Expected Rainfall… or why you shouldn’t use the mean or standard deviation

November 17, 2016

How much rain do we usually get?

There are three common answers to this: the mean (average), the median (halfway point) and the mode (most common). For a “normal distribution” these three are all the same, but in the case of Santa Barbara’s yearly rainfall they are not.

Mean 18.0 inches
Median 15.3 inches
Mode 13.4 inches

Let us look at the rainfall distribution pattern for Santa Barbara. Here I use the horizontal axis to displaying the number of inches of rain that fell in a year (rounded down to the nearest inch) against the count of the number of years that had that much rain. (These data are available from the county public works department.)

rainfall distribution

Santa Barbara’s historical rainfall data stretches back (patchily) to 1868. All in all there are 145 years of data (as of Nov 2016).

The Mode

The first problem with using the mode is calculating it. SB’s yearly rainfall is reported in hundredths of an inch. This level of precision means it is extremely unlikely that any two years will have exactly the same amount of rainfall, so there is no amount that occurs most frequently.

That, of course, is easily solved by dropping precision and just looking at the number of inches that fell in a year (as I have done in the graph above). But there’s a hidden problem with this method. I lumped years together by having a series of intervals that start at 0. But suppose I started at .5 inches instead? If this were a normal distribution that wouldn’t make much difference, but here…

rainfall distribution offset

The distribution looks quite different now. That tends to argue against the utility of the mode.

Probably if I had several thousands of years of data (and the climate didn’t change in that period) much of this variation would smooth out. But I’ve only got 145 years, and the climate is so variable that this isn’t enough.

Now let’s compare our actual distribution to a normal distribution centered on the mode and with a standard deviation set to the square root of the variation about the mode.

rainfalldistributionwithnormal

They do not look alike. Part of the problem is that there can never be less than no rain, but the normal distribution acts is if there could be. The variation less than the mode is much less than the variation above the mode (a range of 9 inches below, but 35 inches above).

The mechanism I choose to calculate the mode is to create a series of bins, each one inch wide and offset from one another by .1 inches. So the first bin would count all years that had between [0,1) inches, the second bin [.1,1.1), and so forth. Clearly any give year will end up in 10 bins rather than just one (but that’s fine). Then I look for the bin with the most number of years. This method suggests that the mode is at 13.4 inches — or in the bin counting years where the rainfall was between [12.9,13.9) inches.

But this does not produce stable results. Below is a graph showing the mean (blue), median (green), mode (red) of accumulated rainfall as the year progresses (rain years in Santa Barbara start in September).
Mean, Median, Mode (year to date)
(Click on the graph to see a more legible version)

The mean describes a very smooth curve. The median has small bumps, but is pretty smooth. On the other hand the mode dances all over the place with a 10 inch jump in April – from 18 inches down to 8.

Again if I had a much larger sample, presumably these fluctuations would calm a bit, but for the noisy mid-sized dataset I have available the mode does not provide a useful tool.

The Mean

The average is what we usually think of as the best metric for looking at the mid-point of a distribution. But with Santa Barbara’s rainfall it doesn’t work very well.

Because we occasionally get 45+ inches of rain this distorts the mean in a way that is not useful when trying to figure out what a normal year looks like. In fact about 61% of years have less rainfall than the average, which makes the average seem rather unusual.
percentiles

The Standard Deviation

The standard deviation is defined as the square root of the variation about the mean (or as the variation about the point which minimizes the variation — which happens to be the mean).

As the mean isn’t useful to us, one might presume that the standard deviation is also not much use.

However that’s to some extent a question of semantics, we could examine the square root of the variation about the median instead.

Here we once again bump up against the asymmetry of our distribution. There is simply more variation above the median than there is below. Calculating the square root of the variation for rainfall below the median gives a value of 4.5 inches, while that above the median is 11.6, and the combined value is 8.8.

So perhaps we should look at negative and positive variation about the median instead of one combined number?
pos/neg variation about median
(the median is the dark green line, the light green solid lines show the positive and negative “standard deviation”s from the median, and the dashed lines show percentiles)

The negative 1 “standard deviation” line tracks close to the 15th percentile, and the positive 1 “standard deviation line tracks close to the 85th percentile. In a normal distribution the 1 standard deviation lines should track the 15.9th percentile and the 84.1th percentile. So my peculiar definition seems as if would describe the variations of this distribution comparably to the standard definition for a normal distribution.

But it’s so complicated to explain and use, that for most purposes using the median with percentile lines is probably better.

A better viewpoint

My friend Dave suggested looking at the logarithms of the rainfall to see if that revealed a better pattern. And it does.
rainfalldistributionlog
It still isn’t perfect, but the mean and median have moved closer together and the standard deviation is similar on both sides of the mean. The mode is still in the wrong place for a normal distribution.

Mean 16.3 inches
Median 15.3 inches
Mode 13.5 inches

Rey Fire Closure

September 11, 2016

I went for a run out to Mono today, thinking I might run along Camuesa Rd a bit to see if I could reach the edge of the burn area for the Rey Fire. And, of course, I checked with Inciweb and the Los Padres website beforehand to see if there were any closures I needed to worry about. Both of these list a closure order for the Rey Fire that went into effect 25 August and “The order will expire when the Rey Fire is fully contained and controlled.”
° Los Padres
° Inciweb
Containment was officially achieved on Monday 5 Sept.
° Rey Fire, Final Update (Inciweb)

Therefore it seemed to me that there were no bars to examining the Rey Fire.

However when I reached the end of Cold Spring trail (about 20ft from the Mono parking lot). I found this sign.
Closure Sign
Now Mono is about 2 miles from the Rey Fire so even if there were a closure I did not expect Mono to be involved.

So I looked harder and found something else:
° Closure order (Inciweb)
Which claims the area will be closed until 1 Dec 2016.

So DAMN IT if it’s closed until December why claim all over the place that it opens on 5 September?

Take care of the sounds…

September 8, 2016

Louis Carroll’s advice for writing poetry was “Take care of the sense and the sounds will take care of themselves.” (An adaption of an earlier phase: “Take care of the pence and the pounds will take care of themselves).

But sometimes I have no sense to take care of.

I was out running the other day and noticed that although it was pleasantly cool in the shade it was rather hot in the sun. And a little rhyme popped into my head: “The sun is hot, the air is not.”

I posted this of FB and my brother asked for the rest of the poem.

Of course there was none.

But I went on another run to figure it out. Cot, dot, got, jot, lot… and then Aeroflot popped into my mind.

The sun is hot,
The air is not.
I seem to think that quite a lot
I should fly on Aeroflot.

So that was the first verse of the rest of the poem. Bit like some styles of improv. Take care of the sounds and the nonsense will take care of itself!

But at this point a little sense had to creep in too.

Fly to where the sun is cool,

Um… boules, fool, ghoul, joule, moules, mule! rule, stool

Fly to where the sun is cool,
There I’ll buy a lovely mule.
Hop it up upon a stool,
Bind its legs to make it drool.

Then the question was what to do with the mule or the drool, or even the stool. Well, I could catch the drool in a pail and see where that lead.

Catch the drool within a pail
Add the gris of one big whale
With a little bit of ale
Bind with mucus from a snail
Stir it with an iron nail.

Ale might cause it to ferment into… well into cheese.

Hang it high within the trees
Churn it up to make some cheese
Then I will be at my ease
Won’t you join me, if you please?

But you can’t just ask someone over for cheese, you’d want at least crackers too. What kind of cheese sort of drools?

Crackers now for droolly brie

Probably a drink too. “Tea”. Of course.

When it’s steeped I’ll serve mule tea

I suspect these substances won’t smell too good. Best keep them downwind.

Set them down well to the lee,
Then a toast to you and me!

But the tea had to come from somewhere… I need a new verse. I guess half the drool goes to make tea, and half to make brie. I can’t put it in a pail, but I could use a hat. Suess has a cat in a hat. Carroll has a “grin without a cat”. Macbeth’s witches use “something of bat.” Slices of lemon traditionally go with tea. And tea needs to steep…

Some for this and some for that
Half the drool goes in a hat.
Pinch of tea and grin of cat.
Lemon slice and what of bat.
Let it steep upon a mat.

The name of the poem was going to be “Mule Drool Cheese”, but at this point it seemed more appropriate to call it “Mule Drool Tea” (in the sense of a meal that could include both tea and brie). But perhaps I should call the name Whale Ale Tale

Let’s see…
When the run was over I put it all together and saw it needed some revision. (Well, I’d been revising all along, but it was easier to see what needed it now with it all spread out in one place (I don’t know how Homer managed)). I needed to look up Macbeth to find what of bat went into the cauldron…

Mule Drool Tea

The sun is hot
The air is not.
I seem to think that quite a lot
I should fly on Aeroflot.

Fly to where the sun is cool,
There I’ll buy a lovely mule.
Hop it up upon a stool,
Bind its legs to make it drool.

Drool for this and drool for that
Half the drool goes in a hat.
Pinch of tea and grin of cat.
Lemon slice and wool of bat.
Let it steep upon a mat.

Rest goes in a nice big pail
Add a little bit of ale
Bind with mucus from a snail
Stir it with an iron nail.

Set it out to catch a breeze
Churn it up to make some cheese
Soon you’ll find me at my ease
Won’t you join me, if you please?

Now all’s done I’ll serve mule tea
Crackers too, for droolly brie.
Set them down well to the lee,
Then a toast to you and me!

Anyone for tea?


On my next run, a few days later…

The sun is hot
The air is not.
I seem to think that quite a lot
I should fly on Aeroflot.

Far away where sun’s in fog,
Shall I find a droolly dog?
Just to take him on a jog.
Bet he’ll leap right in a bog.

Then to chase a spotted skunk
Doesn’t care that he’s been stunk
But it sends me in a funk
Back to bog for a new dunk?

Muddy paws and skunky trace,
Dog leaps up to lick my face.
Dog thinks this is heaven’s grace,
I react with some distaste.

Hydrogen per oxygen
Soda and then detergen
Wash the dog within his den
Dry him out and smell him then
Skunky smell is there again.

Next time shall I bring a leash?
Make frogs safe within their niche.

High Shoals Falls

August 12, 2016

It had rained hard the night before, but by 11 it was partly sunny and I persuaded my brother and his family to go hiking with me for a picnic at High Shoals Falls. None of us had ever been there, but it was close enough and was supposed to be impressive. So we bundled into the car and drove off.

The trail is off Indian Grave Gap Road, a dirt forest service track not far from Unicoi Gap.

The road was a bit more run down than I had anticipated. First we had to ford High Shoals Creek, and then go up a rutted road for a mile or so.

It also proved more popular than I had anticipated and the small parking area was full, so we parked at the side of the road and walked back. It began to spit rain as we walked, but too lightly to worry about.

The trail itself is only a mile or so long, rather steeply downhill.

It began to rain harder, but we decided to press on.

After a quarter mile or so we were in a deluge and we turned and went back.

By the time we reached the highway it had, of course, stopped. I considered turning back, but I was soaked and it just didn’t appeal.


The next morning I decided to try it differently. I couldn’t face asking people to go again. I set out alone to Unicoi Gap, and ran up Rocky Mountain, and down the trail to Indian Grave Gap Rd. and then down the road to the trail head.

No rain this day. Fewer cars too.

On the way down I found some Lungwort Lichen, which I’d never seen before.
Lungwort

There are actually two waterfalls on the trail. The first is Blue Hole Falls (the water drops into a deep pool which is supposed to be blue, though it did not look so to me). Clicking on the image below loads a video.
Blue Hole Falls

Not far beyond that is High Shoals Falls itself
High Shoals Falls

When I researched the trail I read something on the net from the Atlanta Trails group, but I also read a 40 year old trail guide of my father’s. This guide indicated that the trail made a loop, and at the trail head there had indeed been two trails, so I took a side trail that I hoped would lead back to the start.

It didn’t. It lead me to someone’s back yard. Oops.

I turned back, and passed a blooming Rhododendron. This is surprising, because I think of them as blooming in June.
Rhododendron

When I got back to the trailhead I took the other route, but it was clearly not maintained and soon degenerated into nothing. Oh well. Best not to rely on 40 year old trail guides.

I ran back up the road and found an interesting Yellow Fringed Orchid, which I don’t believe I’ve seen before.
orchid

At Indian Grave Gap itself I turned back onto the appalachian trail to run up to the top of Tray Mtn. and back down to Unicoi Gap.

Flowers on Nine Trails

March 25, 2016

My best guess for the flowers on the Nine Trails course tomorrow…


Asparagaceae

Dichelostemma capitatum
blue dicks

JanJuly

Melanthiaceae

Toxicoscordion fremontii
Star Lily

FebJuly

Poaceae

Avena barbata
Slender Wild Oat

MarMay

Apiaceae

Torilis arvensis
Field Hedge Parsley

March
Sanicula arguta
Sharp-Toothed Sanicle

FebMay
Sanicula crassicaulis
Pacific Sanicle

FebMay
Apiastrum angustifolium
Wild Celery

MarMay
Tauschia arguta
southern tauscia

JanJune

Asteraceae

Cotula australis
Southern Brass Buttons

JanJune
Matricaria discoidea
pineapple weed

FebJune
Baccharis salicifolia
Mulefat

JulyMay
Logfia filaginoides
California Cottonrose

FebMar
Pseudognaphalium biolettii
twocolor cudweed

AugMay
Bidens pilosa
Beggar’s ticks

All year
Encelia californica
Bush sunflower

All year
Venegasia carpesioides
canyon sunflower

All year
Senecio vulgaris
Old man of Spring

DecMay
Centaurea solstitialis
Yellow star thistle

MarDec
S. asper
Prickly sow-thistle

DecJuly
Uropappus lindleyi
Silver Puffs

MarJune

Adoxaceae

Sambucus nigra-caerulea
Blue Elderberry

All year

Apocynaceae

Vinca major
periwinkle

All year

Rubiaceae

Galium porrigens
graceful bedstraw

FebAug

Lamiaceae

Stachys rigida
woodmint

DecOct
Salvia mellifera
black sage

DecSep
Salvia spathacea
hummingbirdsage

NovJuly

Oleaceae

Fraxinus dipetala
Flowering Ash

FebApr

Orobanchaceae

Castilleja foliolosa
Woolly Indian Paintbrush

JanJuly

Phrymaceae

Mimulus aurantiacus
sticky monkeyflower

DecSep

Plantaginaceae

Antirrhinum kelloggii
climbing snapdragon

FebJune
Collinsia heterophylla
Chinese Houses

FebJuly

Scrophulariaceae

Scrophularia californica
California Figwort

JanOct

Convolvulaceae

Calystegia macrostegia
Coastal Morning Glory

All year

Solanaceae

Solanum douglasii
white nightshade

All year
Solanum xanti
purple nightshade

All year

Boraginaceae

Amsinckia menziesii
common Fiddleneck

FebJune
Cryptantha sp.
popcornflower

JanAug
Eriodictyon crassifolium
Bicolored Yerba Santa

MarApr
Eucrypta chrysanthemifolia
spotted hideseed

JanJuly
Phacelia grandiflora
large flowered phacelia

FebAug
Phacelia viscida-albiflora
white Sticky Phacelia

JanJuly
Pholistoma auritum
fiesta flower

JanJune

Loasaceae

Mentzelia micrantha
Stick-Leaf

January

Ericaceae

Arctostaphylos glandulosa
Eastwood manzanita

JanMay
Comarostaphylis diversifolia
Summer Holly

FebJuly

Polemoniaceae

Gilia capitata
Globe gilia

FebJuly
Leptodactylon californicum
Prickly-phlox

JanJuly

Grossulariaceae

Ribes speciosum
Fuchsia-flowered gooseberry

DecApr

Saxifragaceae

Lithophragma cymbalaria
Mission Star

FebMay
Micranthes californica
California Saxifrage

FebMay

Amaranthaceae

Chenopodium murale
Nettle-leaved goosefoot

DecJune

Caryophyllaceae

Stellaria media
chickweed

DecJune

Montiaceae

Calandrinia menziesii
Red-maids

JanMay
Claytonia perfoliata
miner’s lettuce

JanJune

Nyctaginaceae

Mirabilis laevis
Wishbone bush

DecJuly

Brassicaceae

Brassica nigra
black mustard

DecJuly
Capsella bursa-pastoris
Shepherd’s purse

JanMay
Cardamine californica
milk maids

DecMay
Cardamine oligosperma
bittercress

JanApr
Caulanthus lasiophyllus
California mustard

FebJune
Hirschfeldia incana
Summer Mustard

All year
Sisymbrium officinale
Hedge Mustard

FebJune
Thysanocarpus curvipes
Fringe Pod

FebMay

Geraniaceae

Erodium botrys
long-beaked storksbill

JanSep
Erodium cicutarium
Red-stemmed storksbill

DecAug
Geranium dissectum
cut-leaved geranium

FebMay

Cistaceae

Helianthemum scoparium
Common Rush-Rose

All year

Onagraceae

C. hirtella
Hairy suncup

FebApr
Eulobus californicus
California suncup

JanAug

Anacardiaceae

Rhus integrifolia
Lemonade Berry

SepApr
Toxicodendron diversilobum
poison oak

DecMay

Cucurbitaceae

Marah fabaceus
common manroot

NovMay
Marah macrocarpus
Chilicothe

JanMar

Fabaceae

Lathyrus vestitus
common pacific pea

SepJune
Lupinus hirsutissimus
stinging lupine

JanJune
Lupinus nanus
sky lupine

FebJune
Lupinus succulentus
arroyo lupine

DecJuly
Acmispon glaber
Deerweed

All year
Acmispon grandiflorus
Chaparral lotus

DecJune
Acmispon maritimus
Coastal Lotus

JanJuly
Medicago polymorpha
Bur Clover

DecJune
Melilotus indicus
yellow sweet clover

SepJuly

Fagaceae

Quercus agrifolia
Coast live oak

JanMay

Rhamnaceae

Ceanothus spinosus
Greenbark

DecAug
Ceanothus thyrsiflorus
Blue Bush

DecJune
Rhamnus crocea
Spiny Redberry

FebMar
Rhamnus ilicifolia
Holly-leaved Redberry

FebMay

Rosaceae

Cercocarpus betuloides
Mountain Mahogany

FebJune
Prunus ilicifolia
Holly-leaved cherry

JanJune
Rubus ursinus
california blackberry

DecAug

Euphorbiaceae

Ricinus communis
Castor bean

All year

Oxalidaceae

Oxalis corniculata
Yellow Sorrel

DecJune
Oxalis pes-caprae
sourgrass

NovJune

Papaveraceae

Dendromecon rigida
Bush poppy

All year
Eschscholzia caespitosa
Tufted Poppy

JanSep
Fumaria parviflora
fine leaved fumitory

JanApr

Ranunculaceae

Clematis lasiantha
wild clematis

JanMay
Delphinium parryi
purple larkspur

FebJune
Ranunculus californicus
California Buttercup

JanMay
Thalictrum fendleri
Fendler’s Meadow-rue

FebMay

Aytoniaceae

Asterella
California Asterella

Dryopteridaceae

Dryopteris
Coastal Wood Fern

Polypodiaceae

Polypodium
California Polypody

Blechnaceae

Woodwardia
Giant Chain Fern
Elgaria
California Aligator Lizard

Nymphalidae

Euphydryas
Variable Checkerspot

Papilionidae

Papilio
Western Tiger Swallowtail

Arionidae

Ariolimax
Pacific Banana Slug

The Waterfall on Gidney Creek

March 9, 2016

Gidney Creek has its headwaters near the little bench on the backside of Cold Spring trail (the one about half a mile down from Camino Cielo with the watertrough beside it). Gidney flows down, roughly parallel to the trail until Forbush Camp at which point it turns west, out of my ken and eventually flows into Gibraltar Reservoir just east of the back side of Gibraltar Rd.

Forbush sits on a divide and on a wet enough day there’s a little spring in the meadow, perhaps 100 yards from Gidney but which flows east down Forbush Canyon to Cottam meadow where it merges with Blue Creek. It’s kind of neat to see a place where two different watersheds diverge.

Gidney Map

Perhaps two thirds of the way down to Forbush there’s a spot where you can turn and look back up the canyon, and if you are lucky you’ll see a waterfall. This doesn’t happen very often, there must be a good flow down Gidney Creek, and I hadn’t seen it for years.

But I saw it yesterday.

There was water flowing near the bench, and I could hear the stream intermittently as I ran downhill, so when I got to the magic spot I turned and looked back and there it was.

It’s hard to get a good look at it because you can’t even see it except at this one spot, and you’re fairly far away there. It’s even harder to take a good picture because, looking north, you are always looking into the sun, and because the waterfall itself is in a shaded nook surrounded by sun.

Maybe if I had a stronger zoom and could get rid of the bright background… But that camera is too heavy to run with.

GidWaterfall1

GidWaterfall2

I ran on down to the Grotto, and then back. The waterfall was still flowing, and I thought what a pity it was not to be able to take a better picture (at this hour the view was even worse because there was more light nearby but still none on the falls.

As I plodded up the trail I was tempted to go down to the creek and look at the falls from close up. After all, who knew when they’d next be running? Eventually I got to the place on the trail which I estimated to be about the closest I could get to the falls.

I cast about and found a spot where there was an opening in the brush and plunged down.

According to my GPS the horizontal distance between the place I left the trail and the creekbed where I ended up is about 65 meters (as the rock plummets). The vertical distance is about 100 meters (take this with a grain of salt, GPS altitudes are not very accurate). Or about a 50° incline on average. It’s steep.

For a while the open space continued, but then the chaparral closed in. Chaparral has lots of tough wiry branches that tangle up with each other. In theory there’s an open space underneath, but not here — too close to the creek probably.

Oh, and it looks as if about half the wiry branches are actually poison oak vines. I don’t usually worry much about poison oak, but then I don’t usually push through thickets of the stuff either.

The chaparral liked my cap too, and kept pulling it off my head. Eventually I just carried it in my hand (which meant one hand less for climbing with).

After I’d been going for a while I realized that I was being stupid. If I had an accident no one would ever find me down here. Cold Spring trail is fairly well traveled (even the back side) and there were people camped at Forbush, so if I had problems on trail someone would find me, but no one would come down here.

Still, I was more than halfway down. It seemed a shame not to continue now.

I ended up about 10 feet above the stream with a fairly vertical drop to reach it. I decided to leave my cap on the rock here while I turned all my hands to climbing. If going down was difficult, how was I going to get up? I decided to ignore that question.

I managed to slither down in one piece.

It took about 15 minutes to cover those 65 meters.

The stream was in a deep channel with closed canopy forest above it. It began to seem unlikely that I’d actually be able to see the waterfall from this angle… but having come so far (or at least having spent so much effort to move such a short distance) it seemed silly not to go and look.

The going was easier now, no plants to hold me back, but the rocks beside the stream were slippery and the stream was steep. I was below the waterfall and had another few decameters to go upstream.

GidCreek

If I had been willing to sit still, it would have been pretty.

Eventually I could see the falls peeping through the trees

GidThroughShrubs

And finally I pulled myself into the open area around the falls. A little shallow pool. A very thin stream of water, but it looked an impressive drop. Hmm.

I wonder…

This cascade seems awfully well screened by trees, perhaps it’s not the fall I saw from the trail, maybe there’s another one right above it?

But I have absolutely no interest in trying to climb higher. This cascade is quite enough for me.

GidneyFalls

I turn back.

Looking, essentially down, the way back looks steep. And slippery.

GidLookingDown

But I manage it, though I do worry a little about finding my route up again. And even that I find eventually.

I go a little below the precipitous drop I took on the way down and find an alternate route up.

I recover my hat.

I follow my footsteps up for a while, but after a bit I lose them. Oh well, I just have to push my way up, I can’t really get lost.

Eventually I reach a spot where I can see, and find the trail to my left and below me, so now I head downward (through a poison oak tangle) and eventually reach the trail.

I’m glad I saw that waterfall, but I don’t think I need to do that ever again.


Next time I ran the trail, nine days later, the waterfall had gone.GidNoFall

Christmas Run

December 25, 2015

Every year I plan to do a run on Christmas Day. Or a bike ride. It’s a peaceful time to be out.

I was thinking I would run from my door to Upper Oso via Arroyo Burro trail, not Hwy 154. I thought it would be considerably shorter than the highway (though a good deal slower than driving).

About a week in advance the weather forecast showed a big rain on Christmas day, so I started thinking I might go out Christmas Eve instead. Then the forecast wiggled around and Christmas Eve was also supposed to be rainy. So I decided I’d do my long run on the 22nd.

rainbowOf course when the morning of the 22nd dawned there was suddenly a 20% chance of rain starting at 9:15. Well, 20% didn’t seem likely. I set out a little after 7, I saw a rainbow and then it started to drizzle.

So much for the forecast.

With the drought there is almost nothing blooming now, so I had my eye out for lichens. Lichens react quickly to the rain and often change color — the outer fungal layer draws back revealing the more colorful algal layer underneath.

I was also looking for fern fiddleheads and liverwort thalli. Last year they were all over the place by now, but this year I’ve just seen a few starts which have since died back.

When I got to the Jesusita mudbank, the mud had reached the point of being slippery, but not yet of being sticky. So it didn’t stick to my shoes, but did make the climb difficult. Still, it wasn’t really cold and the rain was barely noticeable, so after a bit I thought about taking off a layer, but I waited a little longer.

Drizzle
Once I got out of the canyon containing San Roque Creek I felt the wind, which was quite strong and suddenly chilly. I decided I’d keep all my layers on.

I found a wild cucumber vine in bloom, the first I’ve seen this year (and about a month later than I usually see the first). That was an encouraging start, but it was the only winter bloom I saw that day.

Arroyo Burro trail is quite overgrown for about a mile after the 420 rock, but after that there’s a little valley with a nice stream (which had no water in it) and the climb becomes more scenic. This is also the boundary of the Jesusita burn and the vegetation becomes older (probably unburnt since the Coyote Fire in the 60s). Anyway I start to see lichens now.

BigpodLichenThe rain has brought out the yellow in the goldspeck lichen (¿Candelariella rosulans?) which covers the trunks of the shrubs, here on bigpod Ceanothus.

As I climbed up to the pass with Camino Cielo the wind picked up. It is usually more intense on the ridgeline and when it is blustery below it is very windy above… And the wind made the rain seem worse. Or maybe it was worse. Anyway I was soaked and cold.

And my glasses fogged up. I was in a cloud here, so it was naturally foggy too. I couldn’t see where I was going and ended up on a side trail I’d never known was there. I didn’t realize it until I came to the water tank that I also didn’t know about.

So I scrubbed off my glasses, but that didn’t help I still couldn’t see. Eventually I realized that the road had to be downhill of where I was, so down I went. And got across.

The shooting range is still closed because of fire danger. This is a comfort when you run past a range in dense fog.

And down the other side, and out of the wind and fog. I took out a cliff bar, and had to use my mouth to tear it open.

ThalliThe backside of the mountains must have had more rain than the front, I found lots of Polypody fiddleheads, and some Asterella thalli. Neither of these have I seen in the front country this year, though I have seen both on other back country trails.

But there wasn’t anything blooming here.

Further down the trail there are Valley Oaks (Quercus lobata), a species not seen in the front country and I was interested if they had a similar lichen load to the Coast Live Oak of the front country. The problem is that lichens prefer branches in oaks (rather than trunks) and Valley Oaks tend to be tall. Much taller than Coast Live Oaks. Generally too tall for me to see their branches.

But one nice thing about high winds is that you get broken branches lying on the ground
Branch
And here on this one small bit of Oak branch I’ve got at least four different lichens. In the upper right the bushy whitish thing is Oakmoss Lichen (Evernia prunastri), in the middle left the bushy orange thing with the weird circles is Orange Bush Lichen (Teloschistes flavicans), the small yellow areas are probably some kind of Goldspeck Lichen (Candelariella sp.), and the grey flaky patches are probably Common Ruffled Lichen (Parmotrema perlatum). This one little stub of a stick has just about everything I was hoping to see.

FordAt the bottom of Arroyo Burro the mud had turned sticky as well as slippery and I had to run off the trail if I wanted to stay upright. The rain was slackening now, and when I got to the river there wasn’t even a puddle visible in the ford.

It is 12 miles from my house to Paradise Rd. 13.5 miles to Lower Oso, and 14.2 to Upper Oso. At least according to my watch.

When it was time for a bite to eat I found my fingers too cold to open the package. They were too weak even to pull against the grip of my mouth. I pressed my fingers against my thighs in an attempt to warm them, and after about 5 minutes I was able to eat.

On the way back I avoided the worst of the mud but taking an alternate route, but even when I couldn’t avoid it, it seemed much less of a bother going up than coming down.

As I neared the top I felt the wind picking up again, occasional drizzles of rain and my glasses were fogging, so, although it wasn’t time to eat yet, I tore open a packet in case my hands numbed out again.

At the top, I was running with the wind (so warmer) and the fog wasn’t as bad as it had been, though hardly clear. But my hands were warm enough that I could have opened my food package.
Foggy Camino Cielo

A half an hour later I had ducked under the cloud cover and weak sunlight was peaking through, and when I got to the overgrown section it was almost sunny.
Clouds

When I reached the trail bottom and looked back…
NoFog
it’s quite a different view from what I saw 5 hours earlier.

Although I spent about three hours in continuous rain, with a second light drizzle when I got back to the ridgeline, the county’s downtown rain gauge reported no precipitation at all. Looking at how the rainfall went across the county, it looks as if the storm was stronger farther north but petered out when it got to the mountains. So the downtown forecast was somewhat accurate, rain was unlikely there, I had just assumed that meant rain would also be unlikely 5 miles away, but that was not the case.

And, of course, when Christmas did roll around there was absolutely no chance of rain — bright sunny skies, high winds, no clouds. So I biked out to Refugio and then up Refugio Rd.

I always forget just how steep Refugio Road is, and how much steeper it seems when it follows a ~20 mile ride just to get to the base. And the wind came blowing down the canyon too.

I wanted to see if the refugio manzanitas were in bloom. This is a rare species that only grows between Refugio and Gaviota. I met it for the first time last January, but I suspected it would be blooming earlier than that, so I went for a look.

There are a few spots on Refugio Rd. where it grows, and more on Camino Ciello. I didn’t want to have to climb all the way up to the top, so at the first patch I stopped and looked hard at the plants. Two were in bloom, so I didn’t have to go any further.

One had old flowers dropped underneath it so it had clearly been blooming for a while. Next year I’ll need to check even earlier.

Pause or No Pause

December 15, 2015

Has there been a “pause” in Global Warming since 1998?

I contend that there has not, but it really depends on how you define “pause”. My contention is that definitions which show a pause are not statistically useful.

[My analysis is based on NASA’s Global Land-Ocean Temperature Index which may be obtained from here and is described here. Other datasets exist which may show slightly different results. Data extracted on 13 Dec 2015 (so this does not include a full year of 2015 and my analysis stops at 2014)]

So let’s start with the obvious. When was the last time the temperature was at the level of 1998? Why in 2012. And because these data are noisy let’s be a little generous and ask instead: When was the last time the temperature was within .04°C of 1998? In 2013. Since the last year of full data was 2014 you might say “Hey, basically the temperature hasn’t changed at all since 1998.” and draw a flat line on the graph from 1998 to now (or at least to 2013).
Paused

But this is a statistically poor technique. I mean if you look at the scatter plot it’s pretty clear a horizontal line doesn’t fit the points well. It’s sort of saying “Let’s assume there is no trend and see what we get.” A much better way of proving a pause is to say “Let’s assume there is a trend and prove that that trend is zero.”

The data are noisy. You can’t just draw a line from start to end and say “This is what is happening.” The simplest way to extract a trend from noisy data is to apply a linear regression found by least squares — that is to find the line which minimizes the sum of squares of the errors — the error being the difference between what the regression line predicts for the temperature of a year and the actual temperature reading.

If there be no trend, if global warming have paused, then the slope of the line will be near zero. It won’t be exactly zero because the data are noisy.

If we look at each year since 1998 and generate a line based on the data from 1998 to that year then if warming were paused we’d expect that about half the lines would have a positive slope and half a negative one.

Slopes of the regression line for each year since 1998 in °C/year
2000: -.105 2001: -.024 2002: +.013 2003: +.020
2004: +.013 2005: +.021 2006: +.020 2007: +.019
2008: +.012 2009: +.012 2010: +.014 2011: +.012
2012: +.010 2013: +.010 2014: +.011

But that’s not what we see. Instead we see almost no lines with negative slope (and those all in the years immediately following 1998). Instead the slopes roughly average .012°C/year, or about the slope found between 1960 and 1984.
NoPause1998

In other words, the data do NOT show a pause, they show an increase comparable to increase from before the 1990s. The naughties are not paused, they are not anomalous, they are in line with the average over the last half century. It is the nineties which are odd.

But there is another statistical mistake in the claim of a “pause”. This is something called “Data Mining”. The only reason anyone might think there was a pause is because 1998 was an extraordinarily hot year for the time. If you base your data in 1998 you have to wait for a long time for the trend to catch up to the noise.

But if you look at the next year, 1999, there is no way anyone could find a pause in the data. Since 1999 temperatures have simply increased. This, by the way, is data mining in the reverse direction since 1999 was (for the time) a particularly cold year.

Slopes of the regression line for each year since 1999 in °C/year
2001: +.065 2002: +.076 2003: +.061
2004: +.038 2005: +.041 2006: +.034 2007: +.030
2008: +.020 2009: +.019 2010: +.020 2011: +.016
2012: +.014 2013: +.013 2014: +.014

Since we are only data-mining the start time if you wait long enough both trends will converge toward the same slope.

I have been told that the temperature change since 1998 is not statistically significant since it is less than two standard deviations. In a way, this is true, (ΔT(2014-1998): .11°C, σ: .067°C) but it ignores several things. First these years do not stand alone, they are a continuation a trend that started (at least) in 1960 and the change since 1960 is significant. And second 1998 is data-mining. If we pick 1999 as a base year then ΔT(2014-1999): .32°C, σ: .061°C, and the change is about 5σ which is very significant.

So I think the following graph is a much better way of looking at the data. There is no pause. Just three regions where the temperature increases, and in the two regions 1960-1984, 1999-2014 the temperature increases at about the same rate, while in one, 1986-1998, the temperature increases much faster.

Linear regression lines
1960-1984 T=.012*(year-1998)+14.355°C
1985-1998 T=.021*(year-1998)+14.488°C
1999-2014 T=.014*(year-1998)+14.492°C

Nopause

My claim is that there has been no pause. Attempts to see a pause are based on two statistical mistakes, the first being data-mining, and the second being the belief that drawing line between two noisy datapoints is meaningful.

This analysis is based on statistics I learned in 10th grade. It isn’t hard.

El Niño?

December 15, 2015

Where is it?

Or rather, where is the rain it is supposed to bring us?

This rain year (Sept-Aug) has been the 22th driest in the 1 Sept-15 Dec period (out of 146 years recorded), and of those 21 only 3 had above average rainfall. But one of those 3, 1977-1978, had 42.34 inches.

So it’s not unprecedented that we’ll still have a wet year, just unlikely.

A fortnight ago the Independent ran an article claiming that in the big El Niño year of 1997-1998 rainfall in SB was delayed from its usual pattern and the big storms didn’t start until January. That was consoling. But then Weather Underground provided data from all the big El Niño years for SF and LA (but not SB) which said exactly the opposite.

So I grabbed the rainfall data provided by the county from their recording station downtown, and extracted the relevant points.

SB Rainfall Data at County Building
(in inches)
Year Sept Oct Nov 1-15 Dec 1 Sep-15 Dec
1957 0.00 1.41 0.51 2.95 4.87
1965 0.09 0.00 7.86 0.53 8.48
1972 0.00 0.04 5.69 0.73 6.46
1982 2.07 0.63 5.18 0.22 8.10
1997 0.05 0.15 4.30 5.78 10.28
2015 0.10 0.26 0.13 0.19 0.68
Average
1867-2015
0.27 0.69 1.52 1.24 3.72

So the data I can find contradicts the Independent’s claim. In all prior “Big” El Niño years there was rainfall above the long term average at this point of the year at downtown SB.

The general consensus is that we will get a lot of rain this year — eventually.

But I worry.

The current definition of a big El Niño was not one that could be detected until (relatively) recently, thus we only have records for 6 big El Niño events. That’s not a big sample size…

This is supposed to be a bigger El Niño than any recorded, maybe we don’t get rain with exceptionally big El Niños. This is a warmer year than ever before, maybe that means something too… Weather is always random, maybe this year we’re just unlucky.

Paris — COP 21

December 12, 2015

So we have a new climate agreement out of Paris today.

Is it adequate? No.
Can it become adequate? Perhaps. We must hope so. It contains mechanisms within it to ratchet up the commitments as time goes on. Will people? Probably. Will it be enough?
Will people enact it? It is said to be “a legal instrument” which, I think, means the US Senate must approve it as a treaty. Which seems unlikely. So I doubt the US will agree to it. But perhaps there is some wiggle room I am not seeing.
Ah. Only some parts are legally-binding (the emissions commitments are not), and those parts which are binding are technically extensions to an existing treaty and, as such, do not require Senate approval. Tricky. [WeatherUnderground]
Will people live up to it? Let’s hope so.
However on the day after signing India reaffirmed that it intended to double its coal output (India is currently the 4th largest emitter. [Guardian]

What is adequate?

We really have no idea.

Back in the 1990s the best science suggested that a temperature rise of 2°C above pre-industrial temperatures would probably not lead to ecological catastrophe. And this has been the stated goal since then.

This year the average global surface temperature is expected to breach the 1°C mark and we are already seeming effects that 25 years ago were predicted for 2°C. In other words it is no longer possible to avoid catastrophic climate change. We are already too late. [Kevin Anderson]

For instance parts of the antarctic ice sheet have already passed a tipping point and entered a period of irreversible melting. The irreversible loss of the Amundsen ice sheet alone will raise sea-level by 1 meter in the next two centuries. [Guardian] The arctic ice cap is melting faster than expected, destroying ecosystems and the lives of humans dependent on those ecosystems. The incidence of “extreme” weather events is higher than expected.

To some extent this has been recognized at COP21 and the text now includes the aspiration to hold the level of warming to 1.5°C. However this has not resulted in anyone making a further commitment to reduce their emissions.

The commitments on the table are estimated to produce an increase somewhere between 2.7°C and 4°C, depending on whose climate models one looks at.

Some basic science

The earth has a large thermal mass. This means that it heats up slowly. Even if we were to stop producing any CO₂ (from non-ecosystem sources) the earth’s temperature would continue to increase for many decades.

We have a carbon budget. There is a limit to how much we can pump into the air before, eventually, the world will heat up by 2°C. The problem is that we can easily overshot that limit long before the temperature reaches 2°C.

Unfortunately no one knows what the carbon budget should be. We do know that about half of all carbon emitted gets quickly reabsorbed by plants, but the rest hangs around for centuries. Estimates suggest we can emit a range somewhere between another 100-400 gigatons of carbon. That’s a fairly wide uncertainty. [Yale] We are currently emitting approximately 35gigatons of CO₂ a year, and each year we emit more than we did the year before (though that increase is slowing). [Wikipedia, 2013 data] So at this rate we have anywhere from another 6 to 22 years before we would have locked in 2°C of warming. Unfortunately this dataset only includes CO₂ emissions. It does not include methane (which has a greater effect but is released in much smaller quantities), or water vapor, or other gasses. So worst case is we have about 5 years more of business as usual before for we guarantee 2°C warming eventually.

2°C is a global average

Some parts of the world are warming much more quickly than others. The oceans warm more slowly than the land. But there is a about twice as much ocean than there is land, and if the ocean takes longer to get to 2°C then the land will get there faster, and by the time the global temperature has averaged a 2°C increase the land temperature will be much higher.

The arctic heats up faster than the tropics, but the tropics have traditionally had a much narrower range of temperatures so in spite of that fact they will see exceptional conditions become normal much more rapidly. In both cases the ecosystems will not be able to adapt. In the arctic because there are large swings in temperature, polar ice caps disappear. In the tropics because the temperature is simply beyond what plants and animals can handle.

What about carbon capture?

Essentially all of the IPCC models which project that we will limit warming to 2°C require that we will have negative carbon emissions after about 2050. [Kevin Anderson] Not zero emissions, but negative. And this presupposes a technology we do not currently have.

We might develop it.

But as far as I know the funding for research into this area has been drastically cut in recent years. [Guardian]

In other words the paths the IPCC sees that might restrict warming to 2°C all depend on technology which does not exist and isn’t being developed. This is disturbing.

Positive Feedback

There are many areas of potential positive feedback which are not addressed by the IPCC, because we do not yet know enough to quantify them. And they are ignored in our climate models.

Melting permafrost will release a lot of methane into the atmosphere, a more potent heat-trapping gas than CO₂. This in term will lead to higher surface temperatures which will lead to more methane being released. We can see this happening but can’t quantify it. [Katia Moskvitch]

Warming ocean floors will release methane from methane hydrates with a similar feedback effect. [SWERUS-C3]

Warming tropics lead to droughts over the Amazon which leads to the death of rainforest trees which releases more CO₂ which leads to more warming and even fewer trees.

Ice and snow reflect more light and heat than oceans or land. As glaciers and ice caps melt the earth will absorb more heat meaning that more ice and snow will be lost.

This means that our current best guess are probably too conservative.

Sea level rise

With the ice caps and glaciers melting, and the ocean water warming and expanding, sea level is rising.

So far the global average is about half a foot higher now than it was 100 years ago. However the oceans aren’t rising at the same rate and on the east coast of the US the rise has been closer to a foot.

A paper posted on the next by [HansenDiscussion] suggests that the sea level may rise 10ft in the next 50 years and 15ft by 2100. This may be a worst case scenario, but past experience with climate predictions suggests that worst case scenarios have happened more frequently than best case ones. And we are very ignorant here.

Some context: Hurricane Sandy had a storm surge of about 13ft in New York. Hugo had a maximum surge of 20ft near Charleston. Katrina’s surge was about 27ft.

So by the end of the century New York might be constantly under more water than it was at the worst of Hurricane Sandy.

This would wipe out many coastal cities. It would destroy much farmland. Many island nations would no longer exist.

How fast can a marsh adapt? If the sea level rises by 15ft and the shoreline moves inward by many miles then marshes, which are very productive ecosystems will be wiped out.

But I thought climate changed stopped after 1998

This is a lie.

I have had the above statement questioned. So, a brief recap. I pulled down this dataset. I applied a linear regression least squares fit to the following year ranges of the global mean temperature:

1880-2014 T=.0068*(year-1998) + 14.36°C
1960-1984 T=.0118*(year-1998) + 14.35°C
1990-1998 T=.0230*(year-1998) + 14.49°C
1998-2014 T=.0108*(year-1998) + 14.52°C

The important thing to note here is the change/year which was .0068°C/year over the historical record; it was .0230°C/year in the 90s, and .0108°C/year in the period of the hiatus. So not only has the global temperature increased since 1998, but it has increased faster than the historical rate and about the same rate as during the 70s. It did slow down dramatically from the 90s, but that can be explained by the Pacific Decadal Oscillation [Nature].

However surface temperature is not a good indicator of heat transferred to the earth. And since 1998 more heat has gone into the deep ocean than happened before. With this year’s El Niño less heat is going into the ocean deeps and the surface temperature is again increasing quickly.

Remember in the last decade we have seen 8 of the hottest years on record, and the top 13 hottest years have all been since 1997. There is about 1 chance in 3.7 million of this happening if the climate were not warming. [Climate Central] And unless something amazing happens in the next 3 weeks, 2015 will be even hotter.

But isn’t extra CO₂ good for plants? Won’t warmer weather make ecosystems more productive?

There is some evidence that more CO₂ will make plants happier, but the effect is slight.

Basically ecosystems have adapted to current conditions. Changing those conditions will, in almost all cases be a change for the worse.

European grain productivity has already been reduced. [Frances Moore] The current drought exacerbated (and possibly caused) by climate change has reduced California’s agricultural productivity. Global grain productivity is expected to fall at about 1.5% per decade [David Lobell] Grains produce less protein in hot weather.

We don’t have any good metrics for measuring wild ecosystems, except long term extinction rates, but there is certainly evidence that the climate is changing faster than plants and animals can move to keep up. [Union of Concerned Scientists]

The woods I love to hike in will be very different when my niece’s children try them.

But the oceans will be the worst hit. The increase in CO₂ has led to an ongoing acidification of the water which prevents many animals from forming shells. The increase in heat has lead to bleaching coral reeves and the death of many.

More subtle changes happen too. Different species respond differently to climate change, some start breeding sooner than they would normally, others do not. Thus old ecological synchronizations are lost. A predator many start to breed in the spring before its prey does, resulting in starvation of the predator and over-population in the prey.

The oceans’ food chains are being disrupted and they are becoming less productive.

In other words, species are dying off. Humans are losing their food supplies.

Summary

The Guardian says it very well: “By comparison to what it [COP21] could have been, it’s a miracle. By comparison to what it should have been, it’s a disaster.”

The world will be less beautiful in the future.
And there will be less for humans to eat.
And there will be more humans.