Pressure in the Mountains

After hiking a few thousand feet up a slope or taking a lift at some ski area, you open you water bottle and hear a momentary rush of air.   Or after staying at a high-altitude resort and returning home your shampoo container is partially crushed.  On higher peaks we have less energy and move a bit slower.  Even higher and altitude sickness strikes.  Boiling water comes easier and at lower temperatures at high elevations,  causing cooking times to lengthen.

Pressure decreases with height and the effects are sometimes quite noticeable.

Atmospheric pressure decreases with height for a good reason:  it is dependent on the weight of the air above you.  If you move higher, there is less air above you and thus pressure declines.

Interestingly, pressure decreases with height at different rates, depending on your elevation.
Specifically,, pressure falls more rapidly near the surface where the air is dense and less rapidly aloft where the air is thinner (see figure).

Let's explore how pressure declines with elevation.

At sea level, the average pressure is about 1013 hPa.   hPa is a unit of pressure that is also known as a millibar (mb).

By roughly 5000 ft, the pressure has declined about 15% to approximately 850 hPa.

Ascend to about 10,000 ft and the pressure drops to roughly 700 hPa, with 30% less air pressure and oxygen.  No wonder such elevations sap our strength and sometimes lead to headaches and dizziness.

Reach 18,000 ft above sea level and pressure drops to about 500 hPa, about half the pressure measured at sea level.  Few of us can function at this altitude, which is close to the elevation of the highest permanent human settlements.

Altimeters are popular hiking accessories and essentially small barometers.  They make use of the normal change of pressure with height and should be calibrated with a known elevation at the start of a hike. Since the actual change in pressure will typically be a slightly different, altimeters often possess small errors (generally no more than 25-50 ft) over a hike of a few thousand feet in the vertical.  Interestingly, pressure altimeters often provide more accurate elevations than GPS units, which frequently are off by 50-100 feet and are sometimes inoperable in heavy trees.

Many smartphones (such as the Samsung Galaxy series and the Iphone 6) now have pressure sensors and there are a number of altimeter apps available of little or no cost.

Freezing Level Versus Snow Level

Anyone interested in winter recreation cares deeply whether they are in rain or snow, snow generally being preferred, of course.

So it is important to know the current and future elevations of the snow level, the height separating snow from rain.

The snow level can be pretty obvious, as seen in this image of Capitol Hill in Seattle.

And there is another closely related term that is used in weather forecasts:  the freezing level, the altitude at which the temperature drops to freezing.

So let's get educated about these important levels.  What exactly do they mean?  How are they related? And how do they change in time?

In most midlatitude locations, particularly in winter, precipitation starts aloft as snow.    As the snow falls from the colder upper atmosphere into the warmer air below, it often reaches a level at which temperature warms to freezing (32F), the freezing level.   Below that level the snow starts to melt, but it takes a while to do so--on average about 1000 ft (300 meters).    Wet snow, but still snow.   Since melting snow stays at freezing, the melting layer is often at a uniform temperature of 32F.

Eventually the snow melts completely and we reach the snow level, below which only rain is observed.  

The snow level in the mountains is often obvious, with white-clad trees 

above and bare trees below.

Both the freezing level and snow level can change in time as precipitation falls, and the direction is usually down.  The reason?  Cooling due to evaporation and melting.

First evaporation.   The air below the cloud is often unsaturated, which means the relative humidity is less than 100%   As the snow falls into that layer there is evaporation (actually sublimation), which results in cooling.   If the snow turns into rain there still can be evaporation and cooling.   Such cooling continues until the air is saturated, and can cause the freezing and snow levels to drop quickly and substantially (hundreds to even thousands of feet).

And then there is melting.   When snow falls into air warmer than freezing, it melts.  But it takes energy to melt the snow, and thus as melting occurs the surrounding air cools.   Heavier precipitation results in  more melting and more cooling.   Such cooling can occur even after evaporation has stopped (because the air becomes saturated).  Melting thus causes the freezing and snow levels to fall.

The good news about this:  if you are up in the mountains and it starts to rain on you, there is a good chance, particularly if you are near the snow level, for the rain to turn into snow!

Freezing and snow levels can also rise as warm air floods a region, particularly as a warm front approaches.  The highest freezing levels in the western U.S. are generally associated with atmospheric rivers: warm, moist currents of air originating in the tropics and subtropics.  In such events the freezing level can rise to 5000-8000 ft, even in the winter!

 The National Weather Service forecasts often talk about freezing and snow levels and how they will change in time:  information worth being aware of.

The Winter Outlook for the Western U.S.

The big question right now for outdoor enthusiasts in the western U.S. is whether there will be enough snow for outdoor recreation this winter.  Last year was a  mixed bag, with snow drought conditions in California and southern Utah, while Washington State, Idaho, and Montana made up for a dry fall to end up above normal snowpack by early spring.

 The latest snowpack information from the USDA Snotel network indicates well below normal snowpack over the Sierra and Cascades, but near normal conditions over Colorado, Wyoming, Montana, and Idaho.

But what will happen now?   Meteorologists' most useful tool for predicting the nature of western U.S. winters is the correlation between El Nino/La Nina and regional weather.   El Nino years are associated with warmer than normal tropical Pacific waters and  often bring warmer than normal conditions to the western U.S., less snow in the Northwest, and more precipitation in the southwest U.S.

It appears that his winter that we will be in a weak El Nino pattern and  forecasters at the National Weather Service's Climate Prediction Center are predicting a winter with El Nino characteristics.   More precipitation over the southern tier of of the U.S. and drier than normal over the Northwest.

They forecast warmer than normal conditions from the Rockies to the West Coast.  Keep in mind that such long-range forecasts have imperfect skill, analagous to weighting a coin, so that heads occurs perhaps 70% of the time.

The bottom line prediction for snow lovers?  

Below-normal snowpack over the Northwest.   More precipitation in California than last year, which will allow more snow in the high Sierra. Normal year for Colorado.  This forecast has imperfect skill, but it is the best we can do at this point.

Jack Whelan Note on School Board Race

The ballots have arrived, and so I am writing to you this morning to urge you to support all four of the challengers in the Seattle School Board races. The school district has been seriously dysfunctional for over a decade. The current board, (and particularly incumbents running for election in this cycle) has proven itself incapable of providing the vision and oversight necessary to set things right. The challengers are smart, tough, and knowledgeable about district affairs, and while the task for them will be extremely difficulty, they give the district the best chance of bringing back stability and good order. The three board members not running this cycle, are persuadable and will benefit from the energy and vision these four women challengers will bring.

The question is not about whether the incumbents did their best in difficult circumstances--all the the incumbents are decent, committed public servants, who work long hours for no money and who sincerely want what's best for our kids. The question rather is whether they have the mindset that allows them to see the problems and to formulate solutions for them that have a chance of effecting real improvements. I am convinced that they do not, and that the challengers, while unproven, have demonstrated that they see the problems far more clearly and that they have solid ideas about how to solve them. You can't solve problems unless you correctly understand what causes them.

Over the last several months I've gotten to know all four challengers well, and think that each brings something that the current board lacks. Here's my take on why each one deserves your vote and why the challengers don't.

District One. Sharon Peaslee is a mother of two special-needs high-school age kids--one at Hale and the other at Ingraham. She has been a long-time education activist on the East Side with a particular interest in improving math curricula. She understands that one size does not fit all, and will work to find ways to give more power and decision making to parents, teachers, and local schools working collaboratively to meet their students' needs. She will push back hard agains top-down standardization and regimentation of the centralized bureaucracy. Sharon is a high-energy, upbeat, problem-solver--and the district needs her energy and persistence and courage. She's the "Mom on a Mission" Candidate.

Her opponent, Peter Maier, has received in the last election and this election tens of thousands of dollars from people like Steve Ballmer, who don't live in the district. He was more responsible than anyone for the lack of oversight that led to the the Pottergate Scandal. Information about it was brought to his attention early on that he ignored. His real interest is working on the levies, and I think that he should be retired from the board so he can focus his attention exclusively where his interests lie and where his efforts will be appreciated without ambivalence. Peter is the "Don't Bother Me I'm Busy with other Important Stuff" Candidate.

District Two. I know Kate Martin the best of the four because we ran together against the incumbent in the Primary. We were both in it to win it, but we were also both fine if the other won. Kate was the far better candidate, she won, and I support her wholeheartedly. She is a long-time activist who has developed a reputation unfairly as being "angry". Anybody who has had a chance to get to know her knows that she intense and she will not tolerate anybody's b.s, but she is not an angry person; she's passionate, and she is appropriately outraged at what is, in fact, outrageous. I don't know that the board needs seven Kate Martins on it, but it needs at least one. Kate is a dogged policy wonk; she has tons of ideas about improving outcomes for all students, but is particularly concerned with the "average" students who sometimes fall between the cracks. Kate impresses me tremendously with her ability to listen and learn--and to change her mind. Kate is the kind of person who whatever she does, she's all-in, and she could very well give this board the jump start it so desperately needs to break it out of its "process torpor." Kate is the "Catalyst Candidate".

The incumbent in District Two is a very nice, smart Boeing executive. She, like Peter Maier, has received in the last cycle and this tens of thousands of dollars from rich people who don't live here who think they know better. Sherry, in my opinion, embodies this 'process torpor'; she's a study in ambivalence. She is in that respect the polar opposite of Kate. She makes an effort to listen to people in the community, but when push comes to shove, she votes what the power folks downtown want 97% of the time. She often speaks about how she trusted staff when no one really with a lick of sense would take anything at face value coming from a downtown management culture that has proved itself time and again unworthy of that trust. She like the others voted to renew Marie Goodloe-Johnson's contract with a raise about a month before they had to turn around to fire her. Prescient and shrewd are not words that come to mind in describing her. (But that's true for the other incumbents as well.) She's the "Plain Vanilla,Play-it-Safe, Conventional-Wisdom" Candidate.

District Three. Michelle Buetow I know least well among the challengers. She's impressive for the energy and intelligence and knowledge about district affairs that she has brought to the table. She understands what it means to be "engaged". She's been involved in Seattle District affairs for several years and was the earliest of the challengers to enter the race. She has been enormously well organized and effective in her campaigning. Michelle is a communicator and a relationships builder, and that's why I think she needs your vote. Michelle has got just about every legislative district democratic club under the sun to endorse her. She has two elementary-age kids in Seattle Schools and she's someone who is very people oriented and yet knows how to work effectively in the system as it is set up. She's the "I Know How to Get It Done" Candidate.

Her opponent, Harrium Martin-Morris is a decent, thoughtful guy, but is the opposite of Michelle in this respect. He's disengaged and has done little to build relationships. He is the only African American on the board, and his votes have been better than the other three incumbents on some issues, but it's not so much that he's bad as that Michelle would be so much better. If Kate plays the catalyst role, Michelle will play the mediator role, she'll be the one who will help the group to find consensus. Harrium just seems to be in his own world; he's the "I'm in My Own Orbit" Candidate.

District Six. Marty McLaren is a retired Math teacher in Seattle Public Schools, and if elected, she would be the only board member with experience on the ground level in the Seattle Public School System. (Martin-Morris taught kindergarten in Boston Public Schools.) Marty, like Sharon has been a powerful advocate for improving math curricula in SPS and has been a strong critic of the way the board goes through the motions of listening to the community input and then just does what it already decided. Marty, though she might impress you as frail and grandmotherly at first glance, is as tough-minded as they come, and her give and take with her opponent in issues fora has been among the most spirited of this campaign. She's been endorsed by just about everyone that matters. She's the "Grandma with Attitude" Candidate.

The incumbent, Steve Sundquist, is currently president of the board. He comes from a financial services background and exudes a glib, corporate slickness. He is the poster child for the technocratic I-know-better mentality that has characterized neoliberal education reform since No Child Left Behind. He's has received hardly any endorsements from the LD Democratic Clubs. Steve, in my view, is the embodiment of every thing that is wrong with the mindset of the current board and the culture at district headquarters. He's the "Corporate Technocrat" Candidate.

There is so much more to say about why this election is so important, and I will be happy to discuss any of the issues in greater detail with those of you who have questions or concerns. And if you have found this email useful, please forward it to friends who can vote in Seattle to give them information that might play a role in forming their decisions about for whom they should vote.

Best--Jack Whelan

Discovering Math was pronounced “mathematically unsound” by the Washington State Board of Education.

Here is what their consultant mathematicians had to say:

• “Discovering was the weakest, with all three areas considered inadequate.”
• “One way Discovering Algebra and Discovering Advanced Algebra compromise mathematics is by leaving important mathematics undefined and assumed.”
• “The use of technology in Discovering Algebra in lieu of algebraic approaches contributes to the lack of opportunity to develop algebraic skills”
• “The value of studying geometry is partly to learn to solve geometric problems and partly to learn to work in an axiomatic system and develop the associated logic skills. Discovering Geometry’s treatment of the axiomatic system is inadequate.”

Based on the evaluation is was removed from the State’s Recommended High School Programs List

Independent University mathematicians have strong negative evaluations of Discovering Math. For example, this is what UW’s Professor Jack Lee had to say about Discovering Math’s geometry and algebra books:

“I would strongly discourage the District from choosing this book. It represents a highly risky and experimental approach to teaching geometry, and I think the experiment, while well-intentioned, is unlikely to have the desired effect” (Geometry)

“ these books have far too much verbiage for students to read, and too little in the way of clearly stated mathematical principles. Definitions, computational algorithms, and formulas seem to be stated vaguely when they are stated at all” (Algebra)

Major school districts like San Diego have dropped Discovering Math after a few years of use.

Discovering Math

This blog will provide facts about the weaknesses of Key Curriculum's Discovering Math Series