ATMS 411/611 Atmospheric Physics [main page] [homework] [2019 notes] [2018 notes] [2017 notes] [2015 notes] [2010 notes].



 

Week 15: 30 Nov

Monday-Thursday

Tuesday December 1st, begin presentations for student projects.

December 6th, reports due for 611 students.

Start Aerosol and Cloud Microphysics:
This article is a current update on cloud and aerosol related microphysics and is easy to read. Read it first.
Then read chapter 6 on cloud microphysics from Wallace and Hobbs. We will discuss parts of chapter 5 to help with chapter 6.
Begin cloud physics chapters 5 and 6 presentation.

Reminder of final project,

Class Notes:

 

Related Information:

 

 

 

 

Week 14: 23 Nov

Monday-Wednesday

Review direct and diffuse radiation with the cloud image.

Energy balance at the surface including absorbed shortwave radiation and absorbed and emitted longwave radiation.
Resulting surface and atmosphere temperature Slides 17 and 18. Write energy balance equations at surface and TOA.
Role of black carbon aerosol in solar radiation absorption. Short presentation on black carbon aerosol.
Aerosol light absorption, scattering, and extinction measurements at 532 nm from the roof of the Physics building at UNR.

Take solar radiation from the top of the atmosphere to the surface, showing effects of gaseous and aerosol absorption and scattering on the spectra See slides 27- 32.

Global radiation balance and deficit See slides 12, 26.

How radiation absorption couples with atmospheric thermodynamics and layer heating.
Layer heating rate = -divergence of net irradiance (also known as flux). Slides 39, 41, 42.

Begin cloud physics chapters 5 and 6 presentation.

Reminder of final project,

Class Notes:

Monday:
Review of problem 2, conditions for maximum diffuse radiation.
One layer atmosphere radiation balance discussion
, and black carbon aerosol.

Tuesday:
Solar transmission through black carbon aerosol (soot) notes for use in problem 1 of the homework.

Wednesday:
Solar radiation transfer through the atmosphere and spectral snow albedo notes.

Global radiation balance notes.

Related Information:

Black carbon (diesel soot, etc) emission, and as a sculpture.

Online Python

Cloud image.

Lenticular cloud image.

Aircraft icing control with carbon soot coatings.

Online Mie Theory light scattering and absorption calculator for spheres.

Online snow albedo calculator as a function of impurities.

 

 

 

 

Week 13: 16 Nov

Monday-Thursday

Summarize scattering and absorption in different regimes using the size parameter, x, and scattering for x<<1, x about 1, and x>>1.
Use the Mie theory calculator to look at the angular dependence of scattered light in each regime.
Slides 82-90.

1 D model for multiple scattering. Slides 20-25, 57-69. Discuss the scattering mean free path.

Energy balance at the surface including absorbed shortwave radiation and absorbed and emitted longwave radiation.
Resulting surface and atmosphere temperature Slides 17 and 18. Write energy balance equations at surface and TOA.

Take solar radiation from the top of the atmosphere to the surface, showing effects of gaseous and aerosol absorption and scattering on the spectra See slides 27- 32.

Global radiation balance and deficit See slides 12 - 13, slide 26.

How radiation absorption couples with atmospheric thermodynamics and layer heating.
Layer heating rate = -divergence of net irradiance (also known as flux). Slide 39.

Reminder of final project,

Class Notes:

Monday: Regimes of scattering, visibility, direct and diffuse beam, extinction cross section and coefficient leading up to homework 5 problem 2.

Tuesday: Multiple scattering by a cloud, especially useful for problem 2 in the homework.

Wednesday:
Cloud image we discussed.
Multiple scattering by a cloud above a reflecting ground notes.
Maximum diffuse radiation calculation notes.

Thursday:
Update of maximum diffusion calculation notes with the Python calculations we did.

Related Information:

Calculate and display results for the electromagnetic scattering and absorption by spherical particles (Mie theory calculator).

Lightning

How greenhouse gases and aerosols affect the diurnal temperature range.

Rainbow images (close, wide) from the RGJ.

Black carbon (diesel soot, etc) emission, and as a sculpture.

Online Python

 

 

 

Week 12: 9 Nov

Monday-Tuesday, Thursday, no class Wednesday, Veterans Day

Homework 4
Continue to work on problem 5 of the homework, downwelling and upwelling infrared radiation. See notes from last Thursday for where we left off.
Problem 3 discussion, Rayleigh scattering strength and polarization. See slides 77-81 and 95-97.
Size parameter, x, and scattering for x<<1, x about 1, and x>>1.

Take solar radiation from the top of the atmosphere to the surface, showing effects of gaseous and aerosol absorption and scattering on the spectra See slides 27- 32.

Global radiation balance and deficit See slides 12 - 13, slide 26.

Energy balance at the surface including absorbed shortwave radiation and absorbed and emitted longwave radiation.
Resulting surface and atmosphere temperature Slides 17 and 18. Write energy balance equations at surface and TOA.

1 D model for multiple scattering. Slides 20-25, 57-69.

How radiation absorption couples with atmospheric thermodynamics and layer heating.
Layer heating rate = -divergence of net irradiance (also known as flux). Slide 39.

Blue sky, white clouds, radar, aerosol.

Reminder of final project,

Class Notes:

Monday: Brightness temperature discussion.

Tuesday: Rayleigh scattering discussion and polarization discussion.

Thursday: Size parameter and electromagnetic penetration depth. Radar backscatter cross section.

Related Information:

Calculate and display results for the electromagnetic scattering and absorption by spherical particles (Mie theory calculator).

Lightning

 

 

Week 11: 2 Nov

Monday-Thursday

Review the meaning of the absorption cross section with regard to absorbed radiation.
Discussion of carbon dioxide, towards molecular cross sectional area.

Look at NASA World View, gain a sense of complexity of planetary albedo.
Look at 3 November 2019 off the coast of CA for ship trails, and Guadalupe Island for gravity waves and von Karman vortices, project ideas.

Homework 4 discussion: Continue setting up problems 4.21 and 4.29, astronomical radiation balance, climate change, and response time of the atmosphere.
Work on problem 5 of the homework, downwelling and upwelling infrared radiation: See slides 34-38 for introduction.

Chapter 4: Radiation transfer (presentation).

Energy balance at the surface.
Blue sky, white clouds, radar, aerosol.

Reminder of final project, and some ideas.

Class Notes:

Thursday:
Homework 5 theory for transmission, emission, upwelling and downwelling radiance, and brightness temperature.
Transmittance calculation and graph.

Wednesday:
Homework 5 part A theory, carbon dioxide cross section, and spreadsheet we worked on during class.

Tuesday:
Updated problem 4.29 discussion on thermal response time of the atmosphere and ocean to sudden radiative perturbations.
Powerpoint presentation for atmospheric radiation transfer, slides 34-38, setting up problem 5 on homework, IR radiative transfer.

Monday:
problem 4.21 discussion.
problem 4.29 discussion.

Related Information:

Sun-Earth distance, seasonal change.

Real and imaginary parts of the refractive index of water (and spreadsheet with values.)
Electromagnetic penetration depth compared with typical hydrometeor diameter.

Measured and Modeled Soundings

 

 

Week 10: 26 Oct

Monday-Thursday

Gravity waves in the atmosphere and stability slides 116, increase of potential temperature with height and stability.

Sound propagation in the atmosphere: slides 140-142.
Ray paths, energy confinement by inversions, and maximum distance to hear thunder in the afternoon.

Visit the UNR weather station and view the downwelling solar and IR radiation for the last week.

Homework 4 discussion.

Chapter 4: Radiation transfer (presentation).
Basic relationships for black body radiation (radiation with a certain spectral distribution). (Planck).
Short wave and long wave radiation
Astronomical energy balance: Sun and Earth. Shortwave and longwave radiation.
Energy balance at the surface.
Blue sky, white clouds, radar, aerosol

Reminder of final project, and some ideas.

Class Notes:

Thursday
Notes on astronomical radiation balance and Venus atmosphere, written on the powerpoint presentation.
Notes on set up of problem 4.21.

Tuesday
Snell's law and water and ice refractive index as a function of wavelength discussion.
UNR weather station data discussion.

Related Information:

Real and imaginary parts of the refractive index of water (and spreadsheet with values.)

Electromagnetic penetration depth compared with typical hydrometeor diameter.

 

 

Week 9: 19 Oct

Monday-Thursday

Student presentations on Homework 3.

Midterm exam announced and discussed.

Gravity waves in the atmosphere and stability slides 114-138.
Recent example for Reno using NASA worldview.
Geostationary satellite gif movie: large scale, zoomed in. (from here). Large scale and zoomed in as .mp4 files.
Sounding later that day.
More on gravity waves.
Gravity wave study from Hawaii.

Sound propagation in the atmosphere: slides 140-142.
Ray paths, energy confinement by inversions, and maximum distance to hear thunder in the afternoon.

Reminder of final project, and some ideas.

 

 

 

Week 8: 12 Oct

Monday - Thursday

Tuesday's class notes on the powerpoint presentation.

Discuss homework 3. (Prepare for class by reading the assignment.)

Atmospheric stability discussion, slides 62-75 for homework 3.
CAPE and precipitable water discussion, for homework 3, slides 91-95.
Do an example of 500 mb meteorology for homework 3 using reanalysis data. (Description of reanalysis data).
Here is the link for obtaining it from reanalysis.
Here's an example from the 28July2017 0z sounding, Lamont Oklahoma located at about 36.62 North and 97.48 West:
Settings
and 500 mb plot. Lamont Oklahoma will be in about the center of the image.
Lamont OK is site location 74646.


Demonstrate other properties using skewT, such as subsidence inversions, slides 87-90.

Mixing of air masses to achieve saturated air, slides 98-100.

Gravity waves in the atmosphere and stability slides 114-138.
Recent example for Reno using NASA worldview.
Geostationary satellite gif movie: large scale, zoomed in. (from here). Large scale and zoomed in as .mp4 files.
Sounding later that day.
More on gravity waves.

Sound propagation in the atmosphere: slides 140-142.
Ray paths, energy confinement by inversions, and maximum distance to hear thunder in the afternoon.

Reminder of final project, and some ideas.

Related Information:

Blank skewT diagram

GPS remote sensing of the Earth's atmosphere pressure and temperature profile. And an update.

 

 

Week 7: 5 Oct

Thursday

Notes from class on the flow over a mountain range.

Announcement: Undergraduate Research Opportunities. See also the UNR Office of Undergrad Research.

Do the important problem 3.48 of flow over a mountain range and consequences of precipitation on the windward side for the air temperature on the leeward side. Slide 61.

Atmospheric stability discussion, slides 62-75 for homework 3.

Demonstrate other properties using skewT, such as subsidence inversions, slides 87-90.

CAPE and precipitable water discussion, for homework 3, slides 91-95.

Reminder of final project, and some ideas.

Wednesday

Announcement: Undergraduate Research Opportunities. See also the UNR Office of Undergrad Research.

Discuss homework, hurricane problem and skewT problem, and illustrate use of Paint3D for following moist adiabat, etc. Study moist adiabats on the left and right of the skewT.

Further discuss latent heat, slides 46-51.
Do the important problem 3.48 of flow over a mountain range and consequences of precipitation on the windward side for the air temperature on the leeward side. Slide 61.

Tuesday

We developed theory for obtaining the dew point temperature from temperature and wet bulb temperature.
We modified the Python program to add the dewpoint calculation from wet bulb, air temperature, and pressure.

Monday

Notes from Monday on the SkewT diagram and how to use it.

Bring questions to class on the online homework and homework 2.

We will work with the skewT diagram to obtain the quantities needed for homework 2,
and develop theory for obtaining the dew point temperature from temperature and wet bulb temperature.

Next is stability of the atmosphere and how to interpret it in with the lapse rate of temperature, potential temperature, and equivalent potential temperature.

Then we will develop theory for CAPE and its interpretation, and for precipitable water in preparation for homework 3.

We will continue Chapter 3 on the theory of atmospheric thermodynamics.

Related Information:

Blank skewT diagram

 

 

Week 6: 28 Sept

Monday-Thursday

Bring questions to class on Endnote for Tuesday.
We will consider the altimeter equation, thermodynamic processes, specific heat capacity and the equipartition theorem, the first law of thermodynamics, internal energy, heat, work, and adiabatic processes.

Here are the hurricane notes from last week.

We will continue Chapter 3 on the theory of atmospheric thermodynamics.

We will discuss how to search for and manage references for the homework. Be sure to follow the steps on Preparation.
Reduction of pressure to sea level equivalent for comparing weather stations.
Choose a question for review from near the end of the presentation.

Preparation:
Endnote and Web Of Science cloud applications for managing and finding published research.
Make an account for each, and install the plugin for microsoft word.

Read chapter 3, Atmospheric Thermodynamics.
Read problem 3.18 and choose some parts of it you're interested in discussing and having discussed.

Check out this video on cloud development, from a UNR student in the ATMS 117 course.

Model soundings to see the variability during the day.

 

 

 

Week 5: 21 Sept

Wednesday-Thursday

We will continue Chapter 3 on the theory of atmospheric thermodynamics.
Geostrophic winds from height contours example.
Schematic view of layer thickness and constant pressure surfaces.
Problem 3.26 as an example of the hypsometric equation applied to hurricanes. (Will use this problem result in the homework).
Develop hurricane wind speed model using cyclostrophic flow theory. (Will use this problem result in the homework too).
Here are the notes from Thursday's class on the hurricane model.
Reduction of pressure to sea level equivalent for comparing weather stations.
Choose a question for review from near the end of the presentation.

Preparation:
Read chapter 3, Atmospheric Thermodynamics.
Read problem 3.18 and choose some parts of it you're interested in discussing and having discussed.


Monday-Tuesday

We will continue Chapter 3 on the theory of atmospheric thermodynamics.
Virtual temperature, water vapor mixing ratio, hydrostatic equation, hypsometric equation, examples.

Preparation:
Read chapter 3, Atmospheric Thermodynamics.

 

 

Week 4: 14 Sept

Thursday

Bring questions to class, especially about homework 1.

We will continue Chapter 3 on the theory of atmospheric thermodynamics.

Preparation:
Read chapter 3, Atmospheric Thermodynamics.

 

Wednesday

Bring questions to class, especially about homework 1.

We will start Chapter 3 on the theory of atmospheric thermodynamics.

Preparation:
Read chapter 3, Atmospheric Thermodynamics.

Chapter 3 topics
We will have several homework assignments from this especially important chapter.
The goals (learning and review objectives)

a. Ideal gas equation applied to dry and moist air.
b. Virtual temperature.
c. Potential temperature.
d. Hydrostatic equation.
e. Increasingly detailed description of the temperature and pressure distribution in the atmosphere.
f. SkewT logP diagrams.
f-g. Relative humidity, absolute humidity.
g. Dew point temperature.
h. Wet bulb temperature.
i. Equivalent potential temperature.
j. Latent heat release and absorption in condensation and evaporation of water.
k. Stability of air parcels.
l. Indices on soundings.
m. Brunt–Väisälä frequency and gravity waves.
o. Sound propagation in the atmosphere.

 

Tuesday

Discuss the color of the sky when smoke is present as a timely topic, using the image in related information below.

Problem 3 of homework 1. Continue scale height of the atmosphere determination.
Bring questions to class.

We will start Chapter 3 on the theory of atmospheric thermodynamics.

Preparation:
Login to your account with Excel, using your netID, to the computers in the classroom or at home, before class so you're ready to go when class starts.
(Students in class will need to first logout of Excel and log back in so that saving to your OneDrive works properly).

Read chapter 3.

 

Monday

Problem 3 of homework 1. Continue with density graphs, and scale height of the atmosphere determination.
Discuss report writing aspects, especially use of equations.

Work on homework 1.

We will start Chapter 3 on the theory of atmospheric thermodynamics.

Preparation:
Login to your account with Excel, using your netID, to the computers in the classroom or at home, before class so you're ready to go when class starts.
(Students in class will need to first logout of Excel and log back in so that saving to your OneDrive works properly).

Read chapter 3.

Related Information:

La Niña conditions to continue into fall.
California's wildfire smoke plumes are unlike anything previously seen, a Washington Post article that references Professor Larue of UNR.
Orange sun due to smoke before class on 14 September 2020.
Clear and smoky days in August 2020.

500 mb level forecast.
The 500 mb level winds are animated here.
Discussion of the 500 mb level.
Additional discussion of the 500 mb level.
Temperature and height of the 500 mb level for Reno Sept 2019. From this spreadsheet.
Observed 500 mb level heights and winds.
Discussion of constant pressure charts.

 

 

 

Week 3: 8 Sept

Thursday

Problem 3 of homework 1. Continue with pressure, temperature, and density graphs.

We will move the due date for homework 1 to next week.

Preparation:
Login to your account with Excel, using your netID, to the computers in the classroom or at home, before class so you're ready to go when class starts.
(Students in class will need to first logout of Excel and log back in so that saving to your OneDrive works properly).

Density of dry and moist air

 

 

 

Wednesday

Discuss the meteorology of the past few days.

Problem 3 of homework 1.
Preparation: Go to Barrow Alaska's and save an image for it, including the Arctic Circle and the North Pole, as we did on Tuesday for Rochambeau.
Login to your account with Excel, using your netID, to the computers in the classroom or at home, before class so you're ready to go when class starts.
(Students in class will need to first logout of Excel and log back in so that saving to your OneDrive works properly).

 

Tuesday

Discuss the Reno and Slidell LA soundings from homework 0. Bring your ideas to class.

Problem 4 of homework 1, obtain graphs of the global surface pressure in summer and winter to check the premise of this problem.
Preparation: Read this discussion from an atmospheric dynamics textbook.

Problem 3 of homework 1.
Preparation: Install Google Earth (free) and Microsoft Office (Excel, etc, free when you login using your netID) on your home computer.
We will use them for problem 3 (and others later).

Outcome: OneNote notes so far for chapter 1.

Related Information:

Creek Fire in the Sierras September 5th, smoke and pyrocumulus cloud. From NOAA.

Smoke in Siberia.

August 25th satellite image of the US showing smoke in the west and hurricane Laura approaching the Southern US in the Gulf of Mexico.
Still image.
Animation.
Image credit

 

Week 2: 31 August

Thursday

Review result from problem 1.20, and discuss the ITCZ and tradewinds.
Satellite imagery showing the IR imagery for the tropical eastern pacific.
Earth School animation of the NOAA Global Forecast System (GFS) model output to view the intertropical convergence zone (ITCZ) and trade winds.

Problem 1.20 Flow associated with tradewinds near the equator, and set up of homework problem 1.21. Resulting HW4 textbook problem 1.21 discussion in class.
Problem 1.20 calculation using the online Python calculator.

Problem 4 of homework 1.

Problem 3 of homework 1.

Preparation: Read problems 1.20 and 1.21. Bring questions to class.
Install Google Earth (free) and Microsoft Office (Excel, etc, free when you login using your netID) on your home computer. We will use them for problem 3 (and others later).

 

Wednesday

Bring questions about homework 0 to class.

Problem 1.20 Flow associated with tradewinds near the equator, and set up of homework problem 1. Class discussion.
Notes on coordinate system set up
.
Satellite imagery showing the IR imagery for the tropical eastern pacific.
Earth School animation of the NOAA Global Forecast System (GFS) model output to view the intertropical convergence zone (ITCZ) and trade winds.

Problem 3 of homework 1.

Problem 4 of homework 1.

Preparation: Read chapter 1 and work on the first homework assignment, due Wednesday. Bring questions to class.

Install Google Earth (free) and Microsoft Office (Excel, etc, free when you login using your netID) on your home computer. We will use them for problem 3 (and others later).

Study the SkewT Mastery module. It covers the basics and advanced applications. You can look at parts of it to help with understanding.

 

Tuesday

Bring questions about homework 0 to class.

Continue with problem 2 of homework 1 on the lapse rate in Antartica. Notes in class.

Problem 1.20 Flow associated with tradewinds near the equator, and set up of homework problem 1.21. Notes on coordinate system set up.

Problem 3 of homework 1.

Problem 4 of homework 1.

Preparation: Read chapter 1 and work on the first homework assignment, due Wednesday. Bring questions to class.

Install Google Earth (free) and Microsoft Office (Excel, etc, free when you login using your netID) on your home computer. We will use them for problem 3 (and others later).

Study the SkewT Mastery module. It covers the basics and advanced applications. You can look at parts of it to help with understanding.

 

Monday

The follow up from last Thursday was turned into a homework assignment due Wednesday, to be submitted through WebCampus.

Continue with the vertical distribution of temperature in general and atmospheric composition. (Overview Presentation).

Discuss the temperature variation with height, lapse rate, and problem 2 of homework 1 on Antartica.

Problem 1.20 Flow associated with tradewinds near the equator, and set up of homework problem 1.21.

Preparation: Read chapter 1 and work on the first homework assignment, due Wednesday. Bring questions to class.

Follow up: Mean free path discussion. Check out the entire discussion for more insights.
Lapse rate notes.

 

Related Information:

The stratosphere.

Very good article on how COVID-19 virus is spread; an Atmospheric Physics problem.

Mean free path between collisions of molecules in a gas discussion. Check out the entire discussion for more insights.

 

 

 

Week 1: 24 August

Thursday

Follow up homework: See the homework page and WebCampus:
1. Download the blank skewT graph to Microsoft Paint, or your favorite image program.
2. From the Reno morning sounding, write down the temperature for pressures in mb of 846, 700, 500, 400, and 250 mb.
3. Put these points on the blank skewT graph using Paint and save your blank skewT image file.
4. Download the actual sounding for the morning and circle the temperature values at the pressures given in part 2.
5. Compare with your skewT from part 3 with the actual sounding in part 4.
6. Bring questions to class.
7. Take a look at the Slidell Louisiana (passing hurricane) 12Z sounding and compare with the Reno sounding. What do you see that's different?

Class Notes: Hurricane discussion. Pressure as a vertical coordinate and skewT log P graphs.
Classroom temperature and pressure on a SkewT log P graph. Reno morning sounding with markups.

Discuss the vertical distribution of temperature in general and atmospheric composition. (Overview Presentation).

Look at real temperature measurements of the vertical distribution. Natural logarithm of pressure as a vertical coordinate.
Balloon soundings, low resolution, high resolution.
Explanation of the lines on these graphs. Discuss how to read these graphs, isotherms and isobars.

Problem 1.20 Flow associated with tradewinds near the equator, and set up of homework problem 1.21.

Wednesday

Discuss pressure in the ocean, and the exponential model of pressure with height in the atmosphere.
Atmosphere scale height relationship. Global distribution of scale height.

Discuss the vertical distribution of temperature in general and atmospheric composition. (Overview Presentation).

Look at real temperature measurements of the vertical distribution. Balloon soundings, low resolution, high resolution.
Explanation of the lines on these graphs.

Follow up: Take a look at the winds at the 250 mb pressure level of the atmosphere and envision the how the pressure is distributed.
Here's another, beautiful look at it with many options for visualization.

Tuesday

Discussed pressure.

Calculated the Earth's atmospheric mass from surface pressure and demonstrated use of the online Python computing language.

Follow up: Make an account for the online Python computing site. Then put in the code as we did in class. Save your code to a project for later reference.

Read chapter 1. Do online Homework 1.

 

First Day Agenda

Geostationary satellite loop for the western US

UNR Smoke Pollution Measurements

Introductions -- each student introduce themselves.
Syllabus.
Homework.
Webcampus for online homework assignments/reading.

Required and Optional Course Materials

Upcoming Homework Assignments

Online Homework 1 is due 30 Aug 2020. See webcampus. This is based on MetEd.

Online Homework 2 is due 6 Sept 2020. See webcampus. This is based on MetEd.

Homework 1 is due 13 Sept 2020, to be turned in through web campus.


Final Project Assignment and Ideas

The final project has been posted.

Homework for this week: Read chapter 1.

This class is:
One part lecture;
One part active class participation/activity involving atmospheric data from around the world;
One part study using online modules for atmospheric science education.

Overview Presentation: Atmospheric Science relies heavily on measurements and models!
Mass of the atmosphere calculation using an online Python editor.

Vertical structure of the atmosphere.


Related Information:

It's hurricane season! Image and animation of the Eastern Pacific. Images from this very useful weather website.
Hurricane track.
Hurricane formation discussion.

It's fire season too! Loyalton fire tornado!
Satellite imagery for 19 August 2020.
Satellite imagery for 20 August 2020 with IR detection of hotspots (NASA polar orbiting satellite).
Animated satellite imagery for 20 August 2020 from GOES 16 (NOAA geostationary satellite).

Fire and meteorology feedback: Air pollution in Reno on the 16th of August. Meteorology on the 15th and 16th of August. Note the difference in stability and boundary layer height.

World record hail stone in Vivian South Dakota. See more on hail.

Reminder of cause for the seasons.

Pittsburgh Spirit Fountain Cloud Physics and coordinate system (click image for larger version.)

The fountain in Pittsburgh PA and its rainbow.