It's the story of one boy and his dog.
Little Zander has the help of Baron, his pet German Shepherd, to help him get ready for bed and go to sleep each night.
From saying his prayers, to tucking him in and giving him a goodnight kiss, Baron takes on the role of a third parent for the four-year-old boy.
A sweet video has been posted to YouTube showing the devoted pair going through their bedtime routine.
The evening wind down begins with Zander and Baron helping to tidy away his toys, placing them inside the toy box, after which it's time for Zander to recite his evening prayers with Baron lending a paw to help secure his place in doggy heaven.
Zander, who by this time is in his pajamas, lies in his bed with his stuffed animal next to him, while the real thing, Baron, covers him over with a duvet and tucks him in.
Then, it's the turn of Zander to read a bed time story for the both of them.
Baron rests on the youngster's bed and appears to be listening intently as his ears prick up when the story gets interesting.
When it's all over, it's time for a goodnight kiss from his faithful dog, although it does appear to be more like a slobbery lick.
Then, Baron jumps up to turn out the lights sending the little boy to sleep.
Baron who is just a one-year-old, is a professionally trained dog and has his own Facebook, Twitter and Instagram accounts.
The video capturing the whole affair has gone viral on YouTube having been viewed almost 60,000 times.
Earlier this year, Baron was seen showing off how he has learned to use a toilet, even putting the lid down after he has finished.
He has also been filmed helping with housework loading the dishwasher by taking utensils from the sink.


>  on /boot like a config. or .config Why ??
dunno. maybe they are somewhere else on your box.  or not installed.
if you have /proc/config.gz, you can zcat that one.
>  Now on to the drbd portion of the.
it does compile, but the rpm does not build.


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To reset your password, provide your SiteName, an email address and a phone number that was provided during registration. Click on "Request".
The SiteName is the EXACT name (First+Middle+Last) that you used to register with . If you specified a Middile Initial or Name, it MUST be provided.
The SiteName is NOT case sensitive, but must contain the precise sequence of letters that make up the name on file.
The phone number you provide must be on file and associated with the SiteName.
A successful comparison on SiteName, Email and Phone Number will generate an Email message to the specified Email address containing instruction to complete the Password Reset.


Shuck and Jive: Tony Feathers Tonight!
I hope you can come to see Tony Feathers in concert at First Presbyterian Church of Elizabethton tonight at seven p.m. It is a benefit for the Edisto Island Open Land Trust in memory of Nancy Herrin. Read about him.


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We are pleased to participate in SuiteWorld 2011, NetSuite's inaugural conference being held in San Francisco this week. During the conference we announced that our two organizations now share over 100 joint customers, which range from venture-backed startups to large corporations, and span multiple industries, including business services, consumer packaged goods, manufacturing, nonprofit and education, retail, and software. NetSuite markets and sells the Adaptive Planning solution and joint integration as NetSuite Financial Planning. These joint clients are taking advantage of the deep and seamless bi-directional integration between the two applications. Featuring a simple, one-time installation process that takes just minutes, the integration allows actual financial data from NetSuite to flow into Adaptive Planning for use in planning, reporting, and analysis, and budget and forecast data to be transferred from Adaptive Planning back into NetSuite for additional reporting and analysis. Additionally, users can drill-through from Adaptive Planning directly into the underlying transactions within NetSuite.
Alongside the exceptional customer traction, Adaptive Planning's Spring 2011 Release continues to deepen the integration between the two applications, which introduced configurable user interface "skins" that allow customers to deploy Adaptive Planning with a NetSuite skin, so users of both applications experience a consistent NetSuite look and feel. The release also further extended the existing integration by enabling users to integrate Adaptive Planning with NetSuite sandbox instances. And, Adaptive Planning introduced the Hosted Connector, a web-based integration platform that allows companies to integrate with other NetSuite applications, such as NetSuite OpenAir and NetSuite CRM.
Establishing a 'single version of the truth' – with tight integration between actual and plan data — is a key best practice for delivering world-class financial management. As such, we're delighted with the tremendous interest in the joint offering to-date. We look forward to continuing to extend the capabilities of the joint solution going forward, and to helping more NetSuite customers move beyond spreadsheet-based budgeting and forecasting to an integrated, automated, cloud-based solution for planning, execution, reporting, and analysis.


text:
Monday, April 27, 2020 | History
2 edition of opposite direction. found in the catalog.
opposite direction.
Heather Buck
Published 1972 by Outposts-Publications in Walton-On-Thames .
LC Classifications PR6052 U27 O6
The Opposite of Matter in Frank Close's book had deflected the path of a set of electrically charged particles — dislocated by a high energy cosmic ray — in the opposite direction.
The evergreen country
Journey to the sun
John Godson.
The sea-mans kalender: or, An ephemerides of the sun, moon, and certain of the most notable fixed stars.
[The Hagerman family.].
The Ant and the Peacock
The Popes Armada
A relative stranger.
Practical Occultism
Proceedings of the 10th International Conference on Coordination Chemistry, Tokyo, September 12, 1967, Nikko, September 13-16, 1967
Ship operation automation, IV
My First Magic Book
Keeping pace with social and technical change
Justiciary records of Argyll and the isles
opposite direction. by Heather Buck Download PDF EPUB FB2
The Opposite Direction Trilogy Paperback – August 7, by Albert Oon (Author) › Visit Amazon's Albert Oon Page. Find opposite direction. book the books, read about the author, and more. See search results for this author. Are you opposite direction. book author. Learn about Author Central Author: Albert Oon.
: Opposite Directions: A Story of Sexual Compulsion (): Mel Small: Books5/5(1). (part 2 of 3) points Compare the normal force exerted on the book by the inclined plane and the weight force exerted on the book by the earth.
Are they equal in magnitude. Yes 2. Their magnitudes cannot be determined since the forces are not in the same direction.
No (part 3 of 3) points Are they opposite in direction. Thank you User for A2A. here is my 18th answer. The book while placed on the top of table exerts a force on the table (book's opposite direction.
book due to gravity), and the table reacts with an equal and opposite force. This is Newton's thir. Bad news is this book should not be read by other people,'" Chapman recalls.
"It wasn't a very interesting book." He decided to "run in the opposite direction," as he says, and write something that required research, empathy, and a main character "wholly different.
How to reverse mouse scrolling direction on Windows If you're using a mouse to navigate on Wind the Settings app doesn't include opposite direction. book. title: breaking out of the mental box -- learning to think in the opposite direction of propaganda to find the truth Resources to aid your Understanding Subtitle: In U.S.
Army Intelligence, I was trained that the truth most often lies in the exact opposite direction of the public rhetoric. A LL men, brother Gallio, wish to live happily, but are dull at perceiving exactly what it is that makes life happy: and so far is it from being easy to attain to happiness that the more eagerly a man struggles to reach it the further he departs from it, if he takes the wrong road; for, since this leads in the opposite direction, his very swiftness carries him all the further away.
opposite to what is usual or to what existed previously. the opposite of what has been said. consisting of two parts that seem to mean the opposite of each other. used for introducing a sentence, or part of a sentence, which says something that is the opposite of the other part.
used for referring to something that is opposite direction. book different from what. just the opposite adj adjective: Describes a noun or pronoun--for example, "a tall girl," "an interesting book," "a big house." informal (completely unalike) tutto il opposite direction.
book She is just the opposite of her sister. È tutto il contrario di sua sorella. opposite direction n noun: Refers to. The standard scrolling direction is where you drag the page in the direction you want the page to move (not the direction opposite direction.
book want to scroll), so dragging upwards makes the opposite direction. book move upwards, which lets you view content further opposite direction.
book the page, so you scroll down. This is the way that touch-based surfaces have worked since they first became.
Reversed definition, opposite or opposite direction. book in position, direction, order, or character: an impression reverse to what was opposite direction. book in reverse sequence. See more. The typical parts of a book's front matter include the following: Half Title (Sometimes Called Bastard Title): Actually, this is just the title of the book.
Frontispiece: This is the piece of artwork on the left (otherwise known as "verso") side of the page opposite the title page on opposite direction. book right (otherwise known as "recto") side. Before explaining what I mean by biological changes having a 'direction', I will share what opposite direction.
book this article. It was a book opposite direction. book 2 by well-known evolutionary biologist Dr Jerry Coyne, of the University of Chicago, who could not resist an opportunity to lash out at the creationists.
3 Amazingly, Coyne uses the train journey analogy himself, reinforcing my point of how evolutionists. In physics, if a force on an object has a component in the same direction as the motion, the work that force does on the object is positive. If a force on an object has a component in the opposite direction to the motion, the work done by that force on the object is negative.
EXAMPLE 1:Moving radar from opposite direction: A police car is going north on a two-lane road at 50 mph. Your vehicle is heading south at 45 mph. Your vehicle is heading south at 45 mph. This means the vehicles are closing in on each other at a combined or relative speed of 95 mph.
"The moment your dreams and your revelation take a special direction while your plans and actions take the opposite direction you commit yourself into a tight box for failure!" ― Israelmore Ayivor, The Great Hand Book of Quotes. The Opposite Direction (Arabic: الاتجاه المعاكس) is a debate TV show handling current events in the Middle East and the Arab topics handled are mostly influenced by political, economical or social topics, But there have been occasions where the discussion visited sensitive religious topics related to the Middle TV show is hosted by Al Jazeera's famous TV.
I meant facing opposite direction* Continue this thread Making-of book retitled "The Secrets of TENET: Inside Christopher Nolan's Quantum Cold War" Discover the secrets of Christopher Nolan's Tenet with this exclusive behind-the-scenes look at 's most anticipated film.
opposite direction n noun: Refers to person, place, thing, quality, etc. (other way, contrary direction) dirección contraria nf + adj: You're going the wrong way. Your house is in the opposite direction. Estás yendo para el otro lado, tu casa está en dirección contraria.
sentido contrario nm + adj. And: If you have a book on a table the book is exerted a force on the table (weight due to gravity), That's where you went wrong. The force that the book exerts on the table is not a gravitational force, it's a normal force. and the table reacts with an equal and opposite force.
The force of friction is NOT ALWAYS directed opposite the direction an object is moving. Consider, for example, an object (like a book) resting on a piece of paper on a table. Reverse definition, opposite or contrary in position, direction, order, or character: an impression reverse to what was intended; in reverse sequence.
See more. Opposite definition is - set over against something that is at the other end or side of an intervening line or space. How to use opposite in a sentence. Synonym Discussion of opposite. The friction force pulls in the opposite direction from the direction the book moves, the work done by friction is given by: Work done by friction = -Fx = -(10 N)(1 m) = Joules.
This means that the friction force removes 10 Joules of energy from the book. So, while you were adding 10 Joules of energy to the book, friction was busy taking. The title (secondary focal point) is placed strategically over an intersection point and in line with the direction of the gaze, as though she is glancing down at it.
If you read the section on focal points for book covers, you know that the human eye will follow the direction of a gaze in an image.
The NOOK Book (eBook) of the Success in Opposite Direction: Strategic Culture and the French Experience in Indochina, the Suez, and Algeria, - Due to COVID, orders may be delayed.
Thank you for your : Progressive Management. The book's weight is acting perpendicular to the table and the reaction of the table on the book is also acting perpendicular to the table, but both thse forces are opposite in direction and equal. The Earth, among other planets, orbits the Sun because the Sun exerts a gravitational pull that acts as a centripetal force, holding the Earth to it, which would otherwise go shooting off into the Sun's pull is considered an action, then Earth simultaneously exerts a reaction as a gravitational pull on the Sun.
Earth's pull has the same amplitude as the Sun but in the opposite direction. A book rests on a level table top.
Which force does Newton's third law imply is equal in magnitude but opposite in direction to the weight of the book. asked in Physics & Space Science by Zuleyka. What makes this clip unique is that at the SK 37E lands, reverses, and takes off in the opposite direction.
Quite unusual for a fighter bomber. How to Invert the Mouseto scroll in the opposite direction original title: Inverting the Mouse. I would like to make my Windows experience more personalized and challenging, so I would like to know if there is a way to invert the up/down motion of the mouse so that when I push it away from me, the pointer moves down.
From the Start screen, type Update, tap Settings, then tap Check for updates. Open the Search charm, tap Settings, then type Devices and Printers.
Tap Devices and Printers in the search results. Tap Refresh (circular arrow) up on the title bar - until the Surface icon looks like Surface. Now open the Trackpad Settings app and see if it. Tesla has been revolutionizing the automotive industry since by heading in the opposite direction from all the other car manufacturers.
Instead of combining gas or diesel engines with batteries to create a hybrid, it eliminated the combustion engine altogether by using only electric motors powered only by batteries in its ever-expanding.
Question: A Book Weighing 5 N Rests On Top Of A TableA Downward Force Of Magnitude 5 N Isexerted On The Book By The Force Ofthetablegravityinertia An Upward Force Of Magnitude _____ Isexerted On The _____ By The Table.A.
6N/tableB. 5N/tableC. 5N/bookD. 6N/book 3. Do The Downward Force In Part A And Theupward Force In Part B Constitute A 3rd Law Pair?yesno4. In Part A, the gravity of the earth exerts a force on the book.
So, the book also exerts a force on the force of gravity of the earth. Or, simply the book also exerts a force on the earth.-Force(earth on book) = Force(book on earth) *Negative sign means the force is in the opposite direction. Part E: d) In Part B, the table exerts a force on.
A vehicle reaches the intersection from the opposite direction and moves straight ahead. You must wait for approaching traffic to go through before you turn. You may enter the intersection to prepare for your left turn if the light is green and no other vehicle ahead of you plans to make a.
The text orientation on book spines appears to follow regional standards. In most places (like the United States, United Kingdom, Benelux countries, and Scandinavia), titles are usually written top-to-bottom. In some continental European countries. How to Change Scroll Direction on Mac Trackpad and Mouse.
By: Salman Patwegar. If you have recently switched from a Windows Computer to a Mac, you may have noticed that the scroll direction on Mac is opposite to what it is on a Windows Computer.
Luckily, it is easy to change the scroll direction on Mac, both for trackpad and the external mouse. To draw more alternating curves, repeat these steps, dragging in an opposite direction each time.
About the Book Author Barbara Obermeier is principal of Obermeier Design, a graphic design studio in California specializing in print and web design. a. The object pdf be pdf to the left, since the net force acts in that direction.
b. The object must be accelerating to the right, as indicated by the force of friction in the opposite direction. c. The object must be moving to the right, as indicated by the force of friction in the opposite direction. d.- greater download pdf magnitude than, and in the opposite direction from, the force on the earth due to the moon.
- greater in magnitude than, and in the same direction as, the force on the earth due to the moon. - equal in magnitude to, and in the opposite direction from, the force on the earth due to the moon.The book signals a shift in direction from her ebook novels.
The first step in this direction will be a discussion with the unions. The story does not go in any particular direction. We can help companies assess the speed and direction of technological change. It .
maisondesvautours.com - Opposite direction. book © 2020

redpajama_set_name: RedPajamaCommonCrawl


For those who enjoy multiple adventurous activities this trip offers some great opportunities. We follow the Mekong River and enjoy a close encounter with the rare and unique Irrawaddy dolphins near the famous sunset town of Kratie. The northeast offers real potential with protected community forests, remote rivers, traditional villages, elephant riding, ethnic minority tribes and overnight jungle trekking and both in Mondulkiri and Ratanakiri we get to experience all of these and more. We survey the mighty waterfalls that thwarted the grand designs of French imperialists in Stung Treng (and which now mark the Lao border). Onto explore Mekong flooded forests at Ramsar Wetlands by kayak.
Kratie Rural Lifestyle and Dolphin Watching.
Kratie to Mondulkiri. Bou Sra Waterfall and Coffe Farm.
Ratanakiri – Overnight Jungle Trek.
Follow Kachoch hill tribe ranger for a hike that will take you in to Kaoh Piek forest which the southern of Virakchey National Park. Starting on the dirt roads to Vun Sai, the banks of the Sesan and O'Lalai rivers, visit small settlements, stay overnight in the jungle, and submerge in a beautiful forest. This 2 day trek does not only focus on nature, but also engage with indigenous communities, learn about local farming and lifestyle. Different sceneries will be presented to you like beautiful panoramic views, mixed forest, secondary forest. Sleep may not be the same without the fire flies speaking across the night sky, but at least you'll always have the memories and dreams of your time.
Stung Treng to Phnom Penh or Siem Reap.
Before leaving behind the remote Stung Treng, we might visit Stung Treng Women's Development Center (open Monday to Friday). STWC or Mekong Blue is where the project focuses on developing life skills that assist in breaking the cycle of poverty and illiteracy for vulnerable people, especially women in their region. You will learn about Cambodian silk weaving and their production, which allows not only preservation but also cultivation of the hundred-year old tradition of silk-weaving. At the end you can shop for souvenirs. We can either drip you in Phnom Penh or Siem Rea for your next destinatoion.
6 lunches: one lunch in Kratie with a local family, one lunch at Bunong Elephant Project in Mondulkiri, two lunches during jungle trekking in Ratanakiri, one lunch in Preah Rumkel with a local family at the homestay and one take away lunch during kayaking.
2 dinners: one dinner during jungle trekking in Ratanakiri and one dinner at Preah Rumkel with a local family at the homestay.


text:
Science World Magazine
This site explores scientific concepts and advances.
IPhone 5 With Induction?
admin February 19, 2016 February 28, 2016
Apple's iPhone 5 is possibly equipped with induction technology. The Samsung Galaxy S3 is known to be equipped with the now very popular induction technology. This makes it possible to charge a device within reach of the induction charger through a magnetic field, so that cable and co. accounts for. Experts and observers expect from Apple, the iPhone 5 is also equipped with this technology. Samsung makes it to you almost for the first time in the history of the Smartphones expected from Apple, that you look down at the competitors. Usually it is the case that all Smartphone manufacturers at Apple look down or at least be inspired.
Samsung has now but managed to escape, so that Apple is forced to act out of this vicious circle. Not only that's why Apple's many technology experts expect that the iPhone 5 is a real grenade, which is also equipped with induction technology. Apple and the induction the developer from Cupertino who know however, that Apple doesn't like to copy ideas 1:1. Usually a kind of is like own creation designed it so that customers in the end the competitors prefer the iDevices. To the Galaxy S3 must be topped once. There are already signs of an induction-like pages Apple technique.
In addition to countless rumors already appeared with the first Ultrabook rumors regarding this technology, there are also alleged statements on the part of Apple, which should confirm such a technology. In Apple news, nothing like that but so far was to read. Apple live ticker on the WWDC in June appear new products from Apple LiveTicker, the iPhone 5 to the devices not heard, which could be presented, because the World Wide Developer Conference is dedicated to software and is available only for selected app developers. Therefore, it is assumed in addition to the software for the Mac "OS X Mountain Lion" also another mobile operating system called iOS 6, which noted many traits in the mountain lion and thus promotes the interaction of both operating system. Will be presented with high Probability of an iMac, MacBook Pro and MacBook Air, possibly with the high-resolution retina display, which often had in the past in the rumors. Therefore, Apple would cooperate and take the steps already with various companies. The 17-inch MacBook Pro to die according to the latest information. Also Apple offers for the time being only the MacBook Pro with 13.3 inch, because it is the most popular model, so the Mac with 15.4 inch follows until some weeks later, the plants enjoy sufficient lead time. Tim Cook has already said: this will be an interesting year.
Categories News	Tags electronics & information technology
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Next: Data Centers
Science World Magazine © 2020


15%60°49°Night - Mostly cloudy. Winds variable at 11 to 13 mph (17.7 to 20.9 kph). The overnight low will be 46 °F (7.8 °C).Breezy with a high of 61 °F (16.1 °C). Winds variable at 11 to 20 mph (17.7 to 32.2 kph).
Tonight - Mostly cloudy. Winds variable at 11 to 13 mph (17.7 to 20.9 kph). The overnight low will be 46 °F (7.8 °C).
Today - Breezy with a high of 61 °F (16.1 °C). Winds variable at 11 to 20 mph (17.7 to 32.2 kph).


Borner earrings hang 2 inches from the ear and are 1.5 inches wide. The piece is hand woven with silk, wool and/or cotton thread. Since each piece is made by hand there may be slight variation.
The colors can be customized. If you are interested in a specific color combination please indicate in the notes at check out.


Jeffrey Adelglass, M.D., F.A.C.S., is the founder and medical director at Skintastic Cosmetic Surgery and Laser Skincare Centers in Dallas and Plano. Dr. Adelglass has been a practicing Cosmetic Surgeon and ENT in the Dallas area for over 25 years. With his practice originally dedicated to ENT (Ear, Nose and Throat), Dr. Adelglass expanded his expertise over two decades ago to facial and cosmetic surgery (FACS) and maintains both practices today. We are privileged to have Dr. Adelglass as our Medical Director.
Beth is a Master Clinical Injector with over 18 years of experience in the aesthetics industry. Beth prides herself ensuring each client is educated through consults prior to aesthetic procedures; learning her clients' needs, evaluate and discussing appropriate treatment options. Her artistic talents for injections result in optimal outcomes.
She currently trains for Merz Aesthetics educating industry professionals and has been elected as an Advanced Aesthetic Experts Educational Congress. Beth has her own independent academy where she trains healthcare providers across the US from the beginning of their aesthetic journey through advanced level courses on the use of fillers, Sculptra and neuromodulators.
Beth feels blessed each and every day doing what she loves both at work and at home…when she is not working she loves spending time with her amazing husband Charles and their three beautiful children.
Lori brings to Define Medical Aesthetics a background in Retail Marketing, Mortgage Brokering, Operations Director of a small business, Software Sales, and Management of a Medical Spa.
Her expertise in organization, policies and procedures and customer service will have our clients feeling welcomed and cared for when they come to us to define their beauty. Our motto is Real Patients Real Results!
Our goal is to keep you looking like you, but better! Her goal is to be sure this happens!
Samantha Daniel O'Neal has joined our team of expert injectors! Samantha is happy to see any existing clients that she has serviced in the past on Tuesdays of every week! Samantha has recently married the love of her life, Brian O'Neal in August of 2018! Please help us in welcoming Samantha to de+fine Medical Aesthetics!
Kerri has been in practice since 2003. Her experience is in emergency medicine as well as medical aesthetics. She is passionate about helping people look and feel their best through the latest non-invasive cosmetic treatment and hormone optimization programs.
Kerri is fully trained and certified in bio-identical hormone replacement therapy, skin rejuvenation, and injectable procedures.
Shana spent many years as a flight attendant, where she fine-tuned her client service skills! After raising her family, Shana began a new career as a Client Relations expert in the Medical Spa world for the past year and a half. Shana has been with Define Medical Aesthetics since its opening. She is proud to work with an excellent group of practitioners and dedicated staff. She enjoys showing attention to detail, and the opportunity to provide excellent customer service. Through her interactions with clients, she makes sure they are knowledgeable and comfortable with every stage of their medical spa experience. She gains real satisfaction in seeing results that are very natural and defined, like only team of experts can do!
Debbie is a nurse with 20+ years of experience. She prides herself with getting to know her patients aesthetic concerns and desires. Debbie is able to achieve optimal aesthetic injectable results through a thorough consult, education and discussion with her patients prior to treatment.
In addition to loving the opportunity to help her clients feel good about themselves " inside and out", she loves spending time with her husband, John, their 4 children and 2 fur babies.
Brian received his Bachelor of Science degree from Texas Christian University. After graduating from TCU, he worked as a staff nurse at Parkland Memorial Hospital and Baylor University Medical Center in the ICU and Emergency Department. While working as a staff nurse, he earned his Master of Science in Nursing from Baylor University and is a board certified family nurse practitioner. Brian has been practicing as a Family Nurse Practitioner for over 15 years and is the senior Nurse Practitioner with Baylor University Medical Center's Interventional Radiology Department performing minimally invasive procedures and teaching Radiology residents how to perform these procedures. He has also been a provider for Aesthetics/Dermatology for the past 5 years performing exams for patients receiving aesthetic treatments.


text:
Journal of Glaciology
Volume 65 Issue 254
Testing and application of a mo...
Core reader
Testing and application of a model for snow redistribution (Snow_Blow) in the Ellsworth Mountains, Antarctica
2. Snowdrift
3.1. Ellsworth Mountains, Antarctica
3.2. Input data
4.1. Wind deflection
4.2. Shelter index and modified wind speed
4.2.1. Aspect index
4.2.2. Slope index
4.2.3. Shelter index
4.3. Curvature index
4.4. Snow transport – erosion
4.5. Snow transport – deposition
4.6. Snow depth index
4.7. Snowdrift index
4.8. Boundary conditions
4.9. Precipitation assumption
4.10. Quantitative assessment
5.1. Qualitative assessment
5.1.1. Areas of net snow gain
5.1.2. Areas of net snow erosion
5.2. Quantitative assessment
7. Conclusions and future work
Journal of Glaciology, Volume 65, Issue 254
December 2019 , pp. 957-970
Stephanie C. Mills (a1) (a2), Anne M. Le Brocq (a3), Kate Winter (a4), Michael Smith (a2), John Hillier (a5), Ekaterina Ardakova (a6), Clare M. Boston (a7), David Sugden (a8) and John Woodward (a4)
1School of Earth, Atmospheric and Life Sciences, University of Wollongong, Wollongong NSW 2522, Australia
2School of Geography, Earth and Environmental Sciences, Plymouth University, Drake Circus, Plymouth, PL4 8AA, UK
3Geography, College of Life and Environmental Sciences, University of Exeter, Exeter EX4 4RJ, UK
4Department of Geography and Environmental Sciences, Faculty of Engineering and Environment, Northumbria University, Newcastle upon Tyne NE1 8ST, UK
5Department of Geography, Loughborough University, Leicestershire LE11 3TU, UK
6Department of Geography, Geology and the Environment, Kingston University London, Penrhyn Road, Kingston upon Thames KT1 2EE, UK
7Department of Geography, University of Portsmouth, Buckingham Building, Lion Terrace, Portsmouth PO1 3HE, UK
8School of GeoSciences, University of Edinburgh, Edinburgh EH8 9XP, UK
Copyright: © The Author(s) 2019
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
DOI: https://doi.org/10.1017/jog.2019.70
Published online by Cambridge University Press: 07 October 2019
Fig. 1. Location map for the study site in the southern Heritage Range, West Antarctica. (a) Horseshoe Valley is situated at the southern extreme of the Ellsworth Mountains. Background imagery is from v5 of the Antarctic Digital Database (ADD). (b) Landsat 7 true colour composite of the Horseshoe Valley field site, from 21 September 2009. Lines in the imagery are the result of scan line issues with Landsat 7. The inset figure shows areas of mapped snow at sites 3 and 4. (c) Wind Rose showing wind direction data and wind speed from the privately operated Patriot Hills weather station, 2008–2009 (marked in panel 1b). (d) REMA (Howat and others, 2018) for the study region, with annotation and inset as in (b). Wind drift tails and blue ice moraines are clearly visible. The dashed lines demarcate BIAs.
Table 1. Summary table of model inputs and user-defined parameters with range used in this paper in brackets
Table 2. Parameter sets for Snow_Blow experiment results centred on the Patriot and independence Hills (Fig. 4)
Fig. 3. (a) Illustration of Eqn (7), snow erosion vs wind speed relationship. The threshold wind speed is set to 5 m s−1, therefore erosion only starts to occur once this threshold is exceeded. Maximum erosion (1) takes place once the wind speed (F) is reached. (b) Illustrates how it is the ratio between the wind speed and threshold wind speed that is important in determining the (integrated) amount of snow eroded, i.e. across the domain, less snow is eroded when the wind speed is close to the threshold wind speed. (c) Snow deposition weightings for deposition distances applied in the experiments in Table 2. (d) Number of cells with a positive snowdrift index in the test area (Fig. 2, inset) over 20 iterations.
Fig. 4. (a) 21 September 2009 Landsat true colour composite for test area, showing mapped snow extent for model comparison. (b–f) Illustration of snow depth index at eight iterations for experiments in Table 2. (g) 21 September 2009 Landsat true colour composite for the wider study area. Dashed line indicates BIAs. (h) Snow depth index at eight iterations for Expt. 5, showing snow deposition in the lee of the mountains and erosion in the BIAs.
Table 3. Quantitative assessment of different parameter values for F, Smax and Cmax
Fig. 5. Snowdrift index for sites 1–4 shown in Figure 1b for a 122.5° and 45° wind direction for various parameter sets (F = wind direction, Smax is the maximum value the slope is set to for each cell, Cmax is the curvature index).
Fig. 6. Positive and negative snowdrift index for sites 1–4 shown in Figure 1b with varying wind directions, using parameter set from Expt. 5. Numbers 1–4 are the snowdrift index values.
Wind-driven snow redistribution can increase the spatial heterogeneity of snow accumulation on ice caps and ice sheets, and may prove crucial for the initiation and survival of glaciers in areas of marginal glaciation. We present a snowdrift model (Snow_Blow), which extends and improves the model of Purves, Mackaness and Sugden (1999, Journal of Quaternary Science 14, 313–321). The model calculates spatial variations in relative snow accumulation that result from variations in topography, using a digital elevation model (DEM) and wind direction as inputs. Improvements include snow redistribution using a flux routing algorithm, DEM resolution independence and the addition of a slope curvature component. This paper tests Snow_Blow in Antarctica (a modern environment) and reveals its potential for application in palaeoenvironmental settings, where input meteorological data are unavailable and difficult to estimate. Specifically, Snow_Blow is applied to the Ellsworth Mountains in West Antarctica where ablation is considered to be predominantly related to wind erosion processes. We find that Snow_Blow is able to replicate well the existing distribution of accumulating snow and snow erosion as recorded in and around Blue Ice Areas. Lastly, a variety of model parameters are tested, including depositional distance and erosion vs wind speed, to provide the most likely input parameters for palaeoenvironmental reconstructions.
The redistribution of snow by wind can play an important role in providing additional mass to the surface of ice masses. The effects of such snowdrift have been shown to be crucial in the distribution of snow on ice caps and ice sheets, where it can increase the heterogeneity of snow accumulation (Zwinger and others, 2015) and can have a significant impact on glacier mass balance (Sauter and others, 2013). This variation in snow accumulation as a function of snowdrift could potentially help in interpreting buckled radio-echo sounding layers in Antarctica (as described by Siegert and others, 2005), especially around the mountainous margins of the continent, as these are a function of accumulation rate, as well as ice flow and basal melting conditions. In areas of marginal (or niche) glaciation, local topoclimatic effects such as topographic shading or enhanced accumulation through avalanching and snowdrift may be crucial for the initiation and survival of glaciers. Reconstructions of former glacier limits have often been used to infer past climatic conditions (e.g. palaeotemperature or palaeoprecipitation) at the equilibrium line altitude (ELA) (e.g. Hughes, 2002; Carr and Coleman, 2007; Carr and others, 2010; Mills and others, 2012). However, the role of topoclimatic effects on the occurrence of small glaciers means that these glaciers could primarily reflect local climatic conditions rather than past regional climatic conditions. It is therefore important to understand the role of these local effects, to adequately assess whether palaeoclimatic reconstructions from former glaciers are an accurate representation of past regional climatic conditions, or whether reconstructed ELAs are substantially altered due to local factors such as snowdrift, which would then need to be accounted for in palaeoclimatic interpretations.
For example, much of the work undertaken in the British Isles regarding the reconstruction of former glaciers does not consider the implications of the role of snowdrift on the derived palaeoclimatic conditions (e.g. Lukas and Bradwell, 2010; Boston and others, 2015). When snowdrift has been considered, the studies have broadly followed the approach of Sissons and Sutherland (1976) which considers that all ground lying above the ELA and sloping towards the glacier surface has the potential to contribute snow to the glacier surface. This method gives a good indication of the potential wind directions most likely to contribute snow to the former glacier surface. Mitchell (1996) and later Coleman and others (2009), refined this method to take into account the uphill movement of wind-blown snow. But, this is still not a complete picture of snow redistribution.
Following Bell and Quine (1996), Purves and others (1999) developed a snowdrift model in a GIS using a shelter index based on a digital elevation model (DEM), to demarcate areas of snow ablation and accumulation due to snowdrift processes. Purves and others (1999) used the model to assess the potential contribution of wind-blown snow to formerly glaciated corries in the Cairngorms. However, this model has not been used subsequently. Despite the potential applicability of the Purves and others (1999) model to any region and the recent advances in GIS and improved DEM accessibility, the Sissons and Sutherland (1976) approach has remained the preferred method for reconstructing snow distribution in palaeoenvironments (e.g. Lewis and Illgner, 2001; Coleman and others, 2009; Mills and others, 2012; Chandler and Lukas, 2017).
Several other snowdrift models exist. These range from simple models, such as the drift routine in SNOWPACK (Lehning and others, 2000) to more sophisticated models such as SnowTran-3D (Liston and Sturm, 1998), PIEKTUK-D (Déry and Yau, 2001), ALPINE3D (Lehning and others, 2006) and snow2blow (Sauter and others, 2013). SNOWPACK is a 1-D momentum, mass- and energy-balance model, while the more sophisticated models (SnowTran-3D, PIEKTUK-D, ALPINE3D and snow2blow), account for spatial and temporal snowdrift variations, incorporating saltation, turbulent-suspended transport and sublimation. These models provide snow depth measurements (w.e.), which can be converted to winter solid precipitation (Liston and Sturm, 2002). One of the main problems in the application of these models to palaeoenvironments is their requirement for meteorological inputs, including air temperature, precipitation and relative humidity. These are often unavailable for palaeoenvironments.
Snow transport due to gravitational processes, such as avalanching are particularly important in areas with steep inclines and can be responsible for substantial accumulation of snow at the base of steep slopes (Gruber, 2007; Bernhardt and Schulz, 2010). Models that exist to replicate these processes include an algorithm which parameterises mass transport and deposition, to simulate avalanching in mountain environments (Gruber, 2007) and SnowSlide, which introduces lateral snow transport into an existing snowdrift model (Bernhardt and Schulz, 2010).
The Purves and others (1999) model differs from these approaches outlined above; it uses a series of rules to describe relative snow accumulation over complex terrain, rather than absolute snow accumulation depths, and so only basic meteorological inputs are needed. This relative snow accumulation field can then be used to create a 'snowdrift index' for any particular glacier system, ranking each system with respect to its neighbours to aid regional interpretation. The aim of the model is to determine the locations most likely to have had the greatest addition of mass through snowdrift rather that the quantitative estimates of the contribution of snow to former glacier surfaces. The advantage of this simpler approach by Purves and others (1999) is that it requires fewer meteorological inputs. It is important, however, to be aware of its limitations, particularly relating to processes which are parameterised or omitted, such as sublimation and avalanching.
In this paper, we present a new and improved version of the Purves and others (1999) snowdrift model, that we call Snow_Blow. We apply Snow_Blow to a contemporary glacial environment to assess the validity of its outputs and to increase confidence in its use in palaeoenvironmental settings. The model is written in the Python scripting environment in ESRI ArcGIS, which makes the model accessible to palaeoenvironmental researchers. The code is freely available online at GitHub and at https://doi.org/10.5281/zenodo.3336070.
To investigate the impact of snowdrift upon glaciers in future palaeoenvironmental settings, we first test Snow_Blow in a contemporary setting in Antarctica. We focus on four specific aspects: (1) testing the sensitivity of the results for a range of parameters, to determine how these impact model outputs for snow deposition (Section 5.1.1). (2) Assess snow erosion in comparison with the distribution of Blue Ice Areas (BIAs) (Section 5.1.2). This allows us to determine the likely number of iterations required to generate snow erosion that is comparable with BIAs, which allows for comparisons with other studies. (3) Undertake a quantitative assessment of parameter sensitivity to determine a most likely set for future model runs (Section 5.2). (4) Create a snowdrift index that takes into account catchment size on the importance of snowdrift, and thus identifies which localities are more susceptible to alteration by snowdrift depending on a particular wind direction (Section 5.3).
Snow transport by wind, or snowdrift, can lead to a significant redistribution of the existing snow cover (Pomeroy and others, 1998; Balk and Elder, 2000; Bowling and others, 2004; Bernhardt and others, 2009). Studies show that the major transport modes of snow are saltation and suspension (Budd and others, 1966; Pomeroy and Gray, 1990), where wind must reach a certain threshold speed before snow particles are picked up and transported. This threshold speed is a function of the snow properties, and a range of estimates are recorded across the literature (e.g. Li and Pomeroy, 1997, Liston and others, 2000, Liston and others, 2007, He and Ohara, 2017). Li and Pomeroy (1997) state that for dry snow, the range is on the order of 4–11 m s−1 ambient wind speed, with an average of ~7 m s−1, whereas Liston and others (2000) give a narrower range of 4–6 m s−1. Liston and others (2007) suggest that 4–5 m s−1 is a commonly used threshold velocity for dry snow. Transport by suspension can also lead to a loss of snow mass to the atmosphere, of the order of 15–25%, which is largely accounted for through sublimation (Pomeroy and others, 1997; Bintanja, 1998).
A generalised pattern of snow erosion on exposed sites such as ridge tops (where wind speeds are high), and snow deposition in sheltered sites such as the lee of ridges, and in topographic depressions (where wind speeds are reduced) can be observed in mountain environments (Benson and Sturm, 1993; Pomeroy and others, 1993; Liston and Sturm, 1998, 2002; Sturm and others, 2001; Mott and others, 2008). Snow_Blow aims to reproduce these patterns of snowdrift by parameterising the above snowdrift processes, using a simple topographic-based shelter-index approach.
We assess the validity of Snow_Blow in Horseshoe Valley, in the Heritage Range of the Ellsworth Mountains, Antarctica (Fig. 1). The mountains that define Horseshoe Valley in West Antarctica protrude 150–300 m above the present ice-sheet surface, reaching elevations of 1200–1600 m a.s.l. (Winter and others, 2015). These mountains break an undisturbed wind fetch of several hundred kilometres, where katabatic winds, that evolve high on the Antarctic plateau (where net long-wave radiation losses cool the near-surface air (Nylen and others, 2004)) replace the less dense air in Horseshoe Valley (Hoinkes, 1960; Ishikawa and others, 1982). This phenomenon initiates and maintains BIAs in the lee of the Heritage Range, particularly along the leeward slopes of the Patriot and Independence Hills (Fig. 1). Landsat imagery reveals wind drift tails behind exposed rock (Fig. 1b), BIAs on the leeward slopes of the mountains, and snow accumulation in the lee of the mountains. These features highlight areas of net snow gain (drift tails and leeward areas) and net snow loss (BIAs), making this region ideal for validating the Snow_Blow model. This observed snow extent (Fig. 1d, inset) is delineated using a threshold reflectance value of 120 (8-bit image) in the blue band of the January 2009 Landsat image (see Burton-Johnson and others (2016) and Supplementary Section 5 for further information).
At this stage, we highlight the distinction between snow and ice ablation in BIAs. Once the snow is removed from the ice surface, ice ablation occurs through sublimation, which effectively draws older ice to the surface. In this paper, we focus on the surface snow processes, rather than ice ablation.
The advantages of using the Ellsworth Mountains for validation are threefold. (1) The katabatic winds blow from a consistent direction (Fig. 1c). (2) There is a clear demarcation of areas of high snow erosion (i.e. the BIAs and snow-free rock surfaces, Fig. 1b, inset) and low snow erosion/deposition in the lee of the mountains (Fig. 1). (3) We assume the snow ablation is solely due to wind-related processes, which eliminates the need to include sublimation processes that exist over coastal areas and BIAs in Antarctica. This eliminates the need to include enhanced melting variables that exist in alpine environments, which result from positive air temperatures and solar radiation. We appreciate that this region represents an extreme end-member environment with high wind speeds, and cold, dry conditions. The other potential disadvantage of validation in this area is that snow depth measurements have not been collected. However, the aim of this paper is to produce patterns of snowdrift and relative depths, so the pattern of blue ice (i.e. snow-free areas) in Horseshoe Valley in the southern Heritage Range forms an appropriate test for the Snow_Blow model.
To assess the assumption in point (3) we have compared the extent of BIAs downwind of the Patriot and Independence Hills, as well as the coverage of snow in the lee of the mountains, in temporally classified Landsat 7 and Landsat 8 imagery. These areas do not change much over time (Supplementary Fig. 1); specifically the 2008–2009 season, which coincides with meteorological data presented in this paper, is similar to the 2016–2017 and 2017–2018 austral summer seasons. Furthermore, there is no clear pattern of increased snow-free area towards the end of each summer season so the variation in extent of BIA over time is more likely to be a function of the time since the last snowfall event, rather than the time of year. These observations confirm that the assumption in point (3) above is an acceptable approximation because BIAs appear to be largely wind-driven features which show stability in extent over decadal time periods.
This study uses the REMA (Reference Elevation Model of Antarctica) Release 1 DEM (Fig. 1d), which is created from stereophotogrammetry, derived from DigitalGlobe satellite imagery (Howat and others, 2018). Although the original DEM is supplied at an 8 m resolution, it is resampled in this study to a 30 m resolution to match the available Landsat imagery; this has the added advantage of decreasing the computational expense of the model. The other essential input to Snow_Blow is a dominant wind direction. Average hourly weather station data were recorded at the Patriot Hills blue-ice aircraft runway during 2008–2009 (data available at: https://geographic.org/global_weather/antarctica/patriot_hills_aws_890810_99999.html). These data show a modal wind direction of 122.5° when converted to polar stereographic grid angles. Mean wind speed is 8.1 m s−1, with a maximum value of 31.2 m s−1, and a std dev. of 5.0 m s−1 (Fig. 1c, Supplementary Fig. 2). As wind speeds higher than the mean can impact the pattern of snowdrift, a wind speed of 15 m s−1 was selected to represent these wind speeds in the period prior to the acquisition of the 2008–2009 Landsat imagery. This is an arbitrary choice and, as demonstrated later, different values can be tested as part of any application of the model.
The Snow_Blow model presented here builds on the model developed by Purves and others (1998, 1999), with additional modifications. The following sub-sections describe both the original Purves model and the modifications added to create the ArcGIS Python-scripted Snow_Blow model. Section 5 assesses the most appropriate parameterisation on the basis of an application to the Heritage Range.
Snow_Blow is a simple model used to derive the relative accumulation of snow in two dimensions. The final output is a 'snow depth index' which ranges from −1 (maximum net snow loss) to 0 (no net change), through to values above 0 (net snow gain). To derive this relative index, the maximum erodible snow in a model gridcell is initially a non-dimensional 1 'unit' of snow. In a model gridcell located on an exposed plain, the whole 1 unit of snow in the cell would likely be eroded, but 1 unit of snow would also be blown in from the neighbouring cells, so there is no net change in the snow depth, i.e. a snow depth index value of zero. If there is no snow blown into an exposed cell, the cell would lose 1 unit of snow but have none blown in from its neighbours (e.g. due to snow starvation as a result of shelter), so the cell would have a net loss of snow and have a negative snow depth index value. Finally, in a sheltered cell, the erosion would be less than the whole snow unit, and snow may be blown in from upwind cells, so this would lead to a net gain of snow, i.e. a positive snow depth value. This value could be higher than 1 in the case of snow being blown in from several neighbours. A number of steps are involved in producing this snow depth index. These steps are outlined briefly below and discussed in more detail in the following sections. It should also be noted here that the model can be run over a number of iterations, representing sustained snowdrift conditions.
As stated previously, inputs into the model are a DEM, wind speed and wind direction (Table 1). An initial wind direction (Θ) is selected (this is the direction the wind is coming from), and a constant wind speed (F) is assumed. Using the DEM, the deflection of wind around the topography is used to calculate a new wind vector field (see Section 4.1). The sheltering effect of the terrain is then computed to produce a modified wind speed (see Section 4.2).
The amount of snow eroded from each cell is then calculated as a function of the modified wind speed (Section 4.4), before the full redistribution of snow is modelled (Section 4.5) and a relative snow depth index produced (Section 4.6).
The input wind direction is modified for the effects of topography for each individual cell, based on slope aspect and inclination relative to wind direction using an empirical equation (Ryan, 1977):
(1)$$F_{\rm d} = -0.225 \times S_{\rm d} \times \sin (2(A-\Theta )),$$
where F d is wind diversion (degrees), S d is the slope (%), A is the slope aspect (degrees) and Θ is the wind direction (degrees) (Purves and others, 1999). Here, we calculate slope using the ESRI ArcGIS 10.5.1 slope function (%), which identifies the steepest downhill descent between the cell and its eight neighbours in Eqn (1), rather than to the horizon downwind as specified in Ryan (1977). We suggest that this is appropriate, given that downwind areas are then isolated in the aspect index calculation outlined in the following section.
The calculations in this section (and the following sections, up to and including Section 4.5) are illustrated in Figure 2 and Supplementary Fig. 3, using the results from Expt. 1 (see Table 2 in Section 5). These illustrations are intended to assist descriptions of the model.
Fig. 2. Experiment 1 calculations highlight Snow_Blow outputs of (a) the Shelter index (Ti), (b) the modified wind speed (F m) and shelter index (T i), (c) snow eroded (Q e), (d) snow deposited and (e–h) the snow depth index from selected iterations (1–15), as labelled.
A shelter index (T i) is employed to define areas in the DEM where wind speed decreases. T i is calculated from an aspect index (A i) and slope index (S i), and these indices are described below.
A slope is assumed to be sheltered if it is within 45° of the lee aspect, where lee aspect is 180° from the dominant wind direction (Θ). The aspect index is 1 if an aspect is directly opposite to the wind direction. The aspect index is linearly scaled to 0 if the lee aspect ≥45°. This follows the suggestion by Purves and others (1999) that the highest aspect index values lie directly in the lee of the dominant wind direction and that this decreases towards zero as the aspect of the slope approaches 45°.
Following Purves and others (1999), a slope is assumed to be sheltered if the slope is >5°. The slope index is then scaled linearly to a value of 1 (maximum shelter) at the maximum slope. The slope index (S i) is calculated in each cell as follows:
(2a)$$S_{\rm i} = \displaystyle{{(S-5)} \over {(S_{{\rm max}}-5)}}\,{\rm \; if}\,S \gt 5$$
(2b)$$S_{\rm i} = 0\quad\quad\quad\quad {\rm if}\,S \lt 5$$
where S is the slope of the cell in question (degrees) and S max is the maximum slope angle in the DEM (degrees).
While the original Purves and others (1999) model setup defines a minimum slope of 5°, the paper does not provide a maximum slope value, as this is derived from the maximum slope in the DEM. This approach limits the transferability of this model to other model domains with a different maximum slope, and limits the number of cells which can reach the upper end of the shelter index values. As a result, a range of S max values are employed to investigate the sensitivity of Snow_Blow outputs to changes in maximum slope, with the aim of suggesting a suitable default value. S i is capped at 1 when S max values in the DEM are greater than that set by the user.
The shelter index (T i) is then expressed as
(3)$$T_{\rm i} = A_{\rm i} \times S_{\rm i}.$$
Values of T i range from 0 (no shelter) to 1 (full shelter) (Figs 2a, b).
The modified wind speed (F m) is then calculated using the maximum wind speed (F) and the shelter index:
(4)$$F_{\rm m} = F(1-T_{\rm i}).$$
This produces a modified wind speed field (Fig. 2b) that is an inverse linear function of the shelter index, so is a simple parameterisation which does not take into account turbulence, or increased wind speed due to funnelling or an upslope.
In the original formulation of the Purves and others (1999) shelter index (Section 4.2), the aspect calculation does not take into account the nature of the slope when it has an aspect in the lee of the wind direction. In a classic cirque morphology, for example, the curvature of the cirque would likely be concave, and, therefore, more sheltered than a slope which has a more convex curvature.
The improved model has an added option to introduce a 'curvature index' (C i) into the shelter index, if one is required:
(5)$$T_{\rm i} = A_{\rm i} \times S_{\rm i} \times C_{\rm i},$$
where C i is a function of the plan curvature of the surface and C is the plan curvature of the cell in question:
(6a)$$C_{\rm i} = 1-\displaystyle{C \over {C_{{\rm max}}}}\quad {\rm if}\,C \gt 0$$
(6b)$$C_{\rm i} = 1\quad\quad\quad\quad {\rm if}\,C \lt 0$$
C max is a specified maximum value at which the curvature index saturates at 1 (Supplementary Figs 4a, b). Cells with convex plan curvature (considered less sheltered) will have a positive curvature value, whereas cells with concave plan curvature (considered more sheltered) will have a negative curvature value. Although profile curvature was considered alongside plan curvature, we found that this measure could not distinguish the start of the sheltered region (e.g. the headwall of a cirque). As with S max, a user-defined value is set rather than extracting C max from the DEM.
Once the wind direction and speed have been adjusted, the snow transport from cell to cell can be calculated. First, the amount of snow eroded from each cell is computed. This value is dependent on the difference between the modified wind speed and the threshold wind speed. Both the Purves and others (1999) model, and our Snow_Blow model implements a cubic relationship between the snow eroded and the proportion of the wind speed above a given threshold speed:
(7)$$Q_{\rm e} = k \times (F_{\rm m}^3 -F_{\rm t}^3 ),$$
where Q e is the amount of snow eroded from a cell, k is a constant, F m is the modified wind speed and F t is the threshold wind speed. Although Purves and others (1999) do not state the threshold value they use, we have selected a standard value for F t of 5 m s−1 for dry snow, following the discussion in Section 2. Values for k are not given in the Purves and others (1999) paper. We remove the need for k by scaling the resulting erosion field from 0 (no erosion) to 1 (full erosion). Scaling the erosion also has the effect of making the absolute value of the wind speed irrelevant; instead it is the ratio of the threshold wind speed (F t) to the wind speed which is important in determining the amount of snow erosion which occurs (Fig. 3a). As a worked example, if the threshold wind speed is chosen as 5 m s−1 (as stated above) and the maximum wind speed is chosen as 15 m s−1 (blue line in Fig. 3b), this corresponds to a ratio of 1 : 3 (blue line in Fig. 3a). However, if the threshold wind speed had been chosen as 4 m s−1, and the maximum wind speed as 12 m s−1, then the erosion field would be identical, despite the maximum wind speed being lower. The full erosion value of 1, therefore, needs to be considered in the context of the ratio between the threshold wind speed and maximum wind speed, rather than the absolute value of the maximum wind speed.
Snow transport distance in the original Purves and others (1999) model was grid dependent and snow could only be blown into one cell over a single iteration. The distance the snow was transported was therefore a function of the number of iterations used. The distance that snow can be physically transported is still a matter of debate in the literature, largely because it depends upon the method of transport (suspension vs saltation). To maintain a simplistic, accessible model these two methods of transport are grouped together to create one parameterisation in Snow_Blow.
In the Snow_Blow model, we introduce a new snow deposition routine which allows the snow deposition to follow the deflected wind direction, independently of DEM cell size. The snowdrift transport distance is modelled using an exponential distribution (see example in Fig. 3c).
Based upon this distribution's cumulative density function (i.e. 1 − eLx), the weighting (B) that governs the fraction of an origin cell's snow that ends up in a target cell is
(8)$$B = \exp (-Lx_2)-\exp (-Lx_1),$$
where x 1 and x 2 are distances from the centre of the origin cell to the nearest and farthest limits of the target cell, respectively. The decay constant, L is
(9)$$L = \displaystyle{1 \over {md}},$$
where md is an externally determined appropriate mean depositional distance. For computational efficiency, md sets a maximum distance that snow can be transported (mxd) as ~4.6 times md as
(10)$$mxd = \displaystyle{{\ln (0.01)} \over {-L}}.$$
This explicitly accounts for 99.0% of the snow, so the weights in Eqn (8) are scaled so as to sum to 1, therefore, accounting for 100% of the snow and conserving snow mass (to within truncation error).
The mean depositional distance in Snow_Blow, and, hence, maximum distance can be modified by the user. Fetch distance in general is believed to be somewhere between 300 m (Takeuchi, 1980) and 500 m (Pomeroy and others, 1993), although larger transport distances have been reported (e.g. up to 800 m) for saltating snow grains (Braaten and Ratzlaff, 1998). The proportion of snow deposited decays rapidly, with the majority deposited within the first 150 m (Braaten and Ratzlaff, 1998). Here, we start with md as 150 m, giving an mxd of 690 m.
The eroded snow (calculated in Section 4.4) is redistributed, based on the weightings listed above using a routing algorithm designed for calculating upslope areas in hydrological modelling (Tarboton, 1997). This is a recursive algorithm which uses a flow direction field to search for the upslope cells contributing to a single cell. The algorithm allows flux from one cell to travel to two of eight possible neighbouring cells (based on the Tarboton (1997) algorithm (Fig. 2d), which introduces grid-orientation dependency), which are selected based on the cells closest to the 'flow' direction. In Snow_Blow the wind direction is substituted for flow direction so snow is redistributed according to the modified wind direction field (derived from the constant background wind input in Eqn (1)). The algorithm stores the number of contributing cells to each given cell, the proportion of snow in each cell which contributes to the given cell, and the distance of contributing cells (number of cells away), up to the maximum distance (mxd). This snow deposition weighting scheme is then applied to calculate the amount of snow that is blown into each cell (Q d).
Initially, a constant and uniform snow depth of 1 is assumed. For each time step the snow depth index (h) at the end of the time step (time = t + Δt), for each cell is then calculated using the snow erosion field (Q e) and the snow deposition field (Q d) calculated above. The difference equation is
(11)$$h(t + \Delta t) = h(t)-Q_{\rm e}(t) + Q_{\rm d}(t),$$
where t is the time at the start of the step and Δt is the length of the time step. Everything within the interval of t to t + Δt is assumed to be a single step (Purves and others, 1999), which means that erosion/deposition is conceptualised as instantaneous. Snow depth evolution over time may be calculated using a number of iterations.
Once the required number of iterations are completed, the snow depth index is scaled to be a difference field: areas of net loss of snow will have values of −1 ≤ h < 0, while areas of net snow gain will have positive values i.e. h > 0. Positive values can be >1 because more than one cell can contribute to the mass gain, as a result of mass loss from other cells. The results from applying different numbers of iterations of the model can be seen in Figures 2e–h. The number of cells with a positive snow depth index decreases with the number of iterations until the Snow_Blow model approaches a steady state; Figure 3d gives an example of this for the southern Heritage Range test area, shown as an inset in Figure 2. The actual amount of snow gained in the cells will continue to increase as long as there is a supply of upwind snow.
Total relative snow accumulation is dependent on the size of the cirque/catchment area. Larger cirques or catchment areas have the potential to accumulate greater amounts of snow if measured in absolute terms. In the Snow_Blow model, we follow the approach of Purves and others (1999), to produce an output of snow depth per unit area over a catchment. This provides a more physically meaningful representation of snow accumulation. We call this the snowdrift index, which is calculated as the mean snow depth index for each gridcell across each defined catchment. We pick four, fairly contrived, sites (shown in Fig. 1b) to demonstrate the process of 'cookie cutting' a catchment to calculate a catchment-based snowdrift index. We choose the sites on the basis that they are sheltered from either a 122.5° or 45° wind direction, to demonstrate how the relative snowdrift index changes for each site with a different wind direction.
The user can choose whether snow is blown into the domain from outside of the domain or not. If this option is chosen, 1 unit of snow is added to every boundary gridcell. We enable this option for the purpose of our experiments. It is important to note that this introduces new snow mass into the domain at the end of every iteration in all boundary cells.
In Snow_Blow, snow accumulation does not vary with altitude (as a result of changes in temperature) and an equal distribution of snow over the whole topography is assumed. While this is a reasonable assumption for a localised Antarctic environment, it may not be appropriate for a more temperate palaeoenvironmental setting. However, once the Snow_Blow model is run, areas below the critical threshold for solid precipitation (i.e. below the snowline) can be excluded from the analysis, if necessary.
To compare Snow_Blow results with observed snow extent in the southernmost Ellsworth Mountains, the January 2009 Landsat image was chosen as this coincides with the meteorological data obtained for the study region (Supplementary Fig. 2). A snow/no snow mask was created on the 30 m grid for quantitative assessment. This was carried out to determine the success of each parameter set used, to provide a recommendation for the parameter choice based on the Ellsworth Mountains case study. A comparison of the observed snow/no snow areas in the January 2009 imagery (see Section 3.1) with the positive/negative values in the snow depth index, was carried out using eight iterations (see Supplementary Section 5 for more details) (Table 2). It should be noted that there is uncertainty in this process (e.g. in the georectification of the imagery, snow area classification, the various model parameters used). However, the results provide a useful measure with which to assess the suitability of each parameter set, and to identify if there is equifinality in the parameter sets. Section 5.4 shows that, in certain circumstances, the choice of parameters is not crucial, despite the uncertainty in this process.
This section presents results from selected Snow_Blow experiments centred on the Patriot and Independence Hills in the southern Heritage Range, Antarctica, with differing model setups and parameters. We vary the depositional distance, wind speed, threshold wind speed, maximum slope angle and curvature index to determine model sensitivity to these. Table 2 gives the parameter sets used in these experiments.
Each experiment outlined in Table 2 was run for the Heritage Range field site, to obtain a 'best fit' with areas of snow distribution from the Landsat imagery. A maximum deposition distance of 690 m was chosen (Expt. 1), and this was run for eight iterations (Fig. 4b). This is based on the match of the negative snow depth index predicted by Snow_Blow, and the BIA extent, mapped from the Landsat 9 January 2009 imagery (see Figs 2f, g). In this experimental output, the number of cells with a positive snow depth index continues to decrease after these eight iterations (Fig. 3d). Values <0 in Figure 4b indicate a net loss of snow, and not necessarily an absence of snow.
In the absence of snow depth measurements, a qualitative assessment of the pattern of the snow depth index against snow distribution in the January 2009 Landsat image was carried out. The initial qualitative indication is that, in general, the area of net snow gain is small relative to the snow extent of the Landsat image (Figs 4a, b show the detail of an example site). There are two potential reasons for this discrepancy, which lead to snow starvation. Firstly, the snow is not being distributed over a long enough distance downwind of an eroded cell. A longer maximum depositional distance would increase snow input to more exposed cells (see shelter index in Fig. 2b), offsetting the erosion in these cells. Due to the relatively high wind speeds in the Heritage Range, and the length of the tails seen in the imagery, there is some justification for this increased depositional distance. Secondly, the erosion may be over predicted in the model for the more exposed cells. Decreasing the amount of erosion occurring at the more exposed cells would enable the snow that is being blown into the cell to offset the erosion. Lowering the erosion in these more exposed cells can be implemented by (1) using a lower wind speed (F) relative to the threshold wind speed (see Fig. 3a), or (2) by lowering the maximum slope (S max) at which the slope index saturates at 1. We do not vary the threshold wind speed as it is the ratio between the wind speed and threshold wind speed that is important (these values are relative in the model), rather than the absolute values. It should be noted here that the maximum erosion for each cell needs to be maintained at 1 unit of snow, but that the overall erosion could be reduced.
To test the impact of increasing the maximum deposition distance, the value in the Snow_Blow model was approximately doubled from 690 to 1381 m (Expt. 2, Fig. 4c). This figure shows that an increase in the deposition distance does serve to increase the area of net snow gain in the sheltered areas, but higher deposition distances produce unrealistically long tails which are not seen in the Landsat imagery (Fig. 4a). The erosion distance is also greatly increased and a best fit to BIAs for this particular experiment is four iterations (doubling the depositional distance effectively halves the number of iterations required). The depositional area does not vary greatly between four and eight iterations; however the net snow accumulation is greater over eight iterations.
The impact of decreasing the snow erosion that occurs in the more exposed cells was tested by halving the wind speed from 15 to 7.5 m s−1 (Fig. 3a). There is a clear effect of a reduced wind speed increasing the area of net snow gain (Expt. 3, Fig. 4d). The model replicates snow accumulation in the upper parts of lee side slopes (the cirques) relatively well; however, there is less agreement in the lower areas with this lower wind speed value.
A very similar result to the above is achieved when S max is lowered (Expt. 4) by applying the default wind speed of 15 m s−1 and an S max value of 20° (for an example run) (Fig. 4e). This results in a greater agreement of snow covered areas in the lower catchment in Expt. 4, compared with Expt. 3. Despite this improvement, there remain large areas of snow accumulation in the lower parts of the valley that are not visible on the January 2009 Landsat imagery.
The curvature index was also tested in the Snow_Blow model using an F value of 15 m s−1 and an S max value of 20° (Fig. 4f). In this model run the areas of snow accumulation in the upper parts of the valley remain a good fit compared with the Landsat imagery, and the areas of snow accumulation in the lower parts (where there is limited mapped snow accumulation) are reduced, suggesting that this model run (Expt. 5) reproduces the best fit for snow accumulation.
BIAs and snow-free areas in Horseshoe Valley indicate snow free areas created by erosion and snow starvation. The extent of the area of net snow loss depends on the number of iterations chosen, but as discussed above, eight iterations provides a snow depth index which allows a reasonable comparison with the snow free areas (Figs 4g, h). There is good general agreement in the pattern of the BIAs and areas of net snow loss, indicating that these areas are the result of a relatively simple process of snow starvation. Where the topography is more complex, e.g. in the lee of the mountains, the model produces more areas of discrepancy. While these findings imply that general trends can be simulated, with Snow_Blow, the simplicity of the shelter index and wind speed modification may not be able to fully reproduce physical processes. For example, the model does not increase the wind speed, in an area of funnelling or on an upslope which may have important consequences in specific regions, such as the areas marked '1' in the example area highlighted in Fig. 4a.
Some of the observed ice-free regions in Landsat imagery, which have a positive snow depth index in the model (marked '2' in Fig. 4a), are in areas where the topography is convex (see Section 4.3). The agreement in these areas is improved by incorporating the curvature index in the shelter index. A moderately high value of C max (0.5) is used in Expt. 5 (Fig. 4f). This creates a decreased area of positive snow depth index in the model output. While this mainly affects areas without observed snow, it can affect some cells with observed snow.
The final snow depth field was compared with the observed snowfield on a pixel by pixel basis. In the model results (for the purposes of comparison) a snow depth index of <0 was considered to be 'no snow' and >0 as 'snow covered'. Table 3 shows the percentage of snow predicted correctly, the percentage of 'no snow' predicted correctly and the overall accuracy (percentage total cells predicted correctly). The results in Table 3 show that there is a degree of equifinality in the parameter sets with a similar level of success across different parameter sets. Lower values for wind speed, F, lead to more 'snow' being predicted correctly, but also more snow present in the domain overall, so the 'no snow' areas suffer a lower level of success. Conversely, lower values of S max lead to more snow being predicted correctly, so can offset the effect of changing the wind speed. Incorporating the curvature index generally improves the prediction of no snow areas, but at a cost to the success of the prediction of snow covered areas.
Table 3. Quantitative assessment of different parameter values for F, S max and C max
Numbers in parentheses represent experiment numbers in Table 2 and Supplementary Table 1. Blue shading represents cells that predict snow/no snow most successfully, while red shading represents those predicting snow/no snow least successfully.
We derive a snowdrift index for individual catchments to determine the importance of snowdrift in relation to catchment size. These catchments were selected to reflect different orientations and presence/absence of snow cover in the Landsat imagery. The choice of values of F, S max and C max will have an impact on the absolute value of the snowdrift index for each site, and as there is no conclusive evidence to support particular values, in this section we aim to demonstrate that the choice of parameters is not critical when considering the relative snowdrift index between different sites. The combination of parameters used in Section 5.3 is used to demonstrate how the relative snowdrift index is not heavily dependent on the choice of parameters.
Sites 2 and 4 are sheltered from the 122.5° wind direction so they have a positive snowdrift index when the wind is from this direction, whereas site 1 is not sheltered from a 122.5° wind direction, so it has a negative snowdrift index (Figs 5a, b). Site 4 has a higher snowdrift index than site 2, suggesting that more snow is gained per unit area at site 4 than site 2, due to the snowdrift processes. There is no overlap in the snowdrift index with the choice of the parameters, as the degree of shelter between the sites is significantly different. However, from a 45° angle, the level of shelter is similar at sites 2 and 4 (though there is no overlap) (Figs 5c, d). The distinction between sites 1 and 3, and, 2 and 4 is still clear from this wind direction. Sites 1 and 3 are the most affected by snowdrift processes with winds from a 45° angle.
Fig. 5. Snowdrift index for sites 1–4 shown in Figure 1b for a 122.5° and 45° wind direction for various parameter sets (F = wind direction, S max is the maximum value the slope is set to for each cell, C max is the curvature index).
Once a parameter set has been chosen, the snowdrift index can be assessed for each site for various wind directions, to determine the wind direction which provides the maximum shelter for a given site and, hence, the highest snow accumulation per unit area (Fig. 6). In the case of sites 1 and 3, a ~45° wind direction would provide the most snow accumulation to these sites, though site 1 has a slightly higher value per unit area compared with site 3. In comparison, sites 2 and 4 would receive the most snow accumulation from ~135° winds, however this would be much more important at site 4 than at site 2. This is most likely due to the steeper headwall at site 4 which is able to trap more snow.
Most of the sites also have a positive snowdrift index when the wind is coming from the opposite of the optimum direction (e.g. site 4, which has positive (although low) snowdrift index values when the wind is coming from ~330°). This output is not the result of sheltering effects, but rather, the deflection of wind, as the prevailing wind direction is re-routed by topography. Although this local deflection redistributes snow into our example sites, it also imposes an equivalent loss of snow in neighbouring areas. This process emphasises the two possible effects of snowdrift; a sheltering process and a wind driven redistribution effect.
The qualitative agreement between areas of net snow gain and loss in Snow_Blow, with present day snow accumulation and snow erosion areas in Horseshoe Valley is encouraging for such a simple model. The good agreement implies that areas of snow erosion and accumulation are governed by the sheltering effect of topography in relation to the local wind flow, as opposed to regional scale wind patterns, where wind direction is constant (dominated by katabatic wind flows or funnelling). This finding is in agreement with other studies, such as that by Zwinger and others (2015). The agreement between the observed snow accumulation/erosion pattern also supports the role of snow starvation in the formation/maintenance of the BIAs in the study area.
Although the strong katabatic winds in Antarctica make our study area an extreme example of snowdrift, the Ellsworth Mountains are similar to alpine environments. Ridges in the mountain range act as a snow fence to the prevailing wind so snow is deposited within a few hundred metres of the crest, where wind speeds fall dramatically in the lee of the mountain range. With appropriate parameters, the extent of modelled snow accumulation in the lee provides excellent agreement with observed snow accumulation areas in Landsat 8 imagery. These results are therefore comparable with other polar and alpine regions, such as Greenland, where Hasholt and others (2003) found significant snow transport and deposition on the lee side of ridges, and in Svalbard, where Humlum (2002) suggested that glacier accumulation areas coincide with areas of low wind speeds, and that glacier-free regions are usually found in exposed areas where wind speeds are high.
Snow_Blow parameterisations of snow erosion and deposition processes introduce some arbitrary choices of deposition distance and erosion parameters. However, by demonstrating that the relative snowdrift index is insensitive to these choices, we show that the impacts of these choices are minimal when the Snow_Blow model is used in a relative sense. Figure 5 demonstrates that the snow erosion formulation does have an effect on the absolute snowdrift index for individual sites. A lower ratio between wind speed and threshold wind speed leads to less erosion overall (Fig. 3a), so more snow is retained in the catchment, reflected in a higher snowdrift index value. However, this can be offset by changing the value of S max in the model.
To compare snowdrift index values across geographical areas, it would be useful to define parameters that can be used as a default set. Although independent studies are encouraged to explore the range of the sensitivity of the model to aspects such as wind speed and threshold wind speed, which can be modified to investigate the impact of varying snow conditions (such as dry and wet snow) and wind speeds. For the Heritage Range we used a representative wind speed of 15 m s−1 and a threshold wind speed of 5 m s−1 (though other wind speeds give a similar level of success). We applied an S max value of 20°, in combination with a C max value of 0.5. This provides a level of quantitative success, which is consistent across different wind speeds (Table 2). Qualitatively, an S max value of 20° improves the prediction of snow in the lower areas of the test catchment. As a result, we recommend that an S max value of 20° be adopted in future runs as a default S max value. Wind speed and threshold wind speed values can then be modified to fit the assumed wind and snow conditions for a given geographic area, e.g. a higher threshold velocity could be applied for wet snow conditions.
This paper presents Snow_Blow, an improved and updated version of the Purves and others (1999) snow redistribution model, with the addition of a flux routing algorithm, DEM resolution independence and the addition of a slope curvature component. This model was applied to a present-day environment in the Ellsworth Mountains, Antarctica, to evaluate the validity of the model for future applications, in palaeoenvironment settings. Snow_Blow reproduces patterns of snow erosion and snow deposition in Horseshoe Valley, where surface features such as snowdrift tails and wind-scoured BIAs validate model outputs. We test a variety of model parameters to define a default set for future model runs. The results show that the simplistic Snow_Blow model is suitable for palaeoenvironmental reconstructions, where meteorological observations are sparse to non-existent. It is predominantly suitable for areas with one prevailing wind direction and where sublimation is negligible, although multiple wind directions could be explored. It is also a potential tool to assess variations in snow accumulation in mountain topography throughout Antarctica, with implications for the interpretation of layers identified by radio-echo sounding (Siegert and others, 2005).
The Snow_Blow model code (written in Python for easy application in ESRI ArcGIS) is freely available online at GitHub and at https://doi.org/10.5281/zenodo.3336070. While it can and should be used for a variety of purposes it is important to interrogate outputs in the context of the uncertainty of parameter values. Uncertainty is minimised when the model is used in a relative sense, for example, to compare different glacier systems. If the model is to be used in an absolute sense – for example, to apply results spatially, to account for additional precipitation onto reconstructed glacier surfaces within a mass-balance calculation – it is important to keep in mind the impact of the uncertainty in the choice of parameters on the model.
Snow_Blow could be used to calculate a snowdrift index for individual catchments (using various wind directions), to investigate how important a particular wind direction was in supplying additional mass to glaciers in palaeo settings. As additional mass will modify glacier mass balance, this type of simulation now appears critical for more robust palaeoclimatic reconstructions. Snow_Blow outputs can therefore help to explain variations in ELAs in neighbouring locations, and provide a guide as to which particular glaciers would have been the most likely representative of regional climatic conditions.
The supplementary material for this article can be found at https://doi.org/10.1017/jog.2019.70
We acknowledge funding from Kingston University to EA for the initial development of the model. Project work in the southern Heritage Range was funded by the UK Natural Environment Research Council (NERC) standard grants NE/I027576/1, NE/I025840/1 and NE/I025263/1. We thank the two anonymous reviewers for their constructive comments.
SM conceived the idea for the model development. SM and AL wrote the manuscript with contributions from all the co-authors. KW, DS and JW provided expert input on the Ellsworth Mountains context as well as commenting on the manuscript. CB, MS and JH provided input into the background context, model methodology/experiment design as well as commenting on the manuscript. KW undertook initial model testing in the Ellsworth Mountains and analysed the wind data. AL ran the model for the study location, designed the model set-ups and parameters, and analysed the data, with advice from SM. AL produced the figures, with editing by SM. EA undertook the initial model development, supervised by MS and SM. SM and MS developed the model further and JH added the exponential distribution for snow transport. AL further developed the model and added the curvature index and snow redistributing flux algorithm.
Balk, B and Elder, K (2000) Combining binary decision tree and geostatistical methods to estimate snow distribution in a mountain watershed. Water Resources Research 36, 13–26.
Bell, PD and Quine, CP (1996) Calculating an index of wind damage for British forests using GIS. In Proceedings of the GIS Research UK 1996 Conference, Canterbury, UK, 10–12 April, Association of Geographic Information, pp. 199–202.
Benson, CS and Sturm, M (1993) Structure and wind transport of seasonal snow on the Arctic slope of Alaska. Annals of Glaciology 18, 261–267.
Bernhardt, M and Schulz, K (2010) Snowslide: a simple routine for calculating gravitational snow transport. Geophysical Research Letters 37, L11502. doi: 10.1029/2010GL043086
Bernhardt, M, Zängl, G, Liston, GE, Strasser, U and Mauser, W (2009) Using wind fields from a high-resolution atmospheric model for simulating snow dynamics in mountainous terrain. Hydrological Processes 23, 1064–1075.
Bintanja, R (1998) The contribution of snowdrift sublimation to the surface mass balance of Antarctica. Annals of Glaciology 27, 251–259.
Boston, CM, Lukas, S and Carr, SJ (2015) A Younger Dryas plateau icefield in the Monadhliath, Scotland, and implications for regional palaeoclimate. Quaternary Science Reviews 108, 139–162.
Bowling, LC, Pomeroy, JW and Lettenmaier, DP (2004) Parameterization of blowing-snow sublimation in a macroscale hydrology model. Journal of Hydrometeorology 5, 745–762.
Braaten, DA and Ratzlaff, KL (1998) An automated tracer dispersal system for snow accumulation and saltation transport investigations. Review of Scientific Instruments 69, 572–577.
Budd, WF, Dingle, RJ and Radok, U (1966) The Byrd Snow Drift Project: outline and basic results. In Rubin, MJ (ed.), Studies in Antarctic Meteorology, Washington, DC: American Geophysical Union, pp. 71–134.
Burton-Johnson, A, Black, M, Fretwell, PT and Kaluza-Gilbert, J (2016) An automated methodology for differentiating rock from snow, clouds and sea in Antarctica from Landsat 8 imagery: a new rock outcrop map and area estimation for the entire Antarctic continent. The Cryosphere 10, 1665–1677.
Carr, SJ and Coleman, CG (2007) An improved technique for the reconstruction of former glacier mass-balance and dynamics. Geomorphology 92, 76–90.
Carr, SJ, Lukas, S and Mills, SC (2010) Glacier reconstruction and mass-balance modelling as a geomorphic and palaeoclimatic tool. Earth Surface Processes and Landforms 35, 1103–1115.
Chandler, BP and Lukas, S (2017) Reconstruction of Loch Lomond Stadial (Younger Dryas) glaciers on Ben More Coigach, north-west Scotland, and implications for reconstructing palaeoclimate using small ice masses. Journal of Quaternary Science 32, 475–492.
Coleman, CG, Carr, SJ and Parker, AG (2009) Modelling topoclimatic controls on palaeoglaciers: implications for inferring palaeoclimate from geomorphic evidence. Quaternary Science Reviews 28, 249–259.
Déry, SJ and Yau, MK (2001) Simulation of blowing snow in the Canadian Arctic using a double-moment model. Boundary Layer Meteorology 99, 297–316.
Gruber, S (2007) A mass-conserving fast algorithm to parameterize gravitational transport and deposition using digital elevation models. Water Resources Research 43, W06412. doi: 10.1029/2006WR004868.
Hasholt, B, Liston, GE and Knudsen, NT (2003) Snow-distribution modelling in the Ammassalik region, south east Greenland. Nordic Hydrology 34, 1–16.
He, S and Ohara, N (2017) A new formula for estimating the threshold wind speed for snow movement. Journal of Advances in Modeling Earth Systems 9, 2514–2525.
Hoinkes, H (1960) Studies of solar radiation and net radiation in the Antarctic. Theoretical and Applied Climatology 10(2), 175–181. doi: 10.1007/BF02246563
Howat, I, Morin, P, Porter, C and Noh, M-J (2018) "The Reference Elevation Model of Antarctica", https://doi.org/10.7910/DVN/SAIK8B, Harvard Dataverse, V1.
Hughes, PD (2002) Loch Lomond Stadial glaciers in the Aran and Arenig Mountains, North Wales, Great Britain. Geological Journal 37, 9–15.
Humlum, O (2002) Modelling late 20th century precipitation in Nordenskiöld Land, central Spitsbergen, Svalbard, by geomorphic means. Norwegian Journal of Geography 56, 96–103.
Ishikawa, N, Kobayashi, S, Ohtake, T and Kawaguchi, S (1982) Some radiation properties at Mizuhu Station, East Antarctica in 1980. Memoirs of National Institute of Polar Research 24, 19–31.
Lehning, M and 5 others (2006) ALPINE3D: a detailed model of mountain surface processes and its application to snow hydrology. Hydrological Processes 20, 2111–2128.
Lehning, M, Doorschot, J and Bartelt, P (2000) A snowdrift index based on SNOWPACK model calculations. Annals of Glaciology 31, 382–386.
Lewis, CA and Illgner, PM (2001) Late Quaternary Glaciation in Southern Africa: moraine ridges and glacial deposits at Mount Enterprise in the Drakensberg of the Eastern Cape Province, South Africa. Journal of Quaternary Science 16, 365–374.
Li, L and Pomeroy, JW (1997) Estimates of threshold wind speeds for snow transport using meteorological data. Journal of Applied Meteorology 36, 205–213.
Liston, GE and 5 others (2000) Snow and blue-ice distribution patterns on the coastal Antarctic ice sheet. Antarctic Science 12: 69–79.
Liston, GE and 5 others (2007) Simulating complex snow distributions in windy environments using SnowTran-3D. Journal of Glaciology 53(181), 241–256.
Liston, GE and Sturm, M (1998) A snow-transport model for complex terrain. Journal of Glaciology 44(148), 498–516.
Liston, GE and Sturm, M (2002) Winter precipitation patterns in Arctic Alaska determined from a blowing-snow model and snow-depth observations. Journal of Hydrometeorology 3, 646–659.
Lukas, S and Bradwell, T (2010) Reconstruction of a Lateglacial (Younger Dryas) mountain ice field in Sutherland, northwestern Scotland, and its palaeoclimatic implications. Journal of Quaternary Science 25, 567–580.
Mills, SC, Grab, SW, Rea, BR, Carr, SJ and Farrow, A (2012) Shifting westerlies and precipitation patterns during the Late Pleistocene in Southern Africa determined using glacier reconstruction and mass balance modelling. Quaternary Science Reviews 55, 145–159.
Mitchell, WA (1996) Significance of snowblow in the generation of Loch Lomond Stadial (Younger Dryas) glaciers in the western Pennines, northern England. Journal of Quaternary Science 11, 233–248.
Mott, R and 7 others (2008) Simulation of seasonal snow-cover distribution for glacierized sites on Sonnblick, Austria, with Alpine 3D model. Annals of Glaciology 49(164), 155–160.
Nylen, TH, Fountain, AG and Doran, PT (2004) Climatology of katabatic winds in the McMurdo dry valleys, southern Victoria Land, Antarctica. Journal of Geophysical Research – Atmospheres 109: D03114, doi: 10.1029/2003JD003937.
Pomeroy, JW and 6 others (1998) An evaluation of snow accumulation and ablation processes for land surface modelling. Hydrological Processes 12, 2339–2367.
Pomeroy, JW and Gray, DM (1990) Saltation of snow. Water Resources Research 26, 1583–1594.
Pomeroy, JW, Gray, DM and Landine, PG (1993) The prairie blowing snow model – characteristics, validation, operation. Journal of Hydrology 144, 165–192.
Pomeroy, JW, Marsh, P and Gray, DM (1997) Application of a distributed blowing snow model to the Arctic. Hydrological Processes 11, 1451–1461.
Purves, RS, Barton, JS, Mackaness, WA and Sugden, DE (1998) The development of a rule-based spatial model of wind transport and deposition of snow. Annals of Glaciology 26, 197–202.
Purves, RS, Mackaness, WA and Sugden, DE (1999) An approach to modelling the impact of snow drift on glaciation in the Cairngorm Mountains, Scotland. Journal of Quaternary Science 14, 313–321.
Ryan, BC (1977) A mathematical model for diagnosis and prediction of surface winds in mountainous terrain. Journal of Applied Meteorology 16, 571–584.
Sauter, T and 5 others (2013) Snowdrift modelling for the Vestfonna ice cap, north-eastern Svalbard. The Cryosphere 7, 1287–1301.
Siegert, M, Pokar, M, Dowdeswell, JA and Benham, T (2005) Radio-echo layering in West Antarctica: a spreadsheet dataset. Earth Surface Processes and Landforms 30, 1583–1591.
Sissons, JB and Sutherland, DG (1976) Climatic inferences from former glaciers in the south-east Grampian Highlands. Journal of Glaciology 17(76), 325–346.
Sturm, M, Liston, GE, Benson, CS and Holmgren, J (2001) Characteristics and growth of a snowdrift in Arctic Alaska, USA. Arctic Antarctic and Alpine Research 33, 319–329.
Takeuchi, M (1980) Vertical profile and horizontal increase of drift-snow transport. Journal of Glaciology 26(94), 481–492.
Tarboton, DG (1997) A new method for the determination of flow directions and upslope areas in grid digital elevation models. Water Resources Research 33, 309–319.
Winter, K and 6 others (2015) Airborne radar evidence for tributary flow switching in Institute Ice Stream, West Antarctica: implications for ice sheet configuration and dynamics. Journal of Geophysical Research: Earth surface 120, 1611–1625.
Zwinger, T, Malm, T, Schäfer, M, Stenberg, R and Moore, JC (2015) Numerical simulations and observations of the role of katabatic winds in the creation and maintenance of Scharffenberbotnen blue ice area, Antarctica. The Cryosphere 9, 1415–1426.
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