It’s occurred to me that I haven’t updated this thing in almost a year, and a lot has happened in that time. My last post left us on the North Dakota prairie during the peak of the spring wildflower bloom. Since then, I picked up the kids, camped with geocaching friends in Medicine Rocks State Park in the southeastern corner of Montana, continued with the kids to North Carolina, spent almost a week in Michigan’s Upper Peninsula with my family, and then moved back to Idaho.
Yes, you read that last part correctly. I left my job at Williston State College to take a faculty position at North Idaho College, and it’s everything I have dreamed of. I am teaching classes that are interesting to me. There is a much more vibrant outdoor community here, more board gamers, a larger geocaching community, and I am close enough to the kids to hang out with them on weekends. Just about every aspect of my life has improved, and I am thankful for this opportunity.
Of course, my rate of geocaching and hiking has slowed down for now. But as spring approaches and the semester comes to an end, the adventures will pick up. In the meantime, enjoy this adventure on Mineral Ridge with the kids in December. This has been a wacky winter. There has been very little snowfall, and with the exception of one week in January that led to sprinkler pipes bursting in the apartment next to mine, temperatures have been incredibly mild. So on one warm day over the Holiday break, I took the kids on a hike.
With the school year over and nice weather upon us, I’ve had some free time to get out and explore the landscape beyond Williston. I’ve been out on the prairie twice to discover the array of early wildflowers in the grasslands. This is the time of year when I feel like I could actually enjoy this place. Unfortunately, it doesn’t last very long.
It’s said that there are only two seasons on the northern plains – a very long winter, and a short summer. Spring and Fall exist, but only for a week. All year round, the wind can blow strong, though there are calm days too. Winter here is tough. We get enough snow to block access to many recreation trails, but not enough snow to take out skis and snowshoes. To be fair, it’s a bit snowier east of here. Summers become very hot and dry. With no forests to take shade in, hiking in the summer heat can be miserable. And then there are the transition seasons. Fall might be more tolerable for hiking. It’s still dry, and the temperatures are more tolerable, but it can be quite windy. Strong winds are just as bad as a strong sun for turning a nice adventure into unpleasantness. Spring is wet. Wet from the snowmelt, and wet from rain. Spring is typically mud season anywhere you go, but here in the Dakota Badlands, the mud is an especially sticky and slick clay that is not only a nuisance to hike through but can be downright dangerous on those badlands slopes. Spring also comes with ticks, though that’s a hazard I can deal with and is not unique to this area.
The prairie greens up in early to mid-May, right around when my semester ends, and with the green comes the first wave of wildflowers. One of the earlier wildflowers is the Pasqueflower, or prairie crocus (Pulsatilla nuttalliana or Pulsatilla patens). This large purple flower dots the brown grasslands as early as March and is certainly a sign that winter is on its way out.
Last weekend, I made a trip down to the national grassland to find a geocache atop a butte. But as part of that hike, I found some flowers in bloom. One of those finds includes Fritillaria atropurpurea, a somewhat uncommon find for this area that blends in so well I almost lost it after getting the camera out to photograph it.
I didn’t take many photos on this adventure, instead opting for a video:
Enamored with my finds on that trip, I decided I had to get back on the prairie before the flowers disappeared to photograph and identify as many species as I could find. I opted for the Summit Trail which stays mostly on top in the prairie while still offering views of the badlands canyons of the Little Missouri River. I was not disappointed. Below is a gallery of my finds, plus a few scenic shots of the badlands. All of the images are also on my Flickr site with species tags. There are twelve distinct species photographed here, though I did see some repeats from last week, and I’m sure there are others I saw and passed up, and even more that I failed to notice.
My trip to the Redwoods had a profound effect on me. I can’t really explain what it was or why. I’ve been to many amazing and beautiful places never come back as humbled and rejuvenated as I had on this last trip. But everything about it just put me at ease and at awe. It was a combination of spending time with the kids while experiencing a mature old-growth forest among some of the oldest and tallest trees on the planet. I came back to Williston ready to take on the world and maybe inspired to leave in search of better country.
And then, not even a week after my return:
The largest geomagnetic storm I have ever witnessed occurred on the evening of March 23. Auroras are usually visible in the northern sky, but this one washed overhead and into the southern sky. I apparently missed the largest peak, but as soon as I learned this was happening, I grabbed my camera and drove west into Montana where the oil rigs are fewer and the sky is darker. I turned up a dirt road where I was hoping to perch myself on a high ridge, but I saw a faint glow rising to the west, a strange sight for an aurora. I wasn’t sure if it was light pollution or fog, so I stopped to grab a picture. I noticed some light beams shining up behind a small butte, so I made that the subject of my image. I was expecting it to light from an oil rig behind it. Instead…
It was the unmistakable green glow of the northern lights. Instead of shining ahead to the north, it was coming out of the west, directly overhead, and continuing to the east.
The fact that it was overhead was novelty enough for me. But it was bright. I ran back and forth taking photos in both directions. The ribbon got wider and split apart, becoming more defined.
Eventually, I got cold and had to get in the car to warm up. I kept watching out the window, but it seemed like the aurora was waning. So I got out to collect my camera and maybe pack it in for the night. But as my eyes adjusted to the darkness, I noticed it wasn’t waning, it was getting brighter… and it was changing color. I thought I saw a red patch with the naked eye. I set up the camera again and confirmed it.
At this point, the ribbon began to take a definitive shape with some bright columns and curves and red spots. And then it started pulsing. And the pulsing continued for the remainder of my time out there. The aurora spread, mostly north, but a little south until it was covering at least 60% of the sky. I’ve seen big and bright auroras before, but never anything like this. It was literally dancing in the sky before my very eyes. I hate that the camera can’t convey the animation that was happening. At one point, the lights took on a web-like structure, still pulsing. The remaining images show the progression as the storm intensified and the red light took over.
This was without a doubt one of the most profound experiences I have ever had. It brought me to tears being out there to witness this spectacle of nature. I came home rejuvenated. The next day, I went to work in a trance, and it wasn’t just due to the lack of sleep. It was maybe a once-in-a-lifetime opportunity and I was part of it.
When I think about the way I travel and the way others travel, there are two extremes at the ends of a spectrum: on one side, we fit in everything we can see during our limited time at a destination; on the other side, we stick to a small area and get to know it really well. Where do you typically fit on this spectrum?
When we book trips to major destinations, there is extensive planning involved as well as the expense of the trip. On top of that, there are seemingly infinite places in the world that we would like to visit someday. So, trips to major destinations might end up being or seeming like once-in-a-lifetime experiences. Thus, we have the temptation to take advantage of our limited time at that location and see all of the sights. The advantage is that we don’t miss out on anything. The disadvantage is that we only get to dabble our toes in the proverbial waters. It can sometimes feel superficial.
On the other end of the spectrum, we could stay in one place and explore it deeply. Yes, you don’t get to hit up all of the touristy highlights, but what you get instead is a deep connection to that one local place. Maybe it’s getting to know the food and drink, maybe it’s really diving into the history, or maybe it’s getting to know the plants and animals and geology. I’m not making any judgments regarding any location along this spectrum. Sometimes the purpose of our travel dictates where we put that trip. And sometimes outside circumstances decide that for us.
Spring Break 2023
Back in October, my daughter told me she wanted to see the redwoods. She must have been learning about them in school and was inspired to see them in real life. I had never been and the northern California coast has been on my list of places to visit for some time. I couldn’t plan a trip over the holiday break. But I could plan one for spring break. So I looked into it. Mid-march isn’t the peak of tourist season. It can be quite rainy and cold, but not so cold as to make it unbearable. So I said, “Let’s do it.” I started looking at things to see and places to stay, and how long it would take us to get there and back. I planned a trip on which we would visit various locations within Redwood National and State Parks, including the Tall Trees in the south, some groves in the north, and some coastal play because you can’t go to the coast and not play in the tide pools or stroll along a Pacific beach.
This year has been an unusually wet and snowy winter for the west coast of the United States. It seems like Northern California has been battered by heavy storms on a weekly basis. A large storm came through at the beginning of January and closed down much of the park. By the end of the month, the roads and trails had been reopened, only for another storm to shut them down again. A week later, another storm. And then another. I was hopeful that maybe the Tall Trees grove would be open by spring break, but no such luck. Even on our drive down, the coast got hit again and I was concerned that we might not even get there, let alone have anything to do.
I ended up booking an AirB&B in Crescent City and was happy to find out that Jedediah Smith Redwoods State Park, the northernmost part of the National-State parks complex, was completely open. So that’s what we did. We spent three days in Crescent City and got to know the local redwood groves quite well, and to be honest, it was nice that way. There was less pressure to drive up and down the coast to see it all and instead enjoy what was right there. Crescent City has a beach as well as a rocky coast with tide pools, and the trees in the park are nothing to scoff at.
It took us two days to drive from Moscow down to Crescent City. We left Saturday morning, stopping for some food supplies in Kennewick, and then stopping at Multnomah Falls outside of Portland. I had never been to the Columbia Gorge or Portland before, so I had to take advantage. We also couldn’t stay and hike much. This might be a trip of its own in the future. But it was good to get out and stretch our legs, and the kids really enjoyed seeing one of Oregon’s iconic scenes. We stopped in Portland for dinner and then found a hotel for the night. We’ll have to do a proper Portland visit another time, but already I’m hooked.
From Portland, we headed south on I-5, stopping in Eugene to pick up lunch and then in Grants Pass to stretch our legs. By then the rain had let up and we had a nice time exploring the town completing a Geocaching Adventure Lab.
It rained pretty hard on our first day. The kids didn’t really want to get out and hike, so we went to the visitors center and then drove Howland Hills Road, the main scenic drive through Jedediah Smith Redwoods State Park. The drive alone is impressive. But the next day, the rain let up to a mere drizzle and we got out to hike some trails. We started on the trail to the Grove of the Titans. These might not be the biggest of the redwoods, but they are certainly impressive.
Walking between giantsA tunnel between fallen treesImpressively BigGazing upon GiantsThe Redwood Forest
After hiking among the Titans, we drove to the Stout Grove, had a quick lunch in the car, and then went out to play in the forest. Adam had a blast exploring behind the trees.
After two hikes, we were fairly wet and cold and done for the day.
The sun came out for our third day, and it was glorious. We spent the morning on the coast playing in the tide pools. Adam stayed on the beach playing in the rocks and sand, but Clara and I explored the diversity of life in the rocky intertidal zone. At first, all we found were some periwinkle snails and hermit crabs. But then we found our first sea star, an orange Ochre Star. After that, they were everywhere, glued to the rocks. Later we spotted a Leather Star. I found a few more in another pool closer to the low tide zone. We found some Green Anemones and some crabs hanging out under the rocks. In a few pools, we saw some Tide Pool Sculpin swimming about.
After lunch, we headed back into the park for one last hike among the redwoods. We hiked the Leiffer Loop trail which brought us to several groves of old-growth forest. The hike ended up being a bit longer than we expected. It was fun, but the kids were exhausted at the end of it. This hike will be showcased in an upcoming video on my YouTube channel, so stay tuned.
We only had time for three days on the Redwood Coast. On Thursday, we started our drive north to get the kids back home and to get me back home in time for the next week of classes. We took a different route, stopping in Bend. This allowed us to gaze upon the many Cascadian volcanoes along our drive. The kids weren’t as impressed as I’d hoped they’d be. They are fascinated with volcanoes and keep asking me to take them to one. But I think they want an actively erupting volcano. For me, it was an awesome spectacle to see Mount Bachelor and the Three Sisters as we were driving into Bend. And the next day, Mount Washington and Mount Jefferson appeared as we were leaving Bend. Then Mount Hood appeared on the horizon. And then Mount Adams, which made Mount Hood look like a dwarf. And finally, as we approached the Columbia River, I could see the top of Mount Rainier peaking up from behind Mount Adams. Unfortunately, I didn’t stop for any photographs of the mountains on our drive back, a mistake I won’t make next time.
This trip was everything I needed – mountains, trees, forests, time away from the drudgery of life, exploration, and photography. I don’t know if or when I’ll be back to see the Redwoods again, but it worked out well to not stress about seeing it all. I feel more relaxed than I have during any other trip with the kids. I dare say that three days in the old-growth forest among the tallest trees on earth may have had a profound effect on me. Or maybe it was having some spring weather and time outside. As we were driving back, North Dakota had another snowstorm that closed down the highways in much of the state. I jokingly thought about turning around and just not going back. But I had to. And I’m glad I did, for less than a week later, I had a second profound experience. But that will be for another post.
It has been quite some time since I last made a post here, so I’d say I’m a bit overdue for an update. For the past two and a half years, I have been living in northwestern North Dakota. Saying this is an adjustment is an understatement. North Dakota is considerably flatter than any place I’ve lived, and there are almost no trees here. Winters are extremely harsh and long. We can have weeks where the daytime high does not exceed 0º F, and the wind will send a chill to your core. Our corner of the state doesn’t get much snow compared to northern Idaho or eastern North Dakota, but when we do get snow, the wind blows it into drifts which can shut down the highways. And winter can persist until May without any sign of spring. Summer has the opposite problem. The wind still blows, but without much shade, the days are hot and dry, except when gnarly thunderstorms roll through dropping large hail and threatening tornadoes. Ok, that last part sounds scary and it is when it happens, but we aren’t technically in Tornado alley, so those events are relatively rare.
There is some fascinating geology on this side of the state. We have the Dakota Badlands carved by the Little Missouri River. But the Badlands terrain is comprised of a sticky and slick clay that, when wet, is quite treacherous. And thus the only time to really get out there and hike it is in the winter, when everything is frozen, or in the summer when everything is dry. Did I mention that the prairie is only green for about a month? I seem to miss it every year. Nevertheless, I do get out once in a while to explore.
Sunset on the Prairie
Theodore Roosevelt National Park lies about an hour to the south of here. There are trails to hike in the badlands. The Little Missouri National Grassland is just beyond the park’s borders. I’ve had some fun exploring this area. There are lots of deer in the area. But we also have pronghorn and prairie dogs, which are a fun treat for me to see in the wild. The national park also has a bison herd as well as some bighorn sheep.
I’ve gotten back into rock collecting while I’ve been here as well. The Yellowstone River is a great source of Montana Moss agates and petrified wood. I even discovered a petrified forest of giant and ancient redwood stumps.
Montana Moss AgaatePetrified Wood
Most of my fun has been on extended breaks. In the winter, I’ve been trekking across Montana back to Idaho to spend time with the kids. For spring breaks, I meet Erin in the middle and bring the kids home with me (except this year). And in the summer, I go pick up the kids and we have a camping adventure back to my place. Then we’ve been making epic road trips to North Carolina where my parents and sister live. Our first trip took us across Minnesota to Michigan’s Upper Peninsula. Last year’s trip took us down to the Black Hills and then across Nebraska, Missouri, a stop to explore the giant things in Casey, Illinois, and a night of camping in southwestern Kentucky. Then we all went to the beach for a few days where the kids got to experience the ocean for the first time. This year’s summer trip is still in planning, but we will all be traveling back to the Upper Peninsula to explore some more.
This year’s spring break was…. well, it was epic, and it will get a post of its own.
It’s been an adjustment living here, and I can’t say that this will be my forever home. It’s been easier now that I’ve found a group of people to play board games with. But I’ve been missing easy access to mountains, forests, and good hiking as well as being closer to the kids.
For many years, I have spent my Fourth of July basking in the part of America that I enjoy the most: its wild and natural beauty. It started in 2011 when I explored the Hobo Cedar Grove for the first time. Then again in 2013 when I hiked Grandmother Mountain. In 2015, I spent the fourth in the Seven Devils with friends. This year, I returned to Grandmother Mountain for what may be my last visit to one of my favorite peaks in the vicinity of Moscow.
America owes its wild places to a conservation movement that began as early as the 19th century, but really took off in the early 20th century. And while we should celebrate that we have set aside land for conservation and recreation, we should also recognize the cost of doing so. Native Americans were displaced from their homelands only to see sacred landmarks turned into tourist spectacles. In the appalachians, many families were forcefully removed from their land without just compensation to create Shenandoah National Park and the Blue Ridge Parkway. The history of conservation and preservation of land isn’t always kind and people have been marginalized as a result. In the case of the Appalachian peoples, there is a deep distrust of the federal government that resides generations later.
I don’t recommend giving the land back and undoing the protections created by national parks and wilderness areas. But we can maybe do better at including the historical land owners and occupants when it comes to decisions about how to maintain and manage the land moving forward. In the West, native american tribes should absolutely have a say as to how their current and ancient sacred places get utilized, whether for tourism and recreation or for commercial resource extraction. And with the the people of appalachia, perhaps we can work to ensure that their historic homesteads aren’t completely forgotten by the ravages of nature.
As I sit on Grandmother Mountain looking over the Marble Creek drainage, I can’t help but wonder who lived on and utilized this land before it was logged clear, and how that impacts the landscape today.
View on Grandmother Mountain
Wildflowers on Grandmother Mountain
In two weeks I will be moving to North Dakota to start teaching biology at Williston State College. While I am excited to begin this next chapter and to have a new home to explore, I will miss many of the attributes of the northwest, including trees and mountains. North Dakota has neither, at least not in abundance. Instead, I will have the unique formations of the Badlands and the biology of the prairie at my doorstep. There will be new plants and animals to learn, as well as new culture and history. I will have Theodore Roosevelt National Park and the Little Yellowstone National Grassland as my local playgound. Canada will be only an hour away. And I will have summers free to explore locally and beyond.
There is much I will miss. Lush forests, flower-laden alpine meadows, mountains, clear creeks and rivers, and hot springs. For now, I will spend my remaining time here relishing the grand landscapes that I have been immersed in for the past 10 years, and know that this is not goodbye, but more of a “see you later.”
Immediately after I published my last post, I wasn’t content with the manner in which I conveyed the SIR model. Simply posting graphs from scenarios that I ran isn’t exciting. It’s passive, and it doesn’t actively demonstrate for the reader how social distancing does work to reduce infection rates. I wanted something interactive. Something that you, my readers, can play with. So I built the model in Shiny.
Shiny is a tool for R that makes data visualization interactive. I had never used Shiny. But with a few hours of reading the introductory tutorial, I had my own custom application built with a basic SIR model. And I’m ready to share it with you.
As a reminder, here is our basic model, graphically and mathematically with a description of the parameters:
The parameters are , a composite that includes the probability any one person interacts with another and the probability that successful transfer occurs with an interaction; , a composite that includes the probability an infected individual recovers or dies (from the disease or naturally); S, I, and R, the number of susceptible, infected, and removed individuals; and N, the total population size which should be equal to S + I + R.
Here’s how you can play with my interactive model. If you are an R user, grab the code here: https://github.com/matthew-singer/ShinyToys. The file you want is called sirapp.r. You will need to install the shiny package, but it’s worth having.
If you are not an R user, you can play with the app which is hosted here: http://mineral2.shinyapps.io/SIRModel. If you are an R user, please download my script from the first link and run it locally because I only get 25 hours of active app time with my shinyapps.io account, and I’d like it to be available for educational purposes to non-science people.
Remember that social distancing acts to reduce the value of . As you play with different scenarios, note that as increases or decreases, what happens to the Infectious curve (Red)? Note the approximate time that infections peak, as well as the quantity of infections at peak. How long does it take for the disease to disappear from the population? How does population size affect the response?
Remember that this isn’t an accurate model of COVId-19. It is a basic and generic model of infectious disease spread. However it is still useful in understanding how our collective and individual behaviors can affect the way diseases spread through the population.
The COVID-19 virus is sweeping the world causing an equally contagious pandemic of fear and confusion. Depending on where you live, you may be ordered to stay home, going out only when necessary, or there may be no restrictions on your life, leaving it up to you to decide how to go about your day during this tumultuous time. Two ideas keep popping up in social media: social distancing and flatten the curve. These often come with memes and infographics explaining why staying home and staying away from other people can help control the spread of this epidemic. I thought I would take a different approach. This post discusses the origin of these ideas by exploring where the curve comes from and just how social distancing influences it. I am going to talk about epidemiological modeling, or how we use math to model and predict the spread and eradication of diseases in a population. Bear with me as there will be math, but I am going to try and make this easy to follow for the non-biologists reading this.
What we are about to create is a dynamic state change model. All that means is individuals exist in different states which can change over time with a certain probability or rate. Let us suppose we have a population of individuals and a new disease gets introduced. We have two states: Infected or Not Infected. Our model is going to explain how people who are not infected become infected and how infected people become not infected. Now we are not so much concerned with the actual mechanisms of infection or disinfection so much as the rates at which changes in state occur.
Depending on the disease, we can further break down the Not Infected state. People can be not infected because they have never come in contact with the disease, in which case we can call them Susceptible. But people can also be not infected because they had the disease and recovered. And if recovered individuals are immune to re-infection, they are not susceptible. So instead we will call them Removed because they can no longer get or transmit the disease. This is how many common diseases work, and to our knowledge, how COVID-19 works. Let us draw this out graphically.
Three states in our model: Susceptible (S), Infected (I) and Removed/Recovered (R) as well as the order of transition between each.
In this model, Susceptible individuals can become Infected, and Infected individuals can become Removed or recovered. From here onward, I am going to refer to this state as Removed because recovery isn’t the only way to get into this state. We will discuss that soon enough. It is worth noting that an individual can go straight from Susceptible to Removed as well, and that is one way epidemiologists use this model to estimate the minimum number of people needed to be vaccinated to prevent an epidemic spread of disease. However, we are going to keep our model simple for now and follow the flow through the states as described.
To form our model, we have to make some assumptions, each of which can be relaxed once the basic model is finished. We are going to assume that the population size doesn’t change, and we are going to assume that everyone is moving about randomly such that any individual as the same probability of coming in contact with any other individual. Thus, there is no geographical limitation. Finally, we’re going to assume that our population is isolated from all other populations.
So we have a population with N individuals. And if nobody is infected, then everybody is Susceptible. But as long as nobody is infected, there is nobody in the population to spread the disease. But as soon as one or more individuals become infected, they can spread the disease to a susceptible individual turning them into an infected individual. The rate at which this happens depends on the number of infected individuals (I) in the population and the probability that an encounter between infected and susceptible individuals results in the successful transfer of the disease. This is called Transmissibility and will be represented as part of the term. also includes the rate of encounters among people in general. Susceptible people turn into Infected people at the rate of .
Susceptible people can also recover or die from the disease, effectively removing them from the model. This happens at a probability of , and the rate at which infected individuals become removed can be modeled as . Here is our diagram again with the transition rates.
Our model with the transition rates.
So we are at time t, and we want to know the number of people in each state at the next time step, t+1. For most diseases, we model time steps as days.
Because infected individuals can only infect susceptible individuals, we expect that the population of susceptible individuals to decrease with each day. We are multiplying the transition rate by because we need to account for the probability that an infected individual contacts a susceptible individual. We can re-write this equation to give us the change in state S as follows:
or
Now let’s look at how the number of infected and removed individuals will change. Infected individuals should grow as susceptible individuals become infected, but we’ll also have to subtract the number of susceptible individuals that become removed and add them to the removed state.
Now we have three equations describing the change in population in each state. Before we look at what this means, I want to pay special attention to the second equation, the one that describes the change in infected individuals. This is a classic birth-death model in which the first term represents “births” as new people get infected and the second term represents “deaths” as people die or recover from the disease and get removed from the model. Some information describing the COVID-19 spread makes reference to a term called (pronounced R-naught). This is the intrinsic rate of growth, or the average number of people an infected individual transmits the virus to. comes from this model:
When , the disease is spreading. When , the disease is in decline.
Let’s look at how this model can be applied to a population. Let’s suggest we Let’s look at how this model can be applied to a population. Let’s suggest we live in a city of 1 million people. Ten of them have confirmed cases of the disease. I have set and . The curves in the graph below represent the total number of individuals in each state on each day.
Note that the number of infected cases rises exponentially until it hits a critical point. This is where there are so many infected or recovered individuals that the disease has a hard time finding susceptible individuals to spread to. Eventually, the number of infected individuals declines and the disease is eradicated from the population. Not everyone was infected – a small minority of lucky individuals made it through the epidemic without catching the disease. It’s also worth noting that it took 26 days from only 10 infections to reach a peak infection of 338,660, or just over 1/3 of the total population infected at one time. Now imagine that 20% of infected individuals required hospitalization. That’s about 70,000 people. Cities of 1 million people do not have 70,000 hospital beds.
Now, these parameters that I have chosen are simply hypothetical and do not represent the actual parameters of COVID-19. I’m not even sure what those parameters are, but this model assumes that 30% of infected patients will recover in one day, when COVID-19 recovery times are more like 10-14 days from the time symptoms present. I could show that by reducing to 0.03 to suggest that 30% of infected patients will recover after 10 days. Doing so exaggerates the lag in the removed growth curve, but also highlights that the infection would spread to be even more prevalent.
Results of the model with beta=0.9 and gamma=0.03
In this scenario, we reach peak infection at 24 days with a total of 859,948 or 86% of the population infected. Nobody gets spared from the disease.
Social Distancing – Why you’re working from home.
When we say “flatten the curve,” we’re talking about the red curve in each of these graphs. The curve of number of infected over time. How does social distancing do this? Well, remember that our parameter represents not just the transmissibility, but also the probability of encounters occurring? If we stay home, we reduce the probability of interacting with other people, and thus reduce the parameter . Let’s go back to our first example, where . We hit peak infection of 338,660 on day 26. Let’s suppose social distancing measures were put in place forcing us to stay home as much as possible, reducing to 0.4.
Flattening the Curve
In this scenario, we have “flattened” that red curve. The peak infection takes place on day 102 with a peak infected population of 35,253. If 20% of infected individuals required hospitalization, we’d only need 7,000 hospital beds, which might be realistic for a city of 1 million. The other benefit here is that over half of the population never gets sick. Now again, this supposes that 30% of infected individuals on one day can recover by the next. But it does show how social distancing can work to reduce the strain on healthcare professionals as well as reduce the number of cases of infection in general.
The one cost to social distancing and “flattening the curve” is that it delays the peak infection rate of the disease and delays its eventual eradication. If we prematurely go back to business as usual, as Donald Trump has expressed his desire, cases of COVID-19 will rise faster than we’re seeing today, and our healthcare system will be overrun. Not only will COVID-19 patients not get the required treatment they’ll need to avoid a fatal outcome, but they’ll be utilizing resources that non-COVID-19 patients need for their survival as well. Car crashes, heart attacks, strokes, cancer, other infections and diseases – these will continue to prevail and people won’t get the care they need.
Nobody really knows how long we’ll have to practice social distancing. In my toy model, the peak infection occurred 102 days after the initial 10 person infection. That’s 3 months. And my model doesn’t consider the lag time for recovery, which will not only require more stringent social distancing action, but will offset the time to peak infection even more. It hasn’t been two months since the first case appeared in the United States, and some communities are just now seeing their first cases. In my toy model, the disease is effectively eradicated from the population by day 244. But at day 210, there are 10 individuals left. If social distancing restrictions were lifted at that point, the disease would resurge, slightly worse than the original surge with social distancing in place, but not nearly as bad as if no social distancing were put in place at all.
The real-world data with respect to COVID-19 is messy. For one, we don’t really have good estimates of under normal conditions or social distancing. In the US, social distancing measures aren’t unified, and have been put in place at different points of the epidemic spread for different communities. But the biggest piece making this difficult to predict is the actual number of cases out there. We can guess by adding the 2 week lag from initial exposure to time when symptoms appear. But also, we have been slow to roll out any kind of extensive testing. Most patients are told to go home and self quarantine as though they had the disease, with only a small portion of cases getting tested and confirmed positive. Combine that with the number of people who aren’t taking the disease or social distancing measures seriously and we can only estimate the worst and best case scenarios and update model parameters as more data comes in. But we cannot relax our social distancing measures until the bulk of the epidemic has passed, and that could be months, if not a year, from now.
The model I presented today is called the SIR model for the three states and transitions it describes. It’s a simple, but useful model for understanding the spread of infectious disease. But variants exist to cover the gamut of disease behavior. If there is no recovered immunity, the model is simply an SI model in which Susceptible individuals become Infected, and then become Susceptible again. If a disease is incurable – carried for life, the R portion of the model is modified to only include natural death. We can even account for the spread of pathogens from the deceased to the living, as happened when Ebola broke out in Africa. For diseases like COVID-19 which have age-structured mortality and/or susceptibility, age structure in the population can be built into the model. And of course no population is an island. Our hypothetical city of 1 million has people coming and going from other cities, and we can link models in a metapopulation with migration rates between each subpopulation. We can even include geographic probabilities of encounters to show that a person on one side of a city is unlikely to come in contact with a person on the opposite end. While these complicate the math a bit, they can give us finer scale predictions as to how and where a disease might spread.
These epidemiological models are also used to understand vaccinations. Vaccines are one way of transitioning from susceptible to removed without traveling through the infectious state. From these equations, we can predict the proportion of a population needed to be vaccinated to prevent the spread of a disease and eventual epidemic from forming. This way, the portion of the population that can’t get vaccinated may also stay safe. Remember when the measles was on the rise again after a wave of anti-vaccination fever spread rampant? It’s because the vaccination rates fell below the necessary numbers required to stave off the growth of measles.
You can learn more about epidemiological modelling here, but it gets a bit technical and math dense. The point of this post was to show the origins of the ideas behind “flattening the curve” and social distancing. It does work, but it requires us all to buy in and participate. And we’re in it for the long haul. If you still don’t understand, I’ll be happy to try and explain it over a chat.
If you want to play with your own SIR model, here’s some R code to get you started:
#===========================
# SIR Model of Infectious Disease
SIR <- function(S,I,R,beta,gamma,T=100){
i = 1
N = S+I+R
while(i<T){
dS = -1*beta*S[i]*I[i]/N
dI = beta*S[i]*I[i]/N - gamma*I[i]
dR = gamma*I[i]
S[i+1] = S[i] + dS
I[i+1] = I[i] + dI
R[i+1] = R[i] + dR
i=i+1
}
return(data.frame(Time=1:T,S,I,R))
}
I don’t get out hiking or geocaching often these days. With geocaching, it makes sense. I’ve found nearly all of the geocaches in a close distance to home and town, forcing me to travel farther distances just to make a find. But when it comes to hiking, I have less of an excuse. I don’t live in Moscow. I live near Deary, 25 miles east, which puts me 25 miles closer to the mountains. It puts me at the edge of the mountains, the foothills if you prefer. There are hiking trails all around. The closest is spud hill, from which there is an amazing view from the top. Then there’s the Potlatch River loop with great opportunities for flora and fauna sightings. There are more trails yet back in the Vassar Meadows area and up near Palouse Divide. I don’t have to go very far to get a nature fix. And yet, what keeps me from going out is more of a psychological barrier than a physical or economic one.
Barrier 1: I’ve hiked the trails before. The excuse is rubbish. But deep down, I desire to explore something new. And so I end up passing an opportunity just to get out because I’m hiking the same trails I’ve hiked in the past.
Barrier 2: The trails aren’t that good, or are shared with motorsports. Again, not a good excuse. Yes, many of the trails in the national forest are designed with single track or ATV use in mind. But that doesn’t mean they are terrible for hiking. The White Pine trail is fantastic, even though many people ride it rather than walk it. And yes, many trails don’t lead to a scenic destination – there are no mountain views, no lakes, no waterfalls. But I also enjoy a walk in the woods for its own merit. Yet sometimes these destinations are what bring me to a trail and I forget to just amble for the sake of ambling.
But once in a while, I’ll discover one of these trails through geocaching, and I’ll be quite impressed. Such is the case with the Sand Mountain trail. This trail traverses the ridge of Sand and Mica Mountains, and recently, someone put a geocache along the Sypah Creek. I knew the this trail existed, but ignored it this whole time because it had never shown up on the list of great hikes in the area. But someone recently placed a geocache along this trail, and so I had to find it.
I only hiked a small portion of the trail as it meanders along Sypah Creek for about two and a quarter miles. This section traverses through a lush cedar forest with a carpet of ferns and mosses near the creek. It’s very reminiscent of an inland rainforest, or at least a wet forest. The trail was in good condition, and the climb was gradual – it was 1000 feet up to where I stopped, but I didn’t think we had climbed that high until I looked at the GPS. The trail crosses the creek on a bridge, where we stopped, and then continues up to the ridge and toward the summit of Sand Mountain. I’m not sure if there’s much of a view up there, and I’ll have to return to explore it. But the section I hiked was a beautiful walk in the woods, with a first to find on a geocache as icing on the cake. Watch the video of my hike:
In case you weren’t aware, Geocaching is one of my hobbies turned obsession that fills my life with joy. Geocaching is a game in which people hide containers and post the coordinates on the web for others to enter into a GPS and go out and find. The game began in May of 2000. On May 2, the US Government declassified signals from the GPS satellites making them available to the public. This increased the accuracy of commercial GPS receivers from around 100m down to 10m. The next day, Dave Ulmer hid a stash in the woods outside of Portland, OR and posted the coordinates to a listserv. A few days later, it was found, and it didn’t take long for this idea to catch on. Within that first year, several hundred geocaches had been hidden world-wide with their coordinates posted for others to find. The largest repository of geocaches is hosted at geocaching.com. It’s free to play, and today, the game doesn’t even require that you have a GPS receiver since smartphones are able to communicate with the GPS satellites.
I was formally introduced to the game in 2007 when I created a lesson on GPS orienteering for a summer camp at the Max McGraw Wildlife Foundation. The activities culminated with me hiding containers around the property and having the kids wander around with some GPS receivers to find them. But it wasn’t until 2011, when I was able to buy my own GPS receiver, that I really started geocaching. Since then, I’ve accumulated 1663 finds, mostly around the inland northwest. It’s the perfect hobby, as it pairs well with my love of hiking, travelling. I’ve explored so many unique places that I would have overlooked if geocaching hadn’t brought me there.
A map of my geocache finds in the northwest.
Geocaching is a spatial game that accumulates a lot of data. Geocaching.com aggregates personal statistics for each user – you can see mine here. However, as fun as it is to analyze my own caching behavior, I’m also interested in larger questions about the game. For example, what places are more active in the game than others? While the game isn’t about the numbers, the numbers can tell us a lot about the game. Defining how a place is geocaching-friendly isn’t easy, and there are a lot of variables to consider. Unfortunately, I don’t have access (at least not easily) to the full data hosted at geocaching.com. So I have chosen the number of geocaches as a proxy for how active an area might be. And my definition of area is going to be at the level of state, because I can easily grab the total number of active geocache hides in each state from state regional searches on the website.
What states or regions of the country are most active in geocaching? Here is my data. The number of caches was collected manually using regional searches on the evening of June 12. The state area and population size were gathered from Wikipedia, and population is a 2018 estimate. Perhaps we’ll do this again when the 2020 census numbers get released.
State
sq mi
Geocaches
Cache Density
Population*
Population Density
Alabama
52420.07
14826
0.28
4887871
93.24
Alaska
665384.04
7591
0.01
737438
1.11
Arizona
113990.30
39083
0.34
7171646
62.91
Arkansas
53178.55
12014
0.23
3013825
56.67
California
163696.32
132475
0.81
39557045
241.65
Colorado
104093.67
26075
0.25
5695564
54.72
Connecticut
5543.41
8008
1.44
3572665
644.49
Delaware
2488.72
2890
1.16
967171
388.62
District Of Columbia
68.34
248
3.63
702455
10278.83
Florida
65757.70
41034
0.62
21299325
323.91
Georgia
59425.15
14254
0.24
10519475
177.02
Hawaii
10931.72
2442
0.22
1420491
129.94
Idaho
83568.95
18557
0.22
1754208
20.99
Illinois
57913.55
30905
0.53
12741080
220.00
Indiana
36419.55
21611
0.59
6691878
183.74
Iowa
56272.81
21753
0.39
3156145
56.09
Kansas
82278.36
11676
0.14
2911505
35.39
Kentucky
40407.80
16920
0.42
4468402
110.58
Louisiana
52378.13
5663
0.11
4659978
88.97
Maine
35379.74
9388
0.27
1338404
37.83
Maryland
12405.93
12116
0.98
6042718
487.08
Massachusetts
10554.39
16871
1.60
6902149
653.96
Michigan
96713.51
34800
0.36
9995915
103.36
Minnesota
86935.83
29094
0.33
5611179
64.54
Mississippi
48431.78
7136
0.15
2986530
61.66
Missouri
69706.99
13898
0.20
6126452
87.89
Montana
147039.71
8059
0.05
1062305
7.22
Nebraska
77347.81
9602
0.12
1929268
24.94
Nevada
110571.82
22599
0.20
3034392
27.44
New Hampshire
9349.16
11436
1.22
1356458
145.09
New Jersey
8722.58
14081
1.61
8908520
1021.32
New Mexico
121590.30
17722
0.15
2095428
17.23
New York
54554.98
32343
0.59
19542209
358.21
North Carolina
53819.16
22174
0.41
10383620
192.94
North Dakota
70698.32
3020
0.04
760077
10.75
Ohio
44825.58
28631
0.64
11689442
260.78
Oklahoma
69898.87
14428
0.21
3943079
56.41
Oregon
98378.54
31066
0.32
4190713
42.60
Pennsylvania
46054.35
39347
0.85
12807060
278.09
Rhode Island
1544.89
3613
2.34
1057315
684.40
South Carolina
32020.49
5701
0.18
5084127
158.78
South Dakota
77115.68
9354
0.12
882235
11.44
Tennessee
42144.25
18136
0.43
6770010
160.64
Texas
268596.46
67902
0.25
28701845
106.86
Utah
84896.88
29369
0.35
3161105
37.23
Vermont
9616.36
4988
0.52
626299
65.13
Virginia
42774.93
15162
0.35
8517685
199.13
Washington
71297.95
29634
0.42
7535591
105.69
West Virginia
24230.04
5708
0.24
1805832
74.53
Wisconsin
65496.38
29874
0.46
5813568
88.76
Wyoming
97813.01
5772
0.06
577737
5.91
There is tremendous variation in the number of geocaches hidden in each state. Excluding the District of Columbia, with only 248 active hides, the state with the fewest geocaches is Hawaii at 2442, and on the mainland, it’s Delaware at only 2890. Meanwhile, California leads the way with the most geocaches hidden at 138,475. That’s quite a spread, though the median number of hides per state is 14,826.
The first question that comes to mind is whether the number of hides is limited by the size of the state. After all, California is a huge state. Delaware and Hawaii are pretty small. And given that people who run Geocaching.com have set a rule that geocaches must not be placed within 0.1 mile of another geocache, there is a limit to the number of caches that can be hidden in a finite area.
The number of geocaches in each state as a function of the size of the state. Both axes are log transformed.
There is certainly a trend here. Larger states, on average, have more geocaches. Though the larger the area, the larger the variation in hide count. Without that D.C. outlier, we still have a positive slope, though it’s less steep. To gage just how much area influences the number of caches, we should look at the density, or the number of caches placed per square mile. We are looking for no effect of area on density of hides.
Cache Density as a function of state size. Axes are log transformed.
What we see is a negative association between the density of caches placed and the area of the state. So even though smaller states have fewer caches, overall, they are more densely packed with geocaches. In some ways, this makes sense. The large states of the western half of the country have a lot of open land, public and private. Some of this land, including national parks and designated wilderness areas, is off limits to physical geocaches. Some of this area is just difficult to get to. And some of it is private property – big ranches and farms where the public doesn’t have permission to trespass. When you look at states like Colorado, Montana, California, you’ll notice that geocaches are densely packed into cities with fewer caches in rural areas. Though still, in popular hiking areas, there are still a lot of geocaches hidden along the trails.
But small states have rural places, too. So wouldn’t this affect the density of geocaches? Well, yes. But maybe these small states have less rural land than the larger states. The rural land is broken up into smaller parcels with more public right of ways with which to put a geocache. Or maybe it’s not about the land at all, but about the people living there. Perhaps more people just means more geocachers, which means more geocaches being hidden in a given area.
Cache Density as a function of Population Density by state. Both axes are log transformed.
Here we see our tightest trend. The geocache density appears to be explained rather well by population density. This would also explain why urban areas see so many more caches than rural areas, even within a state. There are still differences among urban centers as to the density of caches, and that may also be explained by population size. Or maybe geocaching is more popular in cities with a higher aptitude for an outdoor lifestyle. Denver, Salt Lake City and Seattle are all some of the densest cities when it comes to geocaches. Perhaps I will find a way to aggregate such data for analysis. But at the state level, the number of people per square mile nicely explains the number caches hidden per square mile.
Let’s look at some maps.
Number of Caches hidden in each state.Density of caches in each state.Population density of each state.
If you’re an avid geocacher, and you want an active geocaching community, where should you live? Well, if we define active geocaching community solely by the number of geocaches placed, it appears that the northeast coast is the place to be. While these states are small and each have a small number of geocaches hidden, collectively, it is the densest area for geocache placement. And this seems to be driven by population density.
Of course, there are more variables to consider. The number of geocaches doesn’t always represent the quality of geocaches. Many people hide film canisters in lamp post skirts in a parking lot. The first time I saw one of these, it was neat. But after a hundred of them, it gets old. Many are placed for the sake of being placed, rather than bringing people to a unique and special area. Judging the quality of hides from numbers is itself a difficult task. Geocaching.com does have a system by which premium members can award favorite points to deserving caches, and this might be one method by which we can estimate the quality of a hide. The number of unique geocachers that are actively hiding and searching in an area will also determine how active a community is with the game. Lewiston and Clarkston once had over 400 hides in a four mile radius. Over half of them were owned by 3 prolific geocachers who have since archived their hides and left the area. Gathering and aggregating data on users is out of my ability at the moment.
And power trails can skew the numbers. These are caches placed 0.1 mile apart along a road or trail for the sole purpose of enhancing find counts. They are typically not quality hides, though a few trails on rural roads do take you into some scenic locations. The famous ET Highway in Nevada boasts over 2000 geocaches. And one prolific hider made power trails all over northern Nevada with over 20,000 hides. They have since been archived, and the state’s hide count dropped considerably.
On the other side of the distribution, South Dakota might be the worst state for a geocacher. With only 3020 caches to find, you’ll quickly be driving long distances if you want to stay active in the game. Montana and Wyoming aren’t much better. Alaska has the lowest density, and rightly so. Of the 7591 caches spread amongst this large state, most are concentrated around Anchorage and the Kenai Peninsula. If you live in this area, there are enough caches to keep you busy for some time. If you live in the small, isolated villages further north, you may quickly find yourself out of a hobby, and even your own hides may only get occasional finds through the years.
This analysis isn’t perfect, but it does give us some insight into where geocaches are hidden in the United States, and what states might be better to live if geocaching is a major part of your life. But don’t read too much into it. Despite Montana’s low ranking on cache density, Missoula, Helena, and Great Falls are all great cities for geocachers, as are Boise, Spokane, and Coeur d’Alene. I wonder, at the city level, how they compare with other comparable cities in other regions, and how they stack up against their larger cousins. That’s a project for another day.
When life prevents you from going out and adventuring, you make your own adventures at home. My latest adventure is making sourdough. Now, I could go out and obtain or buy a starter from a local bakery, but what’s the fun of that? It’s so easy to start my own from scratch, and now I have one that I can truly call my own. My guide for making the starter and baking my first batch of bread comes from King Arthur Flour’s Sourdough Baking Guide.
This all started about 3 weeks ago. I had some whole wheat flour sitting around and wasn’t sure how well it would start, given its age. But I mixed up the 1 cup of flour and half-cup of water and let it sit overnight and sure enough, there wasn’t much activity. But that’s normal. I fed it, and on day two, there were bubbles. Success. So I kept feeding it. Third day, more bubbles, and a ripe odor. Fourth day, still going strong. It was time for two feedings a day. But my starter was growing big. Ooops, I misread the instructions and threw out half a cup each day instead of saving half a cup. So I switched to that motif, keeping half a cup and feeding it, discarding the rest. Activity stopped. It no longer tasted tangy, nor smelled of fermentation. I kept feeding it anyway, hoping it would recover. It didn’t. It wouldn’t rise. Was it too cold? Did I screw something up by not properly feeding it originally? Probably not, but I also wanted to ensure success. So I dumped it and began again.
Adventures in Sourdough, take 2.
When baking, it’s important to get your flour to water ratios right or the dough won’t have the right consistency. I had been measuring my flour and water and starter by volume, which is not really an accurate gauge of how much material I was working with. So I ordered myself a kitchen scale. It arrived and this time I was determined to be more precise. Now I doubt that measuring by volume caused my previous attempt to flop – yeast and bacteria are both hardy creatures, and altering the moisture content can favor one over the other to control the flavor and intensity of your starter. But I was determined to be a bit more precise and deliberate in my measurements.
I weighed out 113g of whole wheat flour, and 113g of water, mixed it together and let it sit overnight. Again, no activity, but with a feeding of 113g of starter, 113g of flour, and 113g of water and another 24 hours of rest, the starter was on track just as before. I also decided to incubate the starter in the oven with the light on for a few hours, just in case room temperature on top of the fridge wasn’t in the ideal range. By day 4, it was starting to rise, and by day 6, it was consistently doubling in volume. In fact, it liked that environment so much that one day it overflowed the jar. I guess it’s a little too warm in the oven.
Friday night, I came home from game night and fed the starter, but instead of keeping the 113g, I expanded each ingredient to 200g so I’d have a total of 600g of starter in the morning – 113 I’d take out to continue culturing, and the rest I’d use to make bread. I followed the Naturally Leavened Sourdough recipe.
To me, breadmaking is zen. There’s a certain satisfaction that comes with mixing the flour and water, kneading, watching it rise, shaping the dough, and tasting the fruits of your labor. I love making pizza for the same reasons. But pizza is cakewalk compared with bread. It doesn’t require as much kneading, only rises once, and you’re stretching it out to put in the oven with the intent of it cooking flat. With bread, you want a rise, and I was pleasantly surprised when my dough rose during each of the resting periods. My natural yeast culture was alive and well and doing its job.
But there is still much to improve. I shaped the bread in bowls because I don’t own a proper bread shaping basket. I mean, a proper basket isn’t really necessary. But in the past, I would shape my loaves and let them rest on the counter, and without the support of the bowl, they would eventually spread out as the gluten relaxed, and when it was time to put them in the oven, they wouldn’t rise upward nearly as much as I wanted them to.
When shaping a loaf in a bowl, the bowl is often lined with a floured cloth. I grabbed the least-textured cloth towels we had, floured them and lined the bowls before dropping the dough in. At the end of the rise, I dumped the dough out, but it stuck to the towels. I mean, really stuck. I’m still trying to get dough out of them. Grr. The loaves deflated and I was pissed. Bummed. I wasn’t sure what to do. So I tried just greasing the bowls and dropping the dough in after reshaping them. I gave them another 2-hour rise and they came out just fine. Unfortunately, they deflated a bit upon scoring and the loaves didn’t puff up so much as out during baking.
My first sourdough loaves.
Now, let me just say that the bread came out of the oven smelling like heaven. After cooling, I couldn’t resist a taste. By all accounts, I think I had success. I had bread, and it tasted great. So it didn’t balloon up all big. So it’s not quite shaped right for any kind of sandwiches. Toast it up with some butter and it goes well with soup, or just on its own. In fact, even though these loaves weren’t ideal for sandwiches, I still stuffed cheese between two slices and grilled them up for the best damn toasted cheese sandwich I have ever made. God, it was heavenly. I made that for breakfast yesterday with two eggs on the side. I had another one this morning for an early lunch.
Making a grilled cheese with my sourdough.
My starter is now living in the fridge where I only have to feed it once a week. I don’t think I’ll be making bread on the regular, maybe every 2 weeks or so, though there are some recipes I’d like to try that use the discard from each feeding. For my next loaf, I may go with a no-knead recipe in which the entire gluten formation process occurs slowly through a process called autolyzation. I also need to work on getting that bread to hold its shape and rise properly in the oven. Some sources suggest the problem stems from letting the dough over-proof during the shaping stage. It rose too much and thus deflated when removing it from the bowl and scoring it. I might also shape it, or just bake it in a sandwich loaf pan just so I have bread that I can make sandwiches with. For now, I have made my first steps into the world of sourdough baking, and I’m eagerly looking forward to mastering the art of breadmaking.
It’s occurred to me that I haven’t been good at writing posts recently. My last update was from May, and that was subsequently my last big hiking trip. Since then, I have been incredibly busy, and that means I haven’t had as much time for fun. I did get out a few times this summer with the family. But there’s a lot to talk about. So here’s what happened in 2017.
I successfully defended my Ph.D. dissertation.
On December 14, I defended my dissertation in front of my committee. This is why I haven’t been very active this year. I had a lot of work to do and little time to do it. But in the end, I got it done. My dissertation and all of the accompanying paperwork has been submitted to the graduate school and I’m on track to receive my diploma in May. So where does that leave me now? Unemployed. I’m currently spending my time feverishly applying for jobs, hoping to get an interview and an offer. These things take time, so for the moment, my adventure hiatus will have to continue until I can afford to go back out and have some fun.
We welcomed the birth of my son.
On January 6, 2018, Adam Isaac Singer made his first appearance into this world. Clara is stoked to have a baby brother, and I’m excited to add another member to my adventure team. Our adventures this summer have been small to accommodate time constraints, a toddler and my pregnant wife. I imagine that in the coming future, most of my adventures will continue to be family-based with only a handful of bigger trips for myself. Of course, it all depends where I end up. I’m hoping there will be mountains and wild places nearby.
It was the summer of car camping and hot springs.
I know I’ve been doing something right when I’ve instilled an adventurous spirit and a love of camping in my daughter. Clara loves camping. This spring we bought a new sleeping bag for her, but it remained wet and cold into June. We finally had our first chance to test it out during a trip to Boise. We were headed down for Erin to see a specialist and decided to make a long weekend out of the ordeal. So we stopped at Pine Flats campground along the South Fork of the Payette River in the Boise National Forest and spent two nights beneath the towering ponderosa pines. Pine Flats happens to have a hot spring a short hike from the campground, and that was quite a treat. In fact, there are a series of hot springs scattered along the banks of the river, and we also spent some time at Kirkham hot springs down the road. We then headed into Boise where we took Clara to the zoo. This adventure was documented in the video below:
In July, we headed up to the Blue Mountains of southeastern Washington. I had been up there several times in the past few years, but Erin had never been up there. We stayed two nights at a remote campground and ended up being the only ones there the entire weekend. See the adventure below:
August came, and the first solar eclipse to cross the United States in my lifetime was forecasted to cross southern Idaho. We couldn’t resist this opportunity. Erin’s friend Alex came to visit as part of a broader tour of the west. She was headed to Yellowstone after the Eclipse. We tried to plan our own epic adventure to Denver, and then back via Yellowstone, but unfortunately we had to cancel that part of the trip. But we did make it back to southern Idaho to experience the eclipse and soak in some hot springs.
I first learned of this plan when we were in Boise in June. I soon found that all of the camping locations along the path of totality had already been booked up. Apparently this was a much bigger deal than I was expecting. I had gone back and forth on whether it was even worth trying to make this trip happen without advanced reservations. But I had a trick up my sleeve. The campgrounds do reserve some spaces as walk-in only, meaning they are available on a first-come first-served basis. The eclipse was on Monday, but the reserved spaces were booked up starting Saturday night. However there were still several spaces at several campgrounds that were available on Friday night. With that knowledge, I figured that there might be some walk-in sites unoccupied Friday night. Alex was arriving Friday evening, and we didn’t want to drive down immediately, so instead we got up early and left at 3:30 am hoping to get down to the campgrounds before the crowds would arrive. We turned down the South Fork of the Payette River and pulled into the first campground, which happened to be Pine Flats. There was one space open, and we took it for three nights.
We visited family too.
My parents flew us east in November to celebrate Thanksgiving and a late 90th birthday for my grandmother. She now lives in Charlotte, and my sister lives an hour north. My aunt and uncle and cousins and their families came in and we had a mini family reunion. It was a nice break. Clara got to meet her cousin for the first time and they just adored each other. We took them to the North Carolina Zoo because the Boise Zoo didn’t have elephants.
Looking ahead for 2018.
As I mentioned at the beginning of this post, I haven’t been good at making regular updates. A lot of that was because my time was spent writing my dissertation. I plan to post more often, even if they aren’t all hiking and adventure stories. For now, I’m spending about as much effort writing job applications. But hopefully I’ll get some time and funds to keep up with some local adventures and not neglect my photography hobby or this website. And maybe I’ll get to write about the next chapter of my life.
It’s not often that I get out to hike these days. But we’ve had a fantastic winter so far, and after a week of insanely cold temperatures and clear weather, I just had to get out and take advantage before the warm weather and rains took over. I’ve always wanted to hike to the lookout on East Moscow Mountain in the winter, but on every attempt, I was thwarted with people who just couldn’t make it all the way up. So on Saturday, I had a nice sunny day and some time to go for a snowshoe hike on my own. Since the temperatures hadn’t really risen above 25º in the past week, the snow was still fresh looking on the trees. I was hoping for a similar experience to my 2013 summit of Spud Hill, but going solo on a trail that is well used and already packed down.
I left rather late, starting the hike after 1:00 pm. That’s ok as I was hoping to catch the soft afternoon light over the Palouse from the summit, but leave enough time to return to the car before it got dark and really cold. I parked the car and put on my snowshoes only to discover a large group of New St. Andrews students also starting their hike. We nodded hello and started up the mountain together, but they took off up another trail while I continued up the road. The first thing that I noticed was that the road was plowed past the parking area. And the gate just beyond was open. This was unprecedented. In the six years I’ve lived here, Tamarack Road has never been plowed beyond the parking area, and the gate has never been opened past October. But then, for the past two summers, the gate hasn’t been open for through traffic either. I’m not sure how far the road was cleared, but it was only limited to Tamarack Road which continues down the back side of the mountain. Moscow Mountain road remained full of snow, and technically I could have driven up and parked by the intersection, but the extra mile each way was good for me.
Tamarack Road is plowed and open this year.
The hike up isn’t bad regardless of the road conditions. It’s about 2.25 miles to the top with a vertical rise of 1000 feet. About a mile up, the trail turns onto Moscow Mountain Road, which traverses the mountain ridge east to west. Since the back side of the mountain is logged, there are many views to the north that open up along this section of the hike.
Views open up to the north on Moscow Mountain Road. In the distance we can see Bald Mountain and Palouse Divide.
Finally, the East Moscow Mountain spur road takes off to the left. This last half mile is up on the ridge and is fairly flat. We start to get a glimpse of the true summit of Moscow Mountain and the Palouse off in the distance, but for the most part, the road is flanked by dense forest on both sides. The road ends with a little turn-a-bout, and suddenly the view opens over the Palouse, about 2500 feet below.
The forest on top of Moscow Mountain.
This day was so clear, that I could see the Wallowas and the Seven Devils poking up above the horizon 100 miles away. The sun had been obscured by some clouds, which made the light a bit flat and challenging to work with, but the relative clarity of the atmosphere provided stunning views all around. I feel as though I made the right choice going up when I did. Though the sky was clearer the next day, there was more haze and the mountains in the distance would have been much less defined.
The Seven Devils are peaking up over the rim of Hells Canyon.
The Wallowas can be seen behind the clouded Lewiston-Clarkston valley and the Blue Mountains.
Moscow Mountain looks over the entire Idaho Palouse, and the southern portion of Washington’s Palouse. Both Moscow and Pullman are visible, though on this day, Pullman is partially hidden by a layer of fog spilling over from the Clearwater and Snake canyons (Lewiston and Clarkston valley). The sun came out just before I headed back to the car giving some definition to the rolling hills on the Palouse. Unfortunately, Kamiak Butte and everything north is obscured by the main summit of Moscow Mountain.
The town of Moscow, home to the University of Idaho.
View of Pullman and the Washington Palouse
The Palouse through the trees.
Looking east toward the Clearwater Mountains. Grandmother Mountain and Freezeout Ridge are visible in this image.
The overlook on East Moscow Mountain
My car, 1000 feet below.
In total, the view from the rocks is around 180º from Freezeout to Pullman, including the ability to see the Mallard Larkins, Selway Crags, Gospel Hump, Seven Devils, Wallowas, Selway/Payette Mountains, the Blue Mountains, a bit of Hells Canyon, and all of the hills of the southern Palouse.
A full panorama of the view on East Moscow Mountain stitched from 28 individual frames.
While it was a pleasant 18 degrees out, my water did freeze while I had my pack off on the summit. As I headed back to the car trying to beat the sunset, the light actually got better and better. A part of me wanted to stay up there just a bit longer to reshoot the views with that last evening light. But the cold had gotten to my batteries, and I wasn’t really prepared to stay up there much longer. Within less than an hour, the temperatures would drop about fifteen degrees. And that’s the problem with having a real winter. It gets so cold so fast that even while keeping my batteries warm in my coat pocket, they get cold in the camera very fast and quit on me. On the way out, I was able to capture the last light of the day glowing off the mountain from below.
This past year, I found myself in a bit of a photographic slump. It’s not that I didn’t create any great images – some of my favorites were made on Steptoe Butte. But I didn’t get out much, and when I did, I didn’t always bring or use the camera. I’m hoping I can crawl out of that slump this year to capture more of this stunning place before leaving it.
The last light of the evening glowing off of the mountain.
We’ve gotten a lot of snow this winter. And then it got cold. Like, really cold. Night time lows below zero, and daytime highs hovering around 20. Â So the only thing to do with this kind of weather is go swimming.
Last year, we took Clara to a developed hot spring near McCall and she loved it. This year we decided to give the undeveloped hot spring a try. Spoiler: She had a blast. Our biggest concern was keeping her warm during the one-mile hike to and from the springs. She did fine in her little blue down suit, but then, it helps that the hike was so short. I’ve written about these hot springs before, and since then, I’ve been back only twice (including this trip). I meant to make it an annual tradition, but after Clara was born, we just couldn’t seem to make it work. Now that we know that hot springs are a hit, I’m hoping we can visit more of them before we end up leaving the northwest.
When I started this site, I never expected to make daily posts. Weekly? Maybe. Monthly? Less desireable. I’m kind of ashamed that it’s been three months with no updates, but there hasn’t been much of excitement to talk about. There haven’t been any big adventures this fall. I’m just plugging away at the Ph.D. thing, which has also made me uninspired to write here. So, here’s my update for now.
It’s snowing. We had our first snowfall that actually stuck, and though it’s only a few inches, it’s enough to put on our boots and snow gear and go out and play. This year Clara is old enough to really appreciate the snow and all the fun that can be had, and that makes me happy. I can’t wait to take her out snowshoeing. I’ve thought about introducing her to skiing this year, but I think I’ll wait on that one for a number of reasons. Until then, she’s happy to make snow angels, build snowmen, throw snowballs, and sled down hills.
In May we bought a new tent to accommodate our growing family on camping trips. I guess the two-person backpacking tent just won’t do it anymore for thee people and two large dogs. So after we bought it, we took it out for its maiden test at a nearby campground. This summer was dubbed the summer of no fun. I was busy writing and Erin was working an internship. To make the summer a bit more bearable, we thought we’d go camping for a night or two once a month just to get out of the house and have some adventure with Clara. June came and I had planned a trip to the Blue Mountains of southeastern Washington. Then Clara got sick and we didn’t go. July came and I had planned a trip down to McCall. Then Clara got sick. And Erin got sick. And we didn’t go. So when Erin finished her internship the first week of August, I put my foot down and said we were going camping.
I’ve always wanted to explore the mountains behind Brundage. In the summer, the road continues past the Brundage Reservoir, Goose Lake with trailhead access to Granite Mountain, and onto Hazard Lake in the alpine valley at 7000 feet. At that elevation, we could escape the heat and dry vegetation on the Palouse. The Hazard Lake campground is remarkably nice for being 20 miles out of civilization on a gravel forest service road. The tent pads are filled with sand which keeps them flat and soft. Every site has a picnic table and a fire pit. The toilets were some of the cleanest I’ve seen at a forest service campground. And there’s potable water available at a central pump. Though the forest service claims the campground doesn’t get heavy use, we were lucky to find an open campsite when we arrived Saturday evening.
Bruin Mountain and Hazard Lake
The campground is on the edge of Hazard Lake, which seems bigger than it appears on maps. Some people brought kayaks with them to paddle around the lake, and it does seem like it would be good for some exploration by boat. Big Hazard Lake is just down the road, and as the name suggests, is a larger lake. A trail leaves the campground for Upper Hazard Lake just 2 miles away. Upper Hazard sits at the base of Bruin Mountain and resembles a more traditional alpine tarn. The hike is easy which means we could it with Clara in just a few hours.
The trail to Upper Hazard Lake.
Upper Hazard Lake
Erin, Clara, and Shadow by Hazard Lake.
We arrived at the campground Saturday afternoon, set up camp and made dinner. We explored the campground, but otherwise just hung out at camp for the evening. On Sunday, we had lazy morning. We heard some thunder off in the distance and decided to wait and see what was going to happen. When the sun came out and it seemed that the storm had passed around us, we head on the trail for Upper Hazard Lake. Half way there, we heard thunder again and almost turned back, but waited to see where it was headed. At first, the storm looked to be heading right for us, but again it passed us by and we continued on to the lake. We had a nice hike and saw more wildflowers than I was expecting for this time of year. We got back and had a late lunch that turned into an early dinner, and then decided to drive back down to New Meadows for a soak at Zim’s hot springs. We stopped at a waterfall and some scenic views along the road and found some geocaches. By the time we got into cell service, we discovered that we’d only have about an hour at most to soak in the springs, so we decided to turn back.
A view of Lloyd’s Lake in the foreground and Patrick Butte in the distance.
An awesome view on Brundage Reservoir Road.
Overlook and view of Goose Creek gorge and Granite Mountain
On Monday, we packed up camp and headed for Granite Mountain. Erin took the dogs on the shorter hike to Twin Lakes since Greta can’t hike much with her injured paw. I hiked with Clara on my back to the summit of Granite Mountain with my mom. Granite Mountain rises 8500 feet above sea level for a fantastic 360 degree view. At that height, the summit sits over 4000 feet above New Meadows. But for us, it was only an 1800 foot climb over 2.8 miles. Did I mention the views at the top? Cascade Lake and the Payette Valley to the south, New Meadows, the Wallowas to the west, the Seven Devils and the Salmon River canyon to the north., the Payette Mountains to the east. I look at Granite Mountain every time I’m skiing at Brundage and every time I’m up at the Seven Devils, so it was nice to finally stand on this peak. It’s a tough hike, especially with Clara on my back, but it’s well worth the effort.
Northern View on Granite Mountain
Phlox on top of Granite Mountain.
Lupine in flower with the Payette Mountains in the distance.
The Hobo Cedar Grove is a nice easy 1-mile hike through a grove of giant old-growth trees. It is the perfect hike for toddlers to explore nature, which is why we brought Clara up there on Sunday. She enjoyed the large trees, but wasn’t into walking the trail much. Eventually Erin had to carry her for most of the hike. In hindsight, she may not have completely gotten over her illness from Friday and Saturday.
I finally got some time to get up to Freezeout to hike Grandmother Mountain. The flowers are out and it’s quite pretty, though it’s not the best year for flowers that I’ve seen. It could be that I got up there a little late. Everything seems to be coming out a little earlier this year than normal. But then, all of the flowers that are out still seem to be in peak bloom. I was especially hoping for a great beargrass year like I got to see three years ago. But even with the lower abundance of flowers, the ones that were there were quite spectacular. I came across a patch of paintbrush on the summit that must have been the best I’ve ever seen, perfect and unblemished and bright and vivid.
Paintbrush on Grandmother Mountain
It’s been a strange summer. Our heat wave came early and has since left for cooler temperatures and rain. Typically by July, we’ve entered the dry spell. But this past weekend it rained pretty hard, letting up just long enough for a hike on Saturday. Since I’ve been to Grandmother Mountain so many times, I don’t have many new photos to share. So instead, I thought I’d try my hand at a video tour of the hike. So enjoy this hybrid blog-vlog post.
It’s been over a month since my last update. There haven’t been any major adventures due to time and financial constraints. As I aim to write and finish my dissertation, the time for such outings decreases and thus this summer will be nicknamed “the summer of no fun.” Fun isn’t completely off the table, but the number and scope of such expeditions will be reduced compared to past years.
City of Austin
I did have one bit of adventure in June. I traveled to Austin for the 2016 Evolution meeting where I presented some results from our behavioral simulation experiments. With our latest zebrafish experiments as inspiration, we’ve put together a program to simulate an animal’s movement in two-dimensional space as it explores its habitat and collects “food” pieces to invest in reproduction. By manipulating aspects of the environment, we can better understand how habitat usage influences risk and thus selection for or against risk-taking behaviors. Movement is determined by a neural network with weights that are heritable and represent the (quantitative) genetic basis of behavior. The simulation is very basic at this point, but already we are seeing some promising results. For example, when a “predator” is introduced represented by an probability of death in a given location, we observe behaviors evolving to avoid, or spend less time in, the high risk areas. However the degree and even direction of selection is dependent not just on the intensity of predation, but also the amount of “food” resources available.
I had a good time at evolution, reconnecting with friends I’ve met at previous meetings, and meeting some new contacts. Rather than stay in the dorms at UT, or the expensive hotels downtown, I stayed in a hostel nearby which enhanced the social factor, as well as my budget. It turned out I wasn’t the only one with that idea and I met plenty of other conference goers at the hostel. Austin is an interesting city. It’s weird. Portland weird. I’d go as far to call it the Portland of the south. It’s a town for live music, good food, arts, and culture. There are nice bike paths and beautiful parks. But during the summer, it’s hot. Very hot. Daytime highs all week were in the mid to upper 90’s with 80-90% humidity.
It’s the 4th of July. On many years past, I’ve taken a hike to celebrate our nation’s independence. Today I spent the day at home. We didn’t even take Clara out to see fireworks in town. It was just a lazy day. That makes up for us being out all day yesterday. We headed up to Spokane to pick up my mom from the airport and spent the afternoon at Riverside Park. After a stop at Target followed by dinner at a very great pizza place, we got home shortly before midnight. Here is some of the fun we had with Clara.
When I moved to the Palouse, I didn’t realize just how photogenic the landscape was. Then I saw ads for the Palouse in Popular Photography. It turns out, people will pay good money to come and photograph the region, and here I am living there not taking advantage of my home turf. I’ve only been on Steptoe Butte once before, and it was in the winter with not much snow on the ground. So I was quite glad when Simon came back to visit and suggested we go out and shoot the Palouse. We hit Steptoe Butte at the right time while it was covered with balsamroot and lupine, and the fields of the Palouse alternate between the green of new wheat and brown of a freshly plowed field. Simon also came with an arsenal of lenses that we shared. I knew I needed to get a nice long lens, but now I really know how much a long lens can complement landscape photography.
Steptoe Butte and a country road.
Steptoe Butte rises behind a Palouse farm.
Arrowleaf Balsamroot
A sea of green.
Plowing fields.
Balsamroot over the Palouse
The small town of Steptoe among the hills.
The fading sun captures the dust of farmers tilling their fields.
There’s not much native prairie left on the Palouse.
Contrasts and patterns of the Palouse.
We had hoped for a sunset, but this is the best we got.
We came across this moose on the way down. It made up for the lack of a sunset.
Good sunsets often occur after a day of rain and storms. The following Saturday, scattered rain storms swept through the area. I was in Moscow with Erin and Clara at the annual renaissance faire, which is more like an arts festival than a true renaissance festival. As evening approached, I noticed an end to the rain on the horizon to the west. I checked the radar and Steptoe Butte was clear. So we headed back up so I could show Erin the beauty of the floral displays, and to capture the sunset over the Palouse. It wasn’t quite as vivid as I wanted, but I got some color in the clouds and it was much better than the sunset on my previous visit.
, a composite that includes the probability any one person interacts with another and the probability that successful transfer occurs with an interaction; 
, a composite that includes the probability an infected individual recovers or dies (from the disease or naturally); S, I, and R, the number of susceptible, infected, and removed individuals; and N, the total population size which should be equal to S + I + R. 
.
. Here is our diagram again with the transition rates. 
because we need to account for the probability that an infected individual contacts a susceptible individual. We can re-write this equation to give us the change in state S as follows:
(pronounced R-naught). This is the intrinsic rate of growth, or the average number of people an infected individual transmits the virus to. 
, the disease is spreading. When 
, the disease is in decline.
and 
. The curves in the graph below represent the total number of individuals in each state on each day.
