μm in radius after growing 1.0 minutes by vapor deposition, what is the radius in μm (1 decimal place) after growing 17 minutes by vapor deposition? Hint: use Equation 5.15 for both times and combine to eliminate the constant C.

8.2

A cloud drop with radius rL = 20 μm (1 μm = 10-6 m) and a mass of 3.3 x 10-8 g begins falling through a cloud in which the mean drop radius, rs, where rs/rL = 0.66. The difference in fall speed for the large drop and smaller drops, (vL-vs) is initially 0.02 m s-1. If the liquid water content of smaller drops is 0.8 g m-3, what is the rate at which the large drop adds mass by collision-coalescence, dmL/dt, in g s-1?

8.8 (For the collision efficiency, assume Ec = 0.09 - 1.5*(rs/rL -0.58)2 + .12*(rs/rL). Multiply your answer by 1012 and enter it with 1 decimal place.)

Consider a water drop growing by vapor deposition. If the drop is 2.0 μm in radius after growing 1.0 minutes by vapor deposition, how large is its radius in μm (1 decimal place) after growing 23 minutes by vapor deposition? Hint: Use Equation 5.15 for both times and combine the equations so that the constant C cancels out.

9.6

The saturation ratio is 0.98. What is the relative humidity (%, 0 decimal places)

98

What is the primary reason that more solar energy is deposited in the tropics than near the poles?

Because the solar irradiance (W m-2) is uniform in a plane perpendicular to Earth's orbit, the irradiance strikes Earth's surface at an angle near the poles and thus spread out over a larger area at the poles than in the tropics.

According to the hydrostatic equation, the density must be constant with height in the atmosphere.

False

If dry air comes in contact with liquid water, net condensation will occur.

False

The relative humidity is 100% when the condensation is greater than evaporation.

False

The saturation vapor pressure depends only on condensation.

False

The vapor pressure always equals the saturation vapor pressure at the ambient temperature.

False

The specific humidity is generally lower in the tropics than in the polar regions.

False (see map from lesson 3.1)

If you know T, you can calculate ws. Relative humidity is just 100* w/ws.

Incorrect. Find w from Td and ws from T. Relative humidity is 100* w/ws.

∂T/∂z, where T is temperature

K/2m

F(λ)=F0(λ)e(−σ n s) where F is an energy per area per unit time, n is a number concentration (number per volume), and s is a length. What are the dimensions of σ?

L2

(w′Θ′)⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯=−K∂Θ∂z where w′ is the vertical velocity and Θ has dimensions of temperature. What are the dimensions for K

L2/t

E=hcλ where E is energy, c is the speed of light, and λ is a length. What are the dimensions of h

ML2/t

Energy, E

ML2/t2

pdxdydz where p is pressure

ML2/t2

Assume that the number concentration of stratospheric ozone is the same for all latitudes at each altitude. Select the following statements below that are true.

More solar UV irradiance is absorbed in the polar regions than in the tropics. More solar UV irradiance is absorbed at sunset than at midday.

Tropospheric ozone is made by the reactions:

NO2+UV→NO+O; O+O2+N2→O3+N2

What does this behavior tell you about the typical change in 500 mb height surfaces as you go from low latitudes where it is warmer to higher latitudes where it is colder?

Since tropics are warmer than the polar regions, the 500 mb surface decreases from low to high latitudes.

Consider a dry air parcel. If the environmental lapse rate is 8.9°C/km, then is the air stable or unstable?

Stable

Temperature Calculation Consider a parcel with the following variables... Pressure: 969 hPa Density: 1.15 kg m-3 Specific Humidity: 7.71 g/kg Calculate the temperature of the air parcel in degrees Celcius (0 decimal places). Use 273 K as the same as 0oC.

T = p/(RdTv) = p/(Rd T(1+0.61q)) 19

Which of the following statements is correct?

The specific humidity q is always less than or equal to the water vapor mixing ratio w

The growth of a falling drop by collision-coalescence depends on which of the following four factors?

The total mass of liquid water per unit volume in the path of the larger drop. The difference in the velocities between the larger and smaller drops. The collection efficiency of the smaller drops by the larger drop.

1. The hydrostatic equation is central to atmospheric science. On a separate piece of paper, go through the derivation of the hydrostatic equation, making sure that you understand each step. Then answer the following questions. To derive this equation, we must assume that the density is constant in the volume element.

True

2. We can translate the hydrostatic equation into other useful equations by making a few simple assumptions. 2a. At some point in the transition from Equation 2.19 to 2.20, one of the integrations gave a logarithm.

True

Earth's spherical curvature causes the amount of solar radiation energy that strikes a square meter of Earth's surface at high latitudes to be less than the amount of solar radiation energy that strikes a square meter of Earth's surface in the tropics.

True

For moist air, the water vapor mixing ratio is always a little greater than the specific humidity.

True

It is possible for the relative humidity to be lower in Dallas, Texas than in Boston, Massachusetts while the specific humidity is higher in Dallas than in Boston.

True (To make this comparison, we need to know the specific humidity (or the relative humidity), and the temperature. This scenario is possible if the temperature in Dallas is higher than the temperature in Boston.)

Even though water can exist in the atmosphere as a solid, liquid, or vapor, water vapor obeys the Ideal Gas Law.

True (Water can change between vapor and liquid or ice, but the water that is in the vapor form obeys the Ideal Gas Law.)

w=−az−12bz2 where w is the vertical wind speed and z is the vertical distance. What are the dimensions of a and b

a=1/t;b=1L/t

Greenhouse gases cause surface warming by

acting as another radiation energy source for the surface.

The sky is blue because

air molecules scatter solar radiation perpendicular to the Sun's rays strongest at the shorter blue wavelengths.

Go back to the equation you found in part a, not part b. Multiply it by Earth's surface area (4πREarth2). What is this new quantity to a good approximation?

atmosphere pressure

Three essentials for cloud formation are:

cooling aerosol moisture

Which equation would you use to solve the following problem? Rain (mass: mliquid) falls into dry air below the cloud and evaporates. The mass of the air is (mair). How much does the temperature of the air decrease?

cpdmairΔTair=lvmliquid

Which equation would you choose to solve the following problem? A mass of rain (mrain) at temperature ToC falls on a snowpatch. What mass of snow (mice) is melted as the temperature of the liquid water from the rain goes to 0oC?

cwmrainΔTrain=lfmice

Averaged over the Earth, the energy going up through any level in the atmosphere must approximately

equal the energy going down through that level at the same time.

All particles immediately fall out of the atmosphere.

false

Cloud drops have different sizes only because their cloud condensation nuclei have different sizes.

false

If one air parcel is three times larger than a smaller air parcel and they mix, then the temperature and the vapor pressure of the mixed air parcel will be 3/4 of the way along the mixing line between the larger parcel and the smaller parcel and nearer to the smaller parcel.

false

No particles come from gases that react in the atmosphere.

false

The Bergeron-Findeisen process works because the saturation vapor pressure over ice is equal to the saturation vapor pressure over supercooled liquid water.

false

The amount of argon in the atmosphere has changed by more than a few percent over the last 20 years.

false

The chlorine catalytic cycle is the only catalytic cycle that destroys stratospheric ozone.

false

The net solar energy that is absorbed by the Earth system is balanced by Earth's infrared radiation going out to space at each and every latitude.

false

The oxidation of all volatile organic compounds produces methane.

false

A cloud drop with radius rL = 20 μm (1 μm = 10-6 m) and a mass of 3.3 x 10-8 g begins falling through a cloud in which the mean drop radius, rs, where rs/rL = 0.61. The difference in fall speed for the large drop and smaller drops, (vL-vs) is initially 0.02 m s-1. If the liquid water content of smaller drops is 0.73 g m-3, what is the rate at which the large drop adds mass by collision-coalescence, dmL/dt, in g s-1? For the collision efficiency, assume Ec = 0.09 - 1.5*(rs/rL -0.58)2 + .12*(rs/rL). Multiply your answer by 1012 and enter it with 1 decimal place.

idk

The solute needs to be soluble in water because:

it must be evenly distributed in the water so that some solute molecules occupy surface sites and attract water molecules.

Energy, E

kgm2/s2

∭pdxdydz where p is pressure

kgm2/s2

Adding water-soluble chemicals to pure water:

lowers the water vapor pressure for which evaporation equals condensation.

Multiply this equation for integral of the density over height by the acceleration due to gravity, g = 9.8 m s-2. What quantity has the same units as the quantity in this equation?

pressure

Consider a dry air parcel. If the environmental lapse rate is 6.5°C/km, then is the air stable or unstable?

stable

The production of tropospheric ozone requires three factors (check three):

sunlight nitrogen oxides volatile organic compounds or carbon monoxide

During radiative cooling (select all that apply):

temperature decreases. relative humidity increases. the saturation water vapor pressure decreases. water vapor pressure decreases. vapor pressure stays the same. -(The temperature decreases as the vapor pressure stays the same, so that the saturation vapor pressure decreases and the relative humidity increases.)

What is the primary reason for the Earth's seasons?

the Earth's rotation axis is not perpendicular to the plane of the Earth's orbit around the Sun

A small drop of pure water evaporates more quickly than a flat pool of pure water because:

the drop curvature makes it easier for liquid water molecules on the drop's surface to break hydrogen bonds and escape.

Raindrops can have which of the following shapes?

top half of a hamburger bun upside down bowl spherical ball

Absorption of radiation by matter depends on the available transitions between energy levels of the atoms and molecules that make up the matter.

true

Cloud drops form only when the relative humidity exceeds 100%.

true

It is possible to change the color of light by sending it through a gas or liquid that absorbs only some of the wavelengths of light.

true

The amount of carbon dioxide in the atmosphere has changed by more than a few percent over the last 20 years.

true

The fraction of backscatter is greatest when the particle radius is small compared to the radiation's wavelength.

true

The fraction of forward scattering is greatest when the size parameter is large.

true

Two objects can have the same total irradiance but different temperatures.

true

You can use the Ideal Gas Law to convert equation (2.20) into an equation of the change in density with height. Assume a constant temperature. Integrate this density equation as a function of altitude from Earth's surface (z=0) to infinity (space), using the constant scale height H. Prove to yourself that the form of this equation for the change in density with height is the same as the equation for the change in pressure with height with the assumption that the temperature is constant. You do not need to put any numbers into these equations for the mathematical manipulations you will do next. Answer the following question: The integral of the density over height from the surface to space is which of the following values? (hint: Use the Ideal Gas Law to relate density to pressure.)

ρoH

The relative humidity is 100% when the condensation equals evaporation.

True

The sequence of three events that lead up to precipitation formation by collisions coalescence

(1.) activation of a cloud drop by vapor deposition (2.) cloud drop growth by vapor deposition occurring as the square root of time (3.) drop growth by collision-coalescence as an exponential function of time

The temperature advection is zero if the air parcel motion is along an isotherm.

True

At -31o latitude, 1o of latitude equals how many kilometers (to 0 decimal places). Earth's radius is 6371 km.

111.0

Convert the math angle of 151 degrees to a meteorology angle in degrees.

119

An air parcel at a latitude of -19o with a velocity 40 m/s and a direction of 200o in math angle. What is the initial direction (math angle) of the Coriolis force (0 decimal places)?

290

An air parcel at a latitude of 37o with a velocity 20 m/s and a direction of 80o in math angle. What is the direction (math angle) of the Coriolis force (0 decimal places)?

-10

An air parcel at a latitude of 9o with a velocity 40 m/s and a direction of 80o in math angle. What is the initial direction (math angle) of the Coriolis force (0 decimal places)?

-10

Measurements of vertical wind velocity (cm s-1) are w = 1.2, 1.1,1.8, 1.3, 2, 1.6, -3.6, 0.8, 1.4, -0.9, and simultaneous measurements of temperature (oC) are T = 19.1, 21.1, 19.1, 18.6, 21.6, 21.3, 20.6, 18, 20.2, 22. What is the turbulent vertical kinematic heat flux (10-3 K m s-1) to 1 decimal place? Multiply your answer by 1000 and enter it in order to get your answer in units of 10-3 K m s-1. (Hint: Remember that the velocity is given in cm s-1 and the answer needs to be in K m s-1).

-4.4

Assume that the horizontal divergence at the surface is 2.2 x 10-5 s-1 and that the height of the tropopause is ztrop = 13.6 km. Assume that the vertical wind varies with height according to the bowstring model and that the level of nondivergence is 1/2 the height of the tropopause. What is the value of w where w has its greatest magnitude? Give your answer (which may be positive or negative) in units of cm s-1 to 1 decimal place.

-7.5

An air parcel has the following characteristics: p = 935 hPa; T = 16 oC; w = 3 g kg-1. What is the temperature of the air parcel at the Lifting Condensation Level, T lcl (in oC, 0 decimal places)?

-8 (Two quantities are conserved with vertical ascent below cloud base: w and potential temperature. Go up the dry adiabat and the constant w lines until they intersect. The temperature at that point will be the LCL temperature.)

An air parcel has the following characteristics: p = 1,002 hPa; T = 14 oC; w = 2 g kg-1. What is the air parcel's dewpoint temperature, Td, (in oC, 0 decimal places)?

-9 (Go to the point at p and w. Td will be the temperature there. Remember w =ws(Td).)

An air parcel in the Southern Hemisphere at a latitude of -20o with a velocity 30 m/s and a direction of 50o in math angle. What is the magnitude of the Coriolis force in 10-4 m s-2 (1 decimal place)? (Multiply your number by 104 and enter it.)

14.9

What is the percent decrease in g* between Earth's surface at midlatitudes and an altitude of 6 km above that spot on the Earth (2 decimal places)? Use Equation 10.6 and set Earth's radius equal to 6371 km.

.19

Assume that the horizontal divergence at the surface is -2.1 x 10-5 s-1 and that the height of the tropopause is ztrop = 9.5 km. Assume that the vertical wind varies with height according to the bowstring model and that the level of nondivergence is 1/2 the height of the tropopause. What is the constant b in Lesson 9.6 (in units of 10-8 m-1 s-1, 2 decimal places, which means that you need to multiply your answer by 108 and enter the number)?

.44

About 1% of the Earth's surface is covered with urban areas and roads. Assume that the albedo of urban areas and roads is on average 0.294 (the same as the mean albedo of the Earth) and that they are evenly distributed across all latitudes. If the albedo of all urban areas and roads were increased to 0.9, how much lower would Earth's surface temperature be (to one decimal place)? Assume that the Earth's surface temperature is given by Equation 7-3 with an IR multiplier of 1.58, a solar constant of 1361 W m-2, and a Stefan-Boltzmann constant of 5.67 x 10-8 W m-2 K-4. Hint: First figure out the new albedo by realizing that 99% of the albedo stays at 0.294, but 1% now has an albedo of 0.9. Then use Equation 7-3 to compute TEarth for the new albedo and the old albedo (0.294).

.6

Assume that the horizontal divergence at the surface is -2.1 x 10-5 s-1 and that the height of the tropopause is ztrop = 8.1 km. Assume that the vertical wind varies with height according to the bowstring model and that the level of nondivergence is 1/2 the height of the tropopause. Is the surface air converging (write 0) or diverging (write 1)?

0

To find the methane lifetime, we used an average value for OH. However, OH varies from being almost nothing at night to its highest value during the middle of the day. In forests, OH is lost mainly by reaction with a volatile organic compound that trees emit into the atmosphere, isoprene (C5H8). What is the OH lifetime in seconds (two decimal places)?

0.09 (If kOH+Isoprene = 1.0 x 10-10 cm3 molecule-1 s-1, the isoprene concentration is 11.4 x 1010 molecules cm-3, and the OH concentration is 1 x 106molecules cm-3)

The C-O chemical bond can be broken with 799 kJ/mol. Find the wavelength of a photon that is energetic enough to break the bond (0 decimal places). The required maximum photon wavelength (nm) =

149

Suppose someone invents a process that can remove carbon dioxide from the atmosphere. Currently, the mass of CO2 in the atmosphere, MCO2, is 3 x 1015 kg. If the process can remove R = 10-1.08 of the atmospheric CO2 per year (units year-1), but the constant production of CO2 is P = 3 x 1013 kg per year, how much CO2 mass will be in the atmosphere in twenty years?

0.86 (hint: Use equation 4.15, but replace [CH4] with MCO2, production with P, and kOH+CH4[OH] with R. This will give you a differential equation that you will need to solve for MCO2. Note that P and R are assumed to be constants.) In 20 years, the carbon dioxide mass will be the following number times 1015 kg (2 decimal places). (i.e., divide your number by 1015 and enter it.) Start with Equation 4.15 and follow the instructions in the problem exactly. Make sure that all your units make sense and that every term in the equation has the same units.

There are two things: thing 1 and thing 2. The ratio of the peak wavelength for thing 1's Planck distribution function spectral irradiance to thing 2's is 1.05. What is the ratio of temperatures of thing 1 to thing 2 to 2 decimal places? That is, find: T(thing 1)/T(thing 2).

1.01 (Incorrect. Take the Wien Displacement Law, set the equation so that T = ..., and then take the ratios of the two sides of the equation.)

There are two things: thing 1 and thing 2. The ratio of thing 1's to thing 2's total irradiance is 6.7 and ratio of thing 1's to thing 2's emissivity 0.52. What is the ratio of thing 1's temperature to thing 2's temperature to two decimal places? That is, find: T(thing 1)/T(thing 2).

1.9 (Use the Stefan-Boltzmann equation that includes emissivity, rearrange it so that T = ..., then take the ratios.)

At a latitude of -21 degrees, how many kilometers does 1 degree of longitude equal to within 5%?

104

Convert the meteorology angle of 163 degrees to a math angle in degrees.

107

An air parcel has the following characteristics: p = 904 hPa; T = 19 oC; w = 3 g kg-1. What is the air parcel's saturation water vapor mixing ratio, ws(in g kg-1, 0 decimal places)?

16 (Remember that w at the point with pressure p and temperature T is ws.)

If the temperature gradient has a magnitude of 0.048 oC/km and a direction of 288o (math angle) and the wind vector has a magnitude of 12 m/s and a direction of 112o (math angle), what is the temperature advection in oC/hour (to two decimal places)?

2.07 (Calculate the gradient and then use the advection equation to find the negative of dot product of the wind with the temperature gradient.)

If the temperature gradient has a magnitude of 0.082 oC/km and a direction of 53o (math angle) and the wind vector has a magnitude of 10.3 m/s and a direction of 245o (math angle), what is the temperature advection in oC/hour (to two decimal places)?

2.97 (Calculate the gradient and then use the advection equation to find the negative of dot product of the wind with the temperature gradient.)

The C-H chemical bond can be broken with 413 kJ/mol. Find the wavelength of a photon that is energetic enough to break the bond (0 decimal places). The required maximum photon wavelength (nm) =

287

An air parcel has the following characteristics: p = 945 hPa; T = 17 oC; w = 4 g kg-1. What is the air parcel's potential temperature, θ (in K, 0 decimal places)?

295 (Find the p, T point on the skew-T and then go down the dry adiabat until it crosses the p=1000 hPa line. The temperature there will be the potential temperature.)

The abundance of carbon monoxide (CO) in the atmosphere is not changing very much, so we can assume that it is in steady-state (i.e., production equals loss). CO is removed from the atmosphere only by the reaction with OH. how much CO is being produced globally, in units of molecules cm-3 year-1 (to 1 decimal place)?

3 (If you look at equation 4.15, replace CH4 with CO, and then set d(CO)/dt = 0, then you see that production matches loss. If the average OH concentration is 8.4 x 105 molecules cm-3, the reaction rate coefficient is 2.3 x 10-13 cm3 molecule-1 s-1, and the average CO concentration is measured to be 5 x 1010 molecules cm-3, divide your answer by 1011before entering it.)

An air parcel has the following characteristics: p = 976 hPa; T = 18 oC; w = 4 g kg-1. What is the air parcel's relative humidity, RH (in %, 0 decimal places)?

30 (If you know T and p, you can go to that point and find ws. RH is just 100*(w/ws).)

An air parcel has the following characteristics: p = 929 hPa; T = 15 oC; w = 3 g kg-1. What is the air parcel's equivalent potential temperature in Kelvin (0 decimal places)?

302 (To find the equivalent potential temperature, you would (1) lift the parcel to the LCL along a dry adiabat, (2) lift the parcel along the moist adiabat all the way to the stratosphere so that all the water vapor condensed into liquid, and (3) bring the parcel down to 1000 hPa along the dry adiabat. Equivalent potential temperature accounts for the effects of condensation or evaporation on the change in the air parcel temperature.)

An air parcel in the Northern Hemisphere at a latitude of 40o with a velocity 40 m/s and a direction of 80o in math angle. What is the magnitude of the Coriolis force in 10-4 m s-2 (1 decimal place)? (Multiply your number by 104 and enter it.)

37.4

If the pressure gradient is 6 hPa over 10 hundred km in the x-direction and the air density is 1.19 kg m-3, what is the pressure gradient force in 10-4 m s-2 (to 0 decimal places)? (Multiply your answer by 104 and enter it.)

5

An airplane is traveling due west at 78.9o latitude. Its westward speed is 451 km hr-1. How many degrees of longitude does it cover in 3 hours? Earth's radius is 6371 km (0 decimal places).

63

Starting with equation 10.34b, the gradient balance with height as the vertical coordinate, do a scale analysis to see which terms in the equation are the important ones for a tornado. Assume a latitude of 35o, a wind speed of 40 m s-1, a tornado radius (R) of 200 m, a pressure drop of 30 hPa from the center to that radius, and a density of 1 kg m-3. Select the terms that are within an order-of-magnitude each other so that you need to keep them in order for the equation to represent the dynamics.

Centripetal Pressure gradient

Tornadoes have large Rossby numbers.

True

Starting with equation 10.34b, the gradient balance with height as the vertical coordinate, do a scale analysis to see which terms in the equation are the important ones for large-scale tropical weather systems. Assume a latitude of 5o, a wind speed of 8 m s-1, a horizontal scale of weather (R) of 1000 km, a pressure drop of 1 hPa over R, and a density of 1 kg m-3. Select the terms that are within an order-of-magnitude each other so that you need to keep them in order for the equation to represent the dynamics.

Centripetal Pressure Gradient Coriolis

578 kg of rain at temperature 7oC falls on a snowpatch. What mass of snow (mice) is melted as the temperature of the liquid water from the rain goes to 0oC? The amount of melted ice (kg) is:

Energy in the heat capacity of the liquid water as it changes temperature from the initial value to near zero oC is used to cause the phase change in the ice, melting it.

According to the figure above, specific humidity, and mean horizontal wind are completely mixed in the typical boundary layer.

False

All particles come from gases that react in the atmosphere.

False

All particles never fall out of the atmosphere.

False

Divergence at Earth's surface leads to a derivative of vertical velocity with respect to height (∂w/∂z) that is positive near Earth's surface and becomes negative above the level of nondivergence.

False

If the Earth were not rotating, we wouldn't need to describe large-scale motion in spherical coordinates.

False

If the air parcel is moving, it is not possible for the temperature advection to be zero.

False

If the derivative of vertical velocity with respect to height (∂w/∂z) is negative near Earth's surface and becomes positive above the level of nondivergence, then the vertical velocity must be positive.

False

The amount of oxygen (O2) in the atmosphere has changed by more than a few percent over the last 20 years.

False

The amount of water vapor in the atmosphere has changed by more than five percent over the last 20 years.

False

The area of an air parcel always changes when it undergoes deformation.

False

The horizontal momentum flux is downward when the mean wind decreases with height in the boundary layer.

False

The nocturnal boundary layer is usually stable and therefore no mixing ever occurs.

False

The saturation vapor pressure depends only on dry air pressure.

False

The vapor pressure always equals the water vapor mixing ratio.

False

Two objects with the same spectral emissivity can have the same temperature but different wavelengths of peak spectral irradiance.

False

all cloud drops have the same size

False

there is no physical limit to how big a raindrop can be - it is limited only by the time it has to collect other drops.

False

When you find μ, the gradient vector angle, by finding the arctangent of the y-gradient divided by the x-gradient (Equation 8.13), the answer you get is always the correct answer.

False (The arctangent has two correct answers separated by 180 degrees within the range of 0 degrees to 359 degrees. Choose the one pointing toward the warm air.)

The assumption that air density is constant for spatial scales important for weather is always true.

False (ex: small air density differences that result from uneven heating of Earth's surface and that result in convection, sometimes leading to massive thunderstorms)

Calculate the temperature gradient direction, μ (o math angle between 0o and 360o, zero decimal places), for a distance between isotherms of d = 100 km and ΔT = 4 oC between isotherms for the following case. Note also that d equals 5 lines on the grid and that you can simply count the number of lines (estimate any fraction of a line) to figure out distances.

First calculate ∂T/∂x and ∂T/∂y. Then use these values to get the direction. Try using the concept of centered differences to determine the gradients in the x and y.

Calculate the temperature gradient magnitude, ∇T (oC/km, 3 decimal places), for a distance between isotherms of d = 100 km and ΔT = 3 oC between isotherms for the following case. Note also that d equals 5 lines on the grid and that you can simply count the number of lines (estimate any fraction of a line) to figure out distances.

First calculate ∂T/∂x and ∂T/∂y. Then use these values to get the magnitude. Try using the concept of centered differences to determine the gradients in the x and y.

The Lagrangian framework has the following properties.

It observes changes of the air parcel over time. It is represented by the DR/Dt term in Equation 8.20. It is related to the Eulerian framework by advection.

The Eulerian Framework has the following properties.

Its observations are made over time. Its observations are fixed in space. It is represented by the partial derivative of R in Equation 8.19.

Pressure

M/Lt2

Consider the fluctuations of pressure (p), temperature (T), and density (), in the Ideal Gas Law for dry air: 𝑝=𝜌𝑑𝑅𝑑𝑇p=ρdRdT Write down p, T, and in terms of a mean part and a perturbation part and then take the Reynolds average to find the terms that remain in the equation for average <p>. Select the terms that are in the equation for <p>. For this question, we will use < > instead of the overbar to mean the Reynolds average.

Rd<Pd'T'> and <Rd<Pd><T>>

Consider a dry air parcel. If the environmental lapse rate is 9.5 °C/km, then is the air stable or unstable?

Stable

Measurements of vertical wind velocity (cm s-1) are w = -4.1, 3.6,4.9, -1.5, -3.8, 4.5, -0.3, 0, -4.8, 0.5, and simultaneous measurements of temperature (oC) are T = 19.5, 19.8, 18.5, 18.4, 21.2, 20.9, 19.9, 22, 20.4, 20.6. What is the turbulent vertical kinematic heat flux (10-3 K m s-1) to 1 decimal place? Multiply your answer by 1000 and enter it in order to get your answer in units of 10-3 K m s-1. (Hint: Remember that the velocity is given in cm s-1 and the answer needs to be in K m s-1).

Take the mean of v and the mean of T, subtract the mean of v from each value of v (i.e., v1'=v1-vmean)and subtract the mean of T from each value of T. Multiply the variations of each v and each T at the same position in the lists together (i.e., v1'*T1', v2'*T2'), add them up and divide by the number of values (i.e., 10). Also divide by 100 to convert cm/s to m/s, which is needed in the final answer. When you enter your answer, first multiply it by 1000 before entering it.

Balance of Forces and Motion essentials

The PGF always points directly toward low pressure. Once force balance is achieved, velocity will be to the right in the NH and to the left in the SH. In the free troposphere, where "friction" is negligible, the Coriolis force opposes the PGF and points toward high pressure. In the upper boundary layer, where "friction" is in the opposite direction as the velocity and must be considered, the the vector sum of Coriolis and friction must balance the PGF. As a result, the velocity is still to the right of the PGF in the NH (left in the SH), but is titled toward the low pressure, but the Coriolis force is still at right angles to the right of the velocity in the NH (to the left in the SH).

Which one of the following is the most likely cause of the observation that surface pollution concentrations are greater during morning rush hour than they are during evening rush hour?

The boundary layer in much shallower in the morning than the evening and so roughly the same amount of pollution gets mixed into a smaller amount of atmosphere in the morning than in the evening.

244 kg of rain at temperature 8oC falls on a snowpatch. What mass of snow (mice) is melted as the temperature of the liquid water from the rain goes to 0 oC (in kg, zero decimal places)?

The rain provides the energy (specific heat capacity times rain mass times temperature change) to melt the snow (enthalpy of fusion at 0oC times snow mass).

A superadiabatic potential temperature profile is always unstable.

True

Even though stratospheric chlorine is less than 10 ppbv (10 parts per billion in air) and stratospheric ozone is more than 1 ppmv (1 part per million in air), chlorine is responsible for the Antarctic ozone hole.

True

If the amount of anything decreases with height, then its turbulent flux is upward.

True

If the derivative of vertical velocity with respect to height (∂w/∂z) is positive near Earth's surface and becomes negative above the level of nondivergence, then the vertical velocity must be positive.

True

If the vertical gradient of anything is negative, then its turbulent eddy flux is upward.

True

In the atmosphere, the water vapor mixing ratio is never the same as the specific humidity.

True

Low clouds radiate more energy to Earth's surface than mid-level or high clouds of the same horizontal extent and thickness.

True

Ozone is made when methane is oxidized in the presence of nitrogen oxides.

True

Satellites can observe radiance from Earth's surface in the infrared atmospheric "windows."

True

The NOAA water vapor channel gives no information about the water vapor near Earth's surface.

True

The fraction of forward scattering is greatest when the particle radius is much larger than the radiation's wavelength.

True

The radiance at each wavelength is related to the temperature of the radiating matter at that wavelength.

True

If one air parcel is three times larger than a smaller air parcel and they mix, then the temperature and the vapor pressure of the mixed air parcel will be 1/3 of the way along the mixing line between the larger parcel and the smaller parcel and nearer to the larger parcel.

True (There are 3 parts of large parcel and 1 part of small parcel for a total of 4 parts. 3/4 of those are from the large parcel, so that weighted average (i.e., 3/4 Tlarge + 1/4 Tsmall) means that the mixed air parcel is 1/4 of the way along the line from the large parcel.)

to derive the hydrostatic equation, we assume that density is constant in the volume element

True (We are shrinking the height of the volume to be infinitesimally small, so we can make this assumption.)

Which of the following factors determine the growth of the boundary layer during the morning?

amount of solar heating land surface type shape of the atmospheric vertical temperature profile

Match each atmospheric gas with its most prominent atmospheric phenomenon in the list.

carbon dioxide - global warming sulfur dioxide - reflective atmospheric aerosol oxygen - stratospheric ozone layer chlorine - Antarctic ozone hole nitrogen oxides - urban ozone pollution

For the following wavelength, determine if the atmospheric emissivity (and thus absorptivity) is closer to 0 or closer to 1. Use the figure in Lesson 6.9. 0.5 µm

closer to 0

For the following wavelength, determine if the atmospheric emissivity (and thus absorptivity) is closer to 0 or closer to 1. Use the figure in Lesson 6.9. 11 µm

closer to 0

For the following wavelength, determine if the atmospheric emissivity (and thus absorptivity) is closer to 0 or closer to 1. Use the figure in Lesson 6.9. 0.2 µm

closer to 1

For the following wavelength, determine if the atmospheric emissivity (and thus absorptivity) is closer to 0 or closer to 1. Use the figure in Lesson 6.9. 3 µm

closer to 1

For the following wavelength, determine if the atmospheric emissivity (and thus absorptivity) is closer to 0 or closer to 1. Use the figure in Lesson 6.9. 7 µm

closer to 1

Consider a drop with a radius and initial supersaturation on its Koehler curve as in the figure. The initial ambient supersaturation is given by the dotted line. For these initial conditions, the drop will:

experience net evaporation and shrink back down to a size for which sk=s.

As radiation travels along a path through a gas or liquid, the amount of radiation decreases

exponentially

A two-dimensional rectangular air parcel that that has a fractional increase in length in one direction that equals the fractional decrease in length in the other direction has positive divergence. Hint: fractional change in x-direction is dx/x.

false

Earth's effective gravity is greatest at the Equator.

false

If an air parcel has a horizontal divergence of -0.002 s-1, that means that it is increasing in area by 0.2% every second.

false

If the typical variation in the horizontal wind speed is 40% of the mean horizontal wind, then the turbulent kinetic energy is 40% of the mean kinetic energy.

false

Satellites detect radiance for all altitudes at every wavelength all the time.

false

The NOAA water vapor channel measures the amount of water vapor near Earth's surface.

false

Consider a drop with a radius and initial supersaturation on its Koehler curve as in the figure. The initial ambient supersaturation is given by the dotted line. For these initial conditions, the drop will:

grow larger than the critical radius and activate into a cloud drop. Remember, if the ambient supersaturation s is greater than the drop supersaturation sk, the drop will experience net condensation until sk=s and stop growing unless s > sc, in which case sk will never match s and the drop will activate (i.e., get bigger than rc) and grow into a cloud drop. If on the other hand sk > s, then the drop will experience net evaporation and shrink back down to a size where sk=s.

For the bowstring model, if there is divergence at Earth's surface, then, with increasing height, the horizontal divergence

has the greatest positive value near Earth's surface and linearly decreases, becoming zero at the level of nondivergence and then continue to linearly decrease to become more negative (convergence) at the tropopause.

Motion types essentials

ind the values of the motion types divergence, vorticity, shearing deformation, and stretching deformation for point E. If you look at the equations for these motions, they all involve changes in u and v with respect to x and y. First you need to find the u and v magnitudes for the points B, D, F, and H, where for the point B. the same analysis should be done for each point. Once you have u and v for each point, then you can calculate the values for the motion types using centered differences between B and H for the y direction and between D and F for the x direction. The distance between two adjacent points is 120 nm, so the distances you should use for two points (e.g., D to F or B to H) is 240 nm. Then find the values for the motion types using the equations:

For a rectangular air mass that conserves mass, if its horizontal area changes, then check the following properties that could change.

its density could change its height could change

For a rectangular air mass that conserves mass and undergoes adiabatic processes, if its horizontal area changes, then check the following properties that could change.

its temperature could change its pressure could change its height could change its density could change

The units of the hydrostatic equation are

kg m^-2 s^-2

Pressure

kg/ms2

Link the wavelength at the following numbers with the object that is radiating with a radiance that is being observed by the satellite at the wavelength.

radiance at wavelength #2: water vapor at 850hPa to 600hPa radiance at wavelength #4: Earth's surface radiance at wavelength #5: Carbon dioxide at 850hPa to 600hPa

The temperature of the air parcel and the environment are the same, but the air parcel has a higher specific humidity. the air parcel will ...

rise (For the same pressure and temperature, the air with the greatest specific humidity is always less dense and has the higher virtual temperature. The virtual temperature is always equal to or greater than the temperature.)

Consider a drop with a radius and initial supersaturation on its Koehler curve as in the figure. The initial ambient supersaturation is given by the dotted line. For these initial conditions, the drop will:

stay the same size because evaporation equal condensation since sk=s.

Convergence at Earth's surface leads to a derivative of vertical velocity with respect to height (∂w/∂z) that is positive near Earth's surface and becomes negative above the level of nondivergence.

true

Earth's shape is not a perfect sphere because it is rotating about an axis.

true

In turbulent heat flux, a downward eddy of colder air gives a heat flux that is in the same direction as an upward eddy of warmer air.

true

The normal vector for the temperature gradient (temperature gradient vector), which is perpendicular to the isotherm, always points toward the warmer air.

true

∂T/∂z, where T is temperature

θ/L

(d2Tdt2) , where T is temperature and t is time

θ/t2