Control Points

The Projection

Chapter 6: Control Points

The weather cleared on the fifth day. The clouds lifted in the late morning, peeling off the ridges like a bandage being removed from a wound, and beneath them the mountains were wet and sharp and new, every rock face running with water, every gully carrying a small stream that had not existed two days ago and would not exist two days from now, the terrain changed and changing, the drainage pattern of the map rewritten by a single storm.

The creek had dropped. Not to its pre-storm level — the water was still higher than it had been when they arrived, still carrying silt, still running fast — but low enough that the banks were exposed and the traverse stations were accessible and the work could resume. Silas checked the stations in the morning, walking downstream from the new camp to each flagged stake, verifying that the stakes were still in place, that the flood had not moved them, that the control points he had established were still where he had put them.

They were. The stakes were standing, the flagging faded but visible, the positions unchanged. Control points were supposed to be permanent, or as permanent as anything driven into gravel could be, and these had survived their first test. Silas noted this in the field notebook with the satisfaction of a builder whose structure had withstood a storm.

Jin was already at the equipment, setting up the R10 over the first station for a check observation. The GPS needed to reacquire the satellite constellation after two days of being stored in the case, and the reacquisition took longer than usual because the almanac data in the receiver's memory had aged and the satellites had moved in their orbits and the receiver had to find them again, searching the sky for signals that were always there but were not always receivable, the signals attenuated by the atmosphere and the terrain and the foliage and the rain.

"Locked," Jin said after ten minutes. "Twelve satellites. PDOP 1.4."

"Good enough. Take a five-minute observation and compare it to the pre-storm position."

Jin waited, watching the data collector, the numbers updating every second as the receiver computed and recomputed its position, each computation slightly different from the last, the position jittering around the true value like a hand trembling around a point, and the five-minute average was the best estimate, the statistical center of the jitter, the position that minimized the residual error.

"Pre-storm: 67.42031 north, 150.18472 west, 2,141 feet," Jin read. "Post-storm: 67.42031 north, 150.18473 west, 2,141 feet."

"One ten-thousandth of a degree in longitude. That's about three meters at this latitude. Well within the observation noise."

"So it didn't move."

"The gravel didn't move. The stake didn't move. The earth beneath the gravel moved, slightly, but not enough to measure. The control point is still valid."

"How do you know the earth moved."

"The earth always moves. Tectonic motion, postglacial rebound, thermal expansion and contraction of the crust. The movements are small — millimeters per year — but they're real. The datum accounts for them. NAD 83, the datum we use, is a fixed-epoch datum, meaning it represents the positions of the control points as they were in 1983. The points have moved since then. Alaska has moved about two centimeters per year to the northwest, which means our position is about ninety centimeters northwest of where NAD 83 says it is."

"Ninety centimeters."

"Less than a meter. Not significant for our purposes. But significant for people who need sub-centimeter accuracy — geodesists, earthquake scientists, people monitoring tectonic deformation."

"The ground is always moving but the map pretends it isn't."

"The map has to pretend something is fixed. If everything moves, there's no reference. No datum. No measurement. The map is an agreement to hold certain things constant so that other things can be measured relative to them. The agreement is a fiction, but it's a necessary fiction."

Jin looked at the mountains. The mountains were moving too, rising slowly as the tectonic plates converged, eroding faster than they rose, the balance between uplift and erosion determining whether the mountains grew or shrank, and the balance had tipped toward erosion millennia ago and the Brooks Range was shrinking, losing elevation at a rate of a few tenths of a millimeter per year, which was too slow to measure with a theodolite but fast enough that the mountains Silas was mapping were not the same mountains that appeared on the 1957 quad sheet, not exactly, not at the level of precision that the instruments could achieve. The difference was trivial. But it was real.

They resumed the traverse. Silas at the theodolite, Jin at the GPS, the rhythm of the work reestablishing itself after the two-day interruption, the familiar sequence of setup, level, sight, read, record, move. They set two new stations in the morning, pushing the traverse past the point where they had stopped before the storm, into terrain that was steeper and rougher and more interesting.

Interesting, in surveying, meant difficult. It meant terrain that did not conform to the simple models — the smooth slopes, the even gradients, the predictable drainage patterns — that made contour interpolation easy. Interesting terrain had surprises: a cliff hidden behind a bench, a stream that appeared from a spring with no visible source, a ridge that turned at an unexpected angle, breaking the pattern of the adjacent ridges. Interesting terrain required more stations, more measurements, more observations, more decisions about where to put the contour lines when the data was ambiguous and the ground was rough and the map required a representation that was clear even when the reality was not.

At station eight, a mile and a quarter from the mouth, they encountered the first cliff. It was not a large cliff — perhaps forty feet high, a step in the valley wall where a resistant bed of quartzite crossed the slope — but it was vertical, and vertical terrain was the cartographer's enemy, because contour lines could not represent a vertical surface. On a vertical cliff, all the contour lines converged to a single line, and the map showed a thick brown band that meant steep but could not say how steep, could not distinguish a forty-foot cliff from a sixty-foot cliff or a cliff from a very steep slope, because the contour interval — twenty feet — was larger than the horizontal distance across the cliff face, and the lines piled on top of each other and became unreadable.

"What do you do with a cliff," Jin said, looking up at the quartzite face.

"You draw cliff symbols. Hachures. Short lines perpendicular to the contour lines, pointing downhill. They tell the map reader: the contour lines are too close together here. The terrain is steeper than the contours can show."

"So you change the symbology."

"You change the representation. The contour lines are still there, mathematically. But they're not drawn individually. They're replaced by a symbol that conveys the same information — steep — in a way that the reader can understand."

"It's a workaround."

"It's a convention. All cartography is convention. The contour line itself is a convention — an imaginary line connecting points of equal elevation. The line doesn't exist on the ground. You can't see it. You can't follow it. It's a human invention, a way of representing three-dimensional terrain on a two-dimensional surface. The cliff symbol is another convention, one that handles the case the contour line can't."

Silas set up the theodolite at the base of the cliff and measured the vertical angle to the top: eighty-three degrees. Nearly vertical. He measured the horizontal distance to the base of the cliff from the station: fourteen meters. He computed the height of the cliff: fourteen meters times the tangent of eighty-three degrees, approximately 113 meters. That couldn't be right. He rechecked. Fourteen meters was the distance to the cliff base, and the tangent of eighty-three degrees was 8.14, which gave 114 meters, which was absurd for a cliff he had estimated at forty feet. He had made an error. He rechecked the angle: eighty-three degrees was the angle from horizontal to the top of the cliff. The height was fourteen times the tangent of eighty-three degrees only if the distance was measured horizontally from a point directly below the top of the cliff, which it was not. The station was fourteen meters from the base, and the cliff leaned slightly. He needed a more careful measurement.

He took a deep breath. He re-leveled the instrument. He sighted on the base of the cliff: vertical angle minus two degrees, fifteen minutes. He sighted on the top: vertical angle plus seventy-one degrees, forty-two minutes. The angular difference was seventy-three degrees, fifty-seven minutes. At a horizontal distance of fourteen meters, the height of the cliff was fourteen times the tangent of seventy-three degrees fifty-seven minutes, which was fourteen times 3.45, which was 48.3 meters. Still too high. He was making an error in the distance. He measured the distance again with the laser rangefinder: twenty-three meters to the base, not fourteen. He had misread the first measurement. Twenty-three meters times the tangent of — no. He needed to compute it differently. The base of the cliff was at an angle of minus two degrees fifteen minutes below horizontal. The top was at plus seventy-one degrees forty-two minutes above horizontal. The slant distance to the base was twenty-three meters. The horizontal distance to the base was twenty-three times the cosine of two degrees fifteen minutes, which was twenty-two point nine eight meters, essentially twenty-three. The height of the cliff above his instrument was twenty-three times the tangent of seventy-one degrees forty-two minutes minus the tangent of negative two degrees fifteen minutes, which was —

He stopped. He was overcomplicating this. He took the rangefinder and shot the distance to the top of the cliff: twenty-six meters. He shot the distance to the base: twenty-three meters. The height was the difference in elevation between the two points, which he could compute from the slant distances and the vertical angles. Top: twenty-six meters times the sine of seventy-one degrees forty-two minutes, which was twenty-six times 0.949, which was twenty-four point seven meters. Eighty-one feet. That was too high for what he saw.

He looked at the cliff again. He had overestimated. The terrain below the cliff was sloping up toward the base, and the instrument was lower than the base, and the angles were larger than they would have been on flat ground. The cliff was perhaps forty feet high. Twelve meters. He needed to measure from the base to the top, not from the instrument to the top.

"Having trouble," Jin said.

"The geometry is tricky when the ground isn't level. I'm going to climb to the base and measure straight up."

He climbed the slope to the base of the cliff, his boots slipping on the wet tundra, and stood at the bottom of the quartzite face. The rock was grey-white, hard, fractured into blocks, the joints running vertically and horizontally like a grid. He pointed the rangefinder straight up and shot the distance to the top: twelve point one meters. Thirty-nine point seven feet. Forty feet, as he had estimated.

The estimate had been right. The instruments had given him the wrong answer because he had used them incorrectly, making assumptions about the geometry that the terrain did not support. The instruments were precise. The operator was fallible. This was always the case.

He climbed back down to the station. He recorded the cliff height in the notebook: 12.1 meters, 39.7 feet, measured vertically from base to top with laser rangefinder. He noted the bed of quartzite, the fracture pattern, the orientation of the cliff face: bearing one hundred ten degrees, facing south-southeast. This was a detail the map would not show — the bearing of the cliff — but it would help him draw the contour lines correctly, because the contour lines had to bend around the cliff in a pattern that was consistent with the cliff's orientation and the slope of the terrain above and below it.

"Margot would have painted that cliff," he thought, and then he put the thought away, not roughly but carefully, the way he put the theodolite away, in its foam-lined case, latching the lid.

They ate lunch at the base of the cliff, sitting on the rocks, looking down the valley toward the Koyukuk. The river was a silver line in the distance, and beyond it the mountains rose, grey-blue, diminishing toward the south. The clouds were breaking up, patches of blue sky appearing, the sun finding gaps and sending shafts of light down into the valley, the light moving across the tundra in visible patches, illuminating one slope and then another, the landscape shifting between light and shadow like a face shifting between expressions.

"What made you want to do this," Jin said.

"Surveying."

"Yes."

Silas unwrapped a granola bar. He chewed. He thought about the question.

"I was twenty-five," he said. "I had a geology degree from the University of Montana and no job. I applied to the USGS because they were hiring field assistants for the summer. They sent me to the Wrangells with a survey party — four of us, two surveyors and two assistants. We spent the summer mapping a river valley, the Nabesna, upper reach. I held the stadia rod. I carried the equipment. I cooked. I did the work that nobody else wanted to do."

"And you liked it."

"I liked the work. The measurement. The precision. The way the numbers turned into a map. The party chief was a man named Henderson, George Henderson, and he was fifty then and he drew the maps by hand and they were beautiful and they were accurate and I watched him draw and I thought: this is what I want to do. I want to turn a landscape into a map."

"So you stayed."

"I stayed. I became a surveyor, then a cartographer. I learned to draw. I learned the projections. I learned the instruments. I spent thirty-eight years learning, and I'm still not as good as Henderson was."

"What happened to Henderson."

"He retired in 1995. He died in 2003. His maps are in the archive in Denver."

"And yours will be."

"And mine will be."

Jin nodded. He ate his lunch. The sun moved across the valley. Silas thought about Henderson, about the way Henderson held the Rapidograph pen, the way his hand moved across the vellum with a steadiness that seemed mechanical but was not, was the product of decades of practice, of drawing thousands of contour lines on hundreds of maps, the hand trained to make the curve that the eye demanded, the curve that followed the terrain and not the ruler, the curve that was a judgment, a decision, a statement about the shape of the ground.

Henderson had told him once: "The map is a conversation between the surveyor and the terrain. The terrain speaks in elevation and slope and drainage. The surveyor listens with instruments. The map is the record of the conversation."

Silas had repeated this to Margot, and Margot had said: "That's exactly what painting is. A conversation between the painter and the light."

And he had said: "But the map is more reliable. The map is based on measurement. The painting is based on perception."

And she had said: "Perception is a measurement. It's just a measurement that includes the measurer."

He had not fully understood what she meant at the time. He understood it now, sitting on the rock at the base of the quartzite cliff, looking down the valley, seeing the light move across the tundra, feeling the wind on his face, hearing the creek, smelling the wet rock and the wet vegetation and the faint mineral smell of the quartzite, which was the smell of metamorphism, of stone that had been transformed by heat and pressure from the sandstone it had been into the quartzite it was, the transformation preserved in the crystalline structure of the rock the way a memory was preserved in the neural structure of the brain, legible to those who knew how to read it, opaque to those who did not.

Margot had known how to read it. Not the geology — she had left that to him — but the visual record, the color and texture and form that told the story of the rock's transformation without equations or analyses. She had painted quartzite in the Wrangells once, a cliff face on the Nabesna River, the same kind of cliff, grey-white, hard, fracturing into blocks, and she had caught the quality that Silas could measure but could not express — the quality of endurance, of a material that had been changed by forces beyond its control and had emerged harder, more coherent, more itself.

He had the painting. It hung in the hallway of the Fairbanks house, between the bathroom and the spare bedroom, a small oil on board, eight inches by ten, the cliff face filling the frame, the fractures rendered in precise dark lines, the surface textured with brushstrokes that mimicked the crystalline grain of the rock. Margot had given it to him for his birthday in 2012 and had said: "I painted your favorite rock."

He had said: "How did you know it was my favorite rock."

She had said: "Because you've measured it more times than you've measured our house."

This was true. He had visited the Nabesna quartzite on three separate surveys, measuring its position, its elevation, its extent, recording its presence on three separate maps at three separate scales. The rock was a constant in his professional life, a benchmark in both the literal and figurative sense, and Margot had recognized this and had painted it for him and the painting was hanging in the hallway and he passed it every day and did not look at it, the way he did not look at any of the paintings, because looking at them was a form of measurement and the measurements they returned were not distances and elevations but losses, each painting a data point in the traverse of grief.

"We should get back to work," Silas said.

They got back to work. They set three more stations in the afternoon, pushing the traverse past the cliff, into the steeper terrain above, where the valley narrowed and the creek ran faster and the ridges closed in on both sides and the sight lines were shorter and the angles were sharper and the work was harder, the theodolite and the GPS working to capture a landscape that was more complex than the lower reach, more folded, more interesting.

At station eleven, a mile and three-quarters from the mouth, Silas stopped and looked upstream. The valley curved to the north, and beyond the curve he could see the terrain steepening further, the ridges converging, the creek falling through a series of small cascades, the water white and loud. The headwaters were up there, another mile and a half, maybe two miles, in the saddle between the ridges. They would reach them in three or four days at the current pace, and then the traverse would be complete, the measurements would be finished, and they would begin the long process of reduction — reducing the data to positions, the positions to contour lines, the contour lines to a map.

The sun was low in the north, making the long shadows of the Arctic evening. The valley was gold and grey and green, the colors of the tundra in June, and the creek was silver where it ran over the gravel and white where it ran over the rocks and dark where it pooled in the eddies behind the boulders.

Silas looked at the valley and saw, for a moment, what Margot would have seen: not the geometry, not the contour lines, not the measured distances and computed elevations, but the color and the light and the shape of the shadow on the ridge, the way the gold of the sun and the grey of the rock and the green of the tundra combined into a palette that was specific to this place and this time and this angle of light, a palette that would change in an hour and change again in two hours and never be exactly this way again.

He saw it. He could not paint it. He could not capture it. He could only note it, the way he noted the other observations that fell between the data points: the color of the light, the sound of the creek, the smell of the tundra, the feeling of standing at the edge of the measured territory and looking into the unmeasured territory beyond, where the tributary continued upstream and the terrain continued upward and the landscape continued forever, unmapped, unmeasured, indifferent to the man with the theodolite and the notebook and the mechanical pencil and the thirty-eight years of training that had brought him to this point, this control point, this fixed place in the open traverse of his career.

He wrote it in the notebook. He did not know why. He wrote it because the notebook would survive and the moment would not, and because preserving moments was what he did, even the moments that did not fit the format, even the moments that the contour lines could not contain.

Station 11. Color of light: gold, low angle, northwest. Creek: silver over gravel. Ridges: grey-blue. Tundra: green, early season. Wind: north, five knots. Temperature: forty-eight degrees.

He did not write: missing Margot. He did not write: wishing she were here. He did not write: the landscape is incomplete without her way of seeing it, the way a map is incomplete without a legend, the way a position is incomplete without a datum.

He wrote the numbers instead. The angles. The distances. The elevations. The things that could be verified.