Working Title:

In Search of a Climate Change Signal in Nova Scotia, 1901-1923

• Madison Culbertson (Applied Mathematics, Northern Kentucky University)
• Laura Farro (Physics and Statistics, Northern Kentucky University)
• Andrew Long (Mathematics and Statistics, Northern Kentucky University)
• Steven Wilkinson (Mathematics and Statistics, Northern Kentucky University)

Abstract

Alexander H. MacKay was the superintendent of public schools in Nova Scotia from 1891-1926 (Sheehan, \cite{Piers1930}). Beginning in 1897 MacKay instructed all the school teachers of Nova Scotia to have their students collect data on the first appearances of numerous plants, animals, and seasonal events, and then summarized the data himself (MacKay(1898)). This continued through 1923, and the data the schools collected is publicly archived in ledgers in the Nova Scotia Museum of Natural History, Nova Scotia (\cite{Austen2000}). A team led by Adam Fenech digitized the data a few years after(\cite{Fenech2005}.

Summaries of the total data collected were produced by MacKay himself and published in either the Proceedings of the Nova Scotian Institute of Science or the Journal of Education. We analyze five species from the summary MacKay data for Nova Scotia from the period 1901-1923, with the objectives of

1. modeling a "climate signal" in the First Appearance Time (FAT) of flowering, based on geographical factors (longitude, latitude) and climatic variables (such as temperatures and sea ice);
2. determining how well our model can predict FATs obtained from other sources, and
3. determining how well MacKay's "phenochrons" for Nova Scotia -- essentially sub-regions of the province for which climate was considered relatively constant -- were chosen. We produce maps of FAT, and consider them in the context of his phenochrons.

Keywords: Alexander H. MacKay, climate change, phenology, phenochrons, Singular Value Decomposition (SVD), tensor SVD (TSVD), linear regression, non-linear regression, temperature, sea ice

Introduction

"Seasonal timing of biological events, phenology, is one of the strongest bioindicators of climate change."\cite{CaraDonna01042014} Our purpose is to use phenological data collected and summarized by Dr. Alexander MacKay to model First Arrival Time (FAT) of flowering of several species of plants in the early 1900s in Nova Scotia. Having obtained a model, we then hope to use it to determine whether we can detect a change in FAT based on climatic variables (e.g. temperatures, sea ice), suggesting that

1. climate is changing, and
2. allowing us to guess how further changes in climate will affect the phenology of these flowering species of plants.

We also use our model to compare our predictions to collections of data on FATs from the late 20th century and early 21st century, as well as from years predating our data.

MacKay presented his phenological study strategy in his 1901 report on the phenology of Nova Scotia (\ref{\cite{Proceedings1901}, pp. 486-501}). He begins: "I present herewith a summary of the phenological observations made in about 450 of the public schools of the Province of Nova Scotia, each county being represented by a greater or less proportion of observers.... The observers are specially directed to the determination of two dates (phenochrons) -- one for the first appearance of the event (leafing, flowering, ripening of fruit, etc.), the other for the date when it may be said to be 'becoming common.'"

As described in the Presidential address of March 14, 1898 recorded in the Proceedings of the Nova Scotian Institute of Science, MacKay's phenological observations "...may lead to some important generalizations regarding the relation of organized life to latitude and other climatic conditions."(\cite{Presidential address, 1898, p. ii)

For the years 1901 to 1923 (with the exception of 1910) we found and digitized published record of summaries of the observations obtained by the public schoolchildren of Nova Scotia. The printed form the teachers and students used in individual schools was published in 1902(\cite{JOEApril1902} (pages 24-27)), along with a report(ibid, pp. 58-63) on difficulties associated with compiling those regional reports of the raw data into Nova Scotian summaries in the case of 1901.

Dr. Alexander MacKay was a beloved member of the Nova Scotian Academy of Sciences, and a brilliant scientist in his own right. Appointed Superintendent for Education for Nova Scotia on Nov. 4th, 1891, he retired nearly 35 years later, on July 31st, 1926. He left an indelible mark on Nova Scotia's public eductional system. "Under his able administration not only the [Pictou] Academy, but the whole province, was co-ordinated into one efficient system of education, in imitation of Ontario and American models."(\cite{Wood-1994}) In another work, we hear that "Under Principal MacKay's strong administration the Academy made rapid strides. It became celebrated throughout the province and far beyond its limits. Students flocked in from all quarters until there was not room enough to receive."(\cite{THE STORY OF PICTOU ACADEMY}) And, while doing so much good for his province, he apparently did so in style as Harry Piers reported in MacKay's obituary: "Only once did I hear him speak with unwonted warmth or perhaps anger, and that was when an educated man seemingly tried to demonstrate to a large audience that the world might be flat!"(\cite{Piers1930}, lii)

The following photograph is the one chosen by the author of his "scientific obituary"(ibid), Harry Piers, as one personally sent to him with MacKay's hand-written inscription ("Yours very truly"): http://www.norsemathology.org/longa/research/MacKay/MacKayObitPhoto.png

In terms of his scientific legacy, those who indexed the Proceedings of the Nova Scotian Institute of Science report that "The phenological data, collected over 31 years by Dr. A.H. MacKay, are a major contribution to Canadian science...." \cite{ProceedingsGeneralIndex}, p. 150 The 31 years referenced include early years, before his citizen science project got underway. MacKay also collected data Canada-wide in the early reports, from a handful of observers across the Commonwealth.

Objective

Our primary objective is to create a model of First Appearance Time (FAT) for the flowering of five species of plants, based on data obtained by MacKay's schools and summarized by him. We suppose that FAT is a function of daylight hours (related to latitude and longitude), air and soil temperatures, precipitation, and ocean effects (e.g. sea ice, moisture and breezes, warmth brought by currents). However it was not possible to find data on each of these variables.

Our surrogate for climatic effects are average monthly temperatures for Nova Scotia and sea ice around Newfoundland. We were able to acquire each of these for the 22 years for which we have published phenological summaries.

Data

While we possess the raw data (digitized by Fenech, et al(\cite{Fenech2005)), we focus on the data as summarized in Dr. MacKay's annual reports from 1901-1923. MacKay and his collaborators carefully chose a subset of the data, and we know that they made a conscious culling of the data to avoid including data poorly or improperly collected, fabricated, etc.: "The various points for consideration in choosing Schedules are a fair distribution of the Stations over the Belt, the number and accuracy of the observations, the sex and temperament of the observer, the neatness of the work, the method of stating dates and in some cases the Compilers personal knowledge of the observer(\ref{JOEApril1902 (pg 59)}). On page 60, we find that "One or two observations are obviously guesses. I strongly suspect that they were all filled out about the close of the term, possibly from memory or aided by the pupils." The more things change, the more they stay the same: researchers make careless, and even fraudulent errors in the collection of data, and those of us who encounter the data later have no idea. We are pleased that we may rely on the judgements of these long-gone compilers at the time of collection to avoid errors that we ourselves would be unable (or at least unlikely) to catch.

Our analyses in this paper pertain to five species that MacKay himself chose for this 1901 report. We suppose that he consciously chose these five, as some that

• he suspected would show the most dramatic results, or
• were easiest for his students to identify.

In some of his reports he discusses the problems encountered during collection: "ladies" wouldn't want to venture into swamps to track down water-loving species, some species would be confused with others, etc.(\ref{JOEApril1902 (pg 61)})

The summary data we studied thus consisted of five species, reported in 9 regions (called "phenochrons" by MacKay, and described below). We can think of this as a 5x9 matrix of data: five rows, for the five species, and nine columns, for the nine locations. One year was missing (1910), and MacKay's report from that time is discouraging (\cite{ProceedingsMay1911}). It appeared for a time that the phenological reporting might cease. However it began again in 1911, and continued unabated until 1923. In several of the years, a few of the 45 data values were missing. We will describe below, in Methods, how we imputed those.

Our final data set is contained in this csv file of Final Dates of Arrival.

One problem that we ran into was that data was not always presented consistently from year to year. In particular, MacKay's "phenochrons" varied over time. For example, some years combined regions 9 and 10 to create one data point. In other years, region 6 was split into two separate parts, 6A and 6B. These inconsistencies lead to problems when it comes to data analysis. We elected to create a standard set of nine regions to utilize for analysis. Regions 1-5 and 7-8 are identical to those created by MacKay. Region "6" is identical to MacKay's region 6 in most cases. Where there is a 6A and 6B in MacKay's original data set, our region "6" is a combination of 6A and 6B. In all cases, regions 9 and 10 were combined to create one region. In the cases where MacKay combined regions 9 and 10, this last region is identical to the original. The final data set used is below:

Region Combinations: A table that lays out how regions were combined:

• "Original" means that the new region is identical to the one created by MacKay. For 6A and 6B, it means that the regions were not originally split into two parts. For regions 9 and 10, this means that the regions were combined by MacKay, and were therefore not changed for the final data set.
• In cases where we had to combine regions, the weighted ratios are given.
• If the ratio is "given," we were able to find the number of reports for each region and use that ratio to weight the data points. For example, in 1917, there were six reports from 6A and fifteen reports from 6B. Therefore, to create a region "6," A was weighted by six and B was weighted by fifteen.
• If the ratio is "estimated," there was no information given on the number of reports from each region. In order to create a ratio to use, we used the total ratio of reports from the years in which a ratio was given. For regions 6A and 6B, the ratio is a combination of the years 1913-1919. For regions 9 and 10, the ratio is a combination of the years 1903, 1906, and 1918. In some cases, the data points given for regions were the same, so the regions ended up being given equal weight.

We imputed the missing data with a method based on the Singular Value Decomposition (SVD), described below.

Climate data for average monthly air temperatures of Nova Scotia was obtained from Environment Canada, using a process described in the appendix. Sea ice data was graciously provided by Brian T. Hill, now retired from the National Research Council Canada, Institute for Marine Dynamics. His data and methods are contained in his publication Historical record of the incidence of sea ice on the scotian shelf and the Gulf of St. Lawrence\cite{HillNFIce}

Methods

In the 1901 report(\cite{Proceedings1901}), MacKay presents a graphic (we'll call it "the 1901 graphic") of the first appearances of Mayflower, strawberry, apple, lilac, and blackberry (summary data rows 3, 13, 51, 57, and 30, as noted in the report, p. 495):

The report includes this remark concerning the graphic: "A plate of graphs showing the relation between the flowering phenochrons in each region of the province of Nova Scotia for the dates 'when first seen' and 'when becoming common' is given on page 496. 'When becoming common' must always be a matter of personal judgement; so that the general conformity of the five pairs of curves for the flowering of the Mayflower, Strawberry, Apple, Lilac, and Blackberry, on the said plate is very interesting."

MacKay and his collaborators were very concerned about accuracy, and actually state that "Care must be exercised in selecting schedules, the observations of which appear to have been carefully made, neglecting any which give reason for doubt, when selecting for summation on the form within. Great care must also be exercised in copying the figures and entering them, so that no slip may occur. Every entry must be checked. One slip may spoil the effect of all the accurate numbers entering into the summation. In like manner, great care has to be taken in adding and averaging the figures; and for this purpose every sum should be done twice in reverse order, so as to give absolute confidence in the accuracy of the work."(1901,p. 490)

This graphic was obtained from summary data, a subset of 450 of the more than 500 data sets submitted by his many teachers. The regions are sorted by latitude: MacKay's apparent supposition was that first appearances would come later the farther northward a locality [ael: does he actually say that in his report? If so, we can replace "obvious" with a reference....].

We began by estimating the missing values from the data[ael: Madison: specifically ....]. Our process for estimating the data is related to another analysis, so we begin by describing that. A glance at the 1901 graphic suggests that the five species first appearances ("when common" also appears in the graphic) are in synch, if not in lockstep. Clearly there is some underlying similarity in the graphics. Our first objective therefore was to try to get a picture of this similarity.

Small Multiples duplicating the 1901 graphic from 1901-1923:

Model results for the FATs:

Rank-One Approximation Using the SVD

Many statistical techniques are built upon the Singular Value Decomposition (the SVD): principal components Analysis (PCA), Factor Analysis, Canonical Coordinates Analysis(CCA), etc. The SVD theorem from linear algebra as used here states that a real matrix ${\displaystyle \left.X\right.}$ can be decomposed into a product of orthogonal matrices and a diagonal matrix, ${\displaystyle \left.X=UDV'\right.}$ where ${\displaystyle \left.D\right.}$ is diagonal with positive entries ("singular values") ordered from largest to smallest (with possible ties and zero values), and ${\displaystyle \left.U\right.}$ and ${\displaystyle \left.V\right.}$ are orthonormal (have columns mutually orthogonal and of unit length).

The SVD Theorem

Every real matrix ${\displaystyle \left.A\right.}$ can be thought of as the product of an orthogonal matrix, a diagonal matrix, and the transpose of an orthogonal matrix. ${\displaystyle \left.A\right.}$ is related to two important symmetric matrices: ${\displaystyle \left.A^{T}A\right.}$ and ${\displaystyle \left.AA^{T}\right.}$. Since each of these two matrices is symmetric, each can be represented as a product

${\displaystyle \left.{\begin{cases}AA^{T}=UD_{1}U^{T}\\A^{T}A=VD_{2}V^{T}\end{cases}}\right.}$

Furthermore, the diagonal matrices ${\displaystyle \left.D_{1}\right.}$ and ${\displaystyle \left.D_{2}\right.}$ have positive entries on the diagonal. We can see that from the spectral decomposition of ${\displaystyle \left.AA^{T}\right.}$ and ${\displaystyle \left.A^{T}A\right.}$ into a sum of outer products of their eigenvalues and mutually orthonormal eigenvectors. For example,

${\displaystyle \left.AA^{T}=\lambda _{1}u_{1}u_{1}^{T}+\ldots +\lambda _{m}u_{m}u_{m}^{T}\right.}$

Hence,

${\displaystyle \left.u_{1}^{T}AA^{T}u_{1}=\lambda _{1}u_{1}^{T}u_{1}u_{1}^{T}u_{1}+0=\lambda _{1}(u_{1}\cdot u_{1})(u_{1}\cdot u_{1})=\lambda _{1}\right.}$,

but since

${\displaystyle \left.u_{1}^{T}AA^{T}u_{1}=A^{T}u_{1}\cdot A^{T}u_{1}=||A^{T}u_{1}||^{2}\geq 0\right.}$, we know that ${\displaystyle \left.\lambda _{1}\geq 0\right.}$.

Theorem: Let ${\displaystyle \left.A\right.}$ be an ${\displaystyle \left.m\times n\right.}$ matrix with real components. Then ${\displaystyle \left.A=U\Sigma V^{T}\right.}$ where ${\displaystyle \left.U\right.}$ and ${\displaystyle \left.V\right.}$ are as defined above, and ${\displaystyle \left.\Sigma \right.}$ is the matrix with positive (${\displaystyle \left.\geq 0\right.}$) entries such that ${\displaystyle \left.\Sigma \Sigma ^{T}=D_{1}\right.}$ and ${\displaystyle \left.\Sigma ^{T}\Sigma =D_{2}\right.}$.

We can easily show that, with ${\displaystyle \left.A=U\Sigma V^{T}\right.}$, the formulas for ${\displaystyle \left.AA^{T}\right.}$ and ${\displaystyle \left.A^{T}A\right.}$ work out:

${\displaystyle \left.{\begin{cases}AA^{T}=U\Sigma V^{T}V\Sigma ^{T}U^{T}=U\Sigma \Sigma ^{T}U^{T}=UD_{1}U^{T}\\A^{T}A=V\Sigma ^{T}U^{T}U\Sigma V^{T}=V\Sigma ^{T}\Sigma V^{T}=VD_{2}V^{T}\end{cases}}\right.}$

Notice that the orthogonal diagonalization of a symmetric matrix is the singular value decomposition in that case.

What follows is an illustration of the SVD, as diagrammed by Cliff Long and Tom Hern in the case of ${\displaystyle \left.R^{2}\right.}$. In this example, the notation is ${\displaystyle \left.U=Q_{1}\right.}$ and ${\displaystyle \left.V=Q_{2}\right.}$.

You see that the action of a general matrix ${\displaystyle \left.A\right.}$ can also be viewed as a rotation, followed by a scaling, followed by a rotation. If ${\displaystyle \left.A\right.}$ is not square, or not full rank, then there will be a null space, and some of the dimensions will be annihilated.

Standard Use of the SVD Theorem

The SVD is sometimes used in image analysis and compression, the idea being that the smallest singular values may well be related to noise in the image, rather than signal: hence, if we set the smaller singular values to 0 in ${\displaystyle \left.D\right.}$, and create the product ${\displaystyle \left.X^{*}=UD^{*}V'\right.}$ we may have cleaned up the image (or possibly have a smaller -- yet less distinct -- image to send across smaller bandwidths).

Our Use of the SVD

The idea we use is similar: there is noise in a data matrix, ${\displaystyle \left.X_{5\times 10}\right.}$. If we're really aggressive, we would set all but the very largest singular value to zero, and reconstruct our matrix to obtain ${\displaystyle \left.X_{5\times 10}^{*}=UD^{*}V'\right.}$ In fact, we can think of this as an "outer product" of two very simple matrices: ${\displaystyle \left.X_{5\times 10}^{*}=d_{11}{\underline {u}}_{1}{\underline {v}}'_{1}\right.}$ where ${\displaystyle \left.{\underline {u}}_{1}\right.}$ and ${\displaystyle \left.{\underline {v}}_{1}\right.}$ are the first two columns of matrices ${\displaystyle \left.U\right.}$ and ${\displaystyle \left.V\right.}$, and ${\displaystyle \left.d_{11}\right.}$ is the first (and largest) singular value.

${\displaystyle \left.X^{*}\right.}$ will then consist of five rows of "simplified" (de-noised, we hope) versions of each of the five variables. But it suggests something rather too simple: that each species responds in exactly the same way based on location, first appearance occurring at relatively earlier or later times only.

The components of ${\displaystyle \left.{\underline {u}}\right.}$ represent the relative times of arrival of the species, and components of ${\displaystyle \left.{\underline {u}}\right.}$ represent the relative ordering of times of arrival at locations.

Data Estimation Using the Rank-One Approximation

Let's now get back to the issue of data estimation. Since we are supposing that there is a strong common response of each of the five species, our estimation strategy is to choose the missing data values of ${\displaystyle \left.X\right.}$ so as to maximize the largest singular value (and hence to maximize the ability of ${\displaystyle \left.X^{*}\right.}$ to replace ${\displaystyle \left.X\right.}$). This is a sort of "maximum likelihood" strategy.

The actual code to perform this estimation is provided in the appendix, and available on-line.

Climate Normals

We were curious as to how climate has changed in Nova Scotia over the past century (or so). Usually a period of 30 years is taken as a representative of climate, averaging out weather. Current climate normals were obtained from climatechange.novascotia.ca, and we used the climate data to construct our own climate normals based on the years 1890 to 1924. There were different amounts of data available for each station. For example, stations like Sydney and Yarmouth had data spanning the years 1890 to 1924, while Pictou had data spanning the years 1890 to 1906. Climate variables used include daily minimum temperature, daily maximum temperature, daily mean temperature, and total precipitation. Climate normals are based on seasonal and annual mean temperatures and precipitation. We compare and contrast climate normals based on our data and the "modern" Nova Scotia data.

Here are tables that compare some historical and modern normals: Climate Normals

• Normals are based on seasonal and annual temperatures and precipitation
• Winter: December-February
• Spring: March-May
• Summer: June-August
• Autumn: September-November

As of right now, there appears to be a small decrease in mean temperatures as well as an increase in total precipitation, but this is only a small sampling of stations.

Results

Data estimation in the event of missing data

[ael: Madison?] While creating small multiples missing data points was a hindrance. We used Singular Value Decomposition(SVD) in order to estimate these missing data points. In the case of one particular odd looking data point, raw data was assessed in order to see if there was a mistake in the data entry for the 1920 yearly summary. It was determined, that the data point entered in the yearly summary was not possible based off of the raw data. Therefore we suspected that fruit ripe was possibly mixed in with the average for the region. Thus, 1920 blackberry region 2 data point was estimated along with the missing data points from years 1919,1920,1922,1923 using SVD.

Differences Regression

A differences regression was used in order to detect a change per each region over the 22 years. The prior year data was subtracted from the previous year data and graphed per region and species. Unfortunately no trend was able to be detected. These graphs are an example of the differences regression for region 1 early and common. The same graph was created for all regions and all 5 species.

Regressions of species on coordinates of 10 regions

Our first objective was to determine if what may have appeared obvious to MacKay (a significant latitudinal effect to first appearance) was actually borne out by the data. We created linear regressions in R to do so. Regressions express arrival date with respect to latitude and longitude of the ten regions created by MacKay. Each region was defined using its "centroid," a set of latitudinal and longitudinal coordinates. Regressions were created using MacKay's summary data for each of the five variables (Mayflower, Strawberry, Apple, Lilac, Blackberry).

Here is the form of each regression: arrival date = A*latitude + B*longitude + C where A, B, and C are the coefficients and intercept found with each regression.

Using R to perform the regressions allows us to see the significance of each coefficient. While it was expected that we would discover a latitudinal effect, there was actually a significant longitudinal effect in some cases.

Regressions were performed for each year from 1901 to 1923, with the exception of 1910, for a total of 22 years.

A strong latitudinal effect is seen with the Mayflower, with 14 of the 22 years presenting a significant latitudinal coefficient (${\displaystyle \left.\ p\leq 0.05\right.}$). Two years (1912 and 1921) presented a significant longitudinal effect (${\displaystyle \left.\ p\leq 0.05\right.}$).

A significant latitudinal effect is presented in six of the 22 years for Strawberry (${\displaystyle \left.\ p\leq 0.05\right.}$), while a significant longitudinal effect is presented in ten of the 22 years (${\displaystyle \left.\ p\leq 0.05\right.}$).

A significant latitudinal effect is presented in one of the 22 years (1917) for Apple (${\displaystyle \left.\ p=0.00742\right.}$), while a significant longitudinal effect is presented in 17 of the 22 years (${\displaystyle \left.\ p\leq 0.05\right.}$).

A significant latitudinal effect is presented in four of the 22 years for Lilac (${\displaystyle \left.\ p\leq 0.05\right.}$), while a significant longitudinal effect is presented in 14 of the 22 years (${\displaystyle \left.\ p\leq 0.05\right.}$).

As for Blackberry, no year presents a significant latitudinal or longitudinal effect.

Regressions of rank-one "Mayflower" on coordinates of 10 regions

Regressions were performed again using the rank-one approximation as discussed previously. Regressions took the same form as before, but now the variable used is a surrogate; it is meant to represent all five species. Again, a longitudinal effect was far more present than a latitudinal effect.

Of the years studied, only two presented a significant latitudinal effect (${\displaystyle \left.\ p\leq 0.05\right.}$), while 14 presented a significant longitudinal effect (${\displaystyle \left.\ p\leq 0.05\right.}$).

It should be noted that this new variable might not be the best representation of all five species, because it does not reflect the strong latitudinal effect seen with the Mayflower, nor the lack of significant effect seen with the Blackberry.

Regressions of rank-two species on coordinates of 10 regions

Regressions were performed using the rank-two approximation.

For Mayflower, nine of the 22 years studied presented a significant latitudinal effect (${\displaystyle \left.\ p\leq 0.05\right.}$), and six years presented a significant longitudinal effect (${\displaystyle \left.\ p\leq 0.05\right.}$).

For Strawberry, four of the 22 years presented a significant latitudinal effect (${\displaystyle \left.\ p\leq 0.05\right.}$), and 15 years presented a significant longitudinal effect (${\displaystyle \left.\ p\leq 0.05\right.}$).

For Apple, three of the 22 years presented a significant latitudinal effect (${\displaystyle \left.\ p\leq 0.05\right.}$), and 13 years presented a significant longitudinal effect (${\displaystyle \left.\ p\leq 0.05\right.}$).

For Lilac, two of the 22 years presented a significant latitudinal effect (${\displaystyle \left.\ p\leq 0.05\right.}$), and 14 years presented a significant longitudinal effect (${\displaystyle \left.\ p\leq 0.05\right.}$).

For Blackberry, two of the 22 years presented a significant latitudinal effect (${\displaystyle \left.\ p\leq 0.05\right.}$), and nine years presented a significant longitudinal effect (${\displaystyle \left.\ p\leq 0.05\right.}$).

p-values for each species are presented below.

Regressions of rank-three species on coordinate of 10 regions

Regressions were performed on the rank-three approximation to Mayflower.

For Mayflower, of the 22 years studied, 15 presented a significant latitudinal effect (${\displaystyle \left.\ p\leq 0.05\right.}$), while one year (1912) presented a significant longitudinal effect (${\displaystyle \left.\ p=0.01732\right.}$).

For Strawberry, four years presented a significant latitudinal effect (${\displaystyle \left.\ p\leq 0.05\right.}$), while 13 years presented a significant longitudinal effect (${\displaystyle \left.\ p\leq 0.05\right.}$).

For Apple, three years presented a significant latitudinal effect (${\displaystyle \left.\ p\leq 0.05\right.}$), while 15 years presented a significant longitudinal effect (${\displaystyle \left.\ p\leq 0.05\right.}$).

For Lilac, five years presented a significant latitudinal effect (${\displaystyle \left.\ p\leq 0.05\right.}$), while 15 years presented a significant longitudinal effect (${\displaystyle \left.\ p\leq 0.05\right.}$).

For Blackberry, one year (1921) presented a significant latitudinal effect (${\displaystyle \left.\ p=0.023\right.}$), and one year (1904) presented a significant longitudinal effect (${\displaystyle \left.\ p=0.034\right.}$).

Replication of the 1901 Graphic

Small multiples discussion and graphics (mention of Tufte, ref).

The 1901 graphic consists of the first appearances of Mayflower, strawberry, apple, lilac, and blackberry over 10 regions. We decided to use this graphic and replicate it over a span of 22 years with the exception of 1910. We call these graphs small multiples, an idea from Tufte. While creating these graphs we ran into some missing data which was estimated using Singular Value Decomposition. Another problem that arose was the difference in regions. Some years combined the regions 9 and 10. In the event of combined regions we listed the same data twice to keep a consistent 10 regions. Also while scaling this data we created a negative scaling system in order to replicate Mackay's graph exactly.

Regression Model for First Appearance Time (FAT)

First Appearance could mean either vegetation, flower, or fruit. We need to distinguish which is being measured in every case.

Quite generally one might write FAT as a function of

• time t,
• Atmospheric temperature,
• soil type and temperature at a particular depth,
• longitude,
• latitude,
• cloud cover,
• winds,
• precipitation,
• humidity

and one might imagine some other stimuli which would be relevant. We need to work with simpler models, given the inaccessibility of some of that information.

First Appearance Time, according to our thinking, relies on soil temperature, which must be estimated. Our conjecture is that a plant appears when it receives the requisite amount of daylight and/or the soil temperature hits a tipping point. Chang, et al.(ref) suggest a model for soil temperature (ST), which one could write as a function of time, soil depth, and atmospheric temperature (AT) as

${\displaystyle \left.ST(t,d)=a_{0}+a_{1}e^{\alpha _{0}d}\left(AT(t)+a_{2}\sin \left({\frac {2\pi t}{365}}-\theta \right)\right)\right.}$

Now let's suppose that, for a particular species (say Mayflower), when the soil temperature ${\displaystyle \left.ST(t,d_{M})=T_{M}\right.}$ the emergence is initiated. Then we're expecting that, for each year, each location, and each species, ${\displaystyle \left.ST(FAT_{i},d_{M})=T_{M}\right.}$, and we compare that with the observed ${\displaystyle FAT_{i}}$ times.

Let us proceed in a "bass-ackwards" fashion, and use a particular species (Mayflower, say) to estimate the coefficients of the ST model. We seek a choice of the parameters such that ${\displaystyle \left.\sum _{i=1901}^{1923}\left(ST(FAT_{i},d_{M})-T_{M}-a_{0}\right)^{2}=\left(a_{1}e^{\alpha _{0}d}\right)^{2}\sum _{i=1901}^{1923}\left(AT(FAT_{i})+a_{2}\sin \left({\frac {2\pi FAT_{i}}{365}}-\theta \right)\right)^{2}\right.}$ has minimal variance (that is, we want to minimize the sum of squares of the right-hand side). Clearly the (senseless) choice of ${\displaystyle \left.a_{1}=0\right.}$ would do that, so we need to divide the left hand side by ${\displaystyle \left.a_{1}e^{\alpha _{0}d}\right.}$: minimize ${\displaystyle \left.\sum _{i=1901}^{1923}\left({\frac {ST(FAT_{i},d_{M})-T_{M}-a_{0}}{a_{1}e^{\alpha _{0}d}}}\right)^{2}=\sum _{i=1901}^{1923}\left(AT(FAT_{i})+a_{2}\sin \left({\frac {2\pi FAT_{i}}{365}}-\theta \right)\right)^{2}\right.}$

We won't find several of the parameters this way; but we get a few of them (at least relative sizes).

Here's my first take on strategy (sorry for the crude image). Then we perform a least-squares minimization on predicted versus realized FATs.

TSVD Model for First Appearance Time (FAT)

The Tensor SVD is a generalization of the SVD: instead of breaking a 2-dimensional matrix into a sum of outer-products of two vectors, each representing a different dimension, a 3-dimensional tensor is broken into a sum of outer-products of three vectors, each trio creating a rank-one outer product in three dimensions. Our data tensor is composed of five species, nine regions, and 22 (out of 23 possible) years of data on FATs.

Unfortunately, one important property of the SVD is not preserved under TSVD: the outer products are not mutually orthogonal with respect to the Frobenius norm. However our sense is that, if we can model the "factors", orthogonal or no, we will have achieved something useful. In the end, we produce a model; if the model is useful, what matter how it was obtained?

There are two aspects of the tensors that need to be modeled:

1. the regional vectors (which we think of as a product of regions' latitude and longitude, primarily, but also perhaps "aspect" and some other features) [Laura is producing some nice results, indicating that these are a function of a "rotated" lat/long coordinate system.]; and
2. the annual vectors, which we model by incorporating temperature, sea ice, and other climatic features.

Modeling Strategy

The strategy we used for doing a TSVD is this:

1. We find the best-fitting outer-product of unit vectors ${\displaystyle {\underline {u}},{\underline {v}},{\underline {w}}}$ to the tensor (in terms of matching the tensor norm, ${\displaystyle {\sqrt {\sum _{i=1}^{l}\sum _{j=1}^{m}\sum _{k=1}^{n}T_{ijk}^{2}}}}$). So we maximize ${\displaystyle E(T,{\underline {u}},{\underline {v}},{\underline {w}})\equiv \sum _{i=1}^{l}\sum _{j=1}^{m}\sum _{k=1}^{n}T_{ijk}u_{i}v_{j}w_{k}}$.
2. Having maximized ${\displaystyle E(T,{\underline {u}},{\underline {v}},{\underline {w}})}$ to find ${\displaystyle {\underline {u}}^{1},{\underline {v}}^{1},{\underline {w}}^{1}}$, we iterate: if we define ${\displaystyle T^{1}\equiv \lambda _{1}{\underline {u}}^{1}\otimes {\underline {v}}^{1}\otimes {\underline {w}}^{1}}$ as the best rank-one approximation to ${\displaystyle T}$, then let ${\displaystyle R^{1}\equiv T-T^{1}}$ indicate the residual tensor, we then maximize ${\displaystyle E(R^{1},{\underline {u}},{\underline {v}},{\underline {w}})}$ to find ${\displaystyle T^{2}}$ and ${\displaystyle R^{2}}$, and so on.
3. We continue until a certain level or percentage of the original norm has been achieved with ${\displaystyle p}$ rank-one tensors. Then we write ${\displaystyle T\approx \sum _{i=1}^{p}T^{i}}$, hoping that this captures the signal within the noise of the data.

If we think of the vector ${\displaystyle {\underline {u}}}$ as the "species" vector, of length 5, and we think of ${\displaystyle {\underline {v}}}$ as the region vector of length 9, then the vector ${\displaystyle {\underline {w}}}$ represents the variation of the FAT of each species in time. We model each of the vectors ${\displaystyle {\underline {v}}}$ and ${\displaystyle {\underline {w}}}$, using the linear regression equations, to yield the model ${\displaystyle T(i,lat,long;temps,ice)\approx \sum _{i=1}^{p}\lambda _{i}u^{i}v^{i}(lat,long)w^{i}(temps,ice)}$.

Tensor Decomposition Results

Let's take a look at the vectors in the year dimension, ${\displaystyle {\underline {w}}^{i}}$, which are 22-component vectors. Out of 10 vectors (of 18) that showed a significant relationship with mean monthly Nova-Scotian temperatures, the first three factors had highest ${\displaystyle R^{2}}$ values, followed by three vectors which were not signficantly coerrelated with temperatures or ice:

 1:R Squared:      0.333677
2:R Squared:      0.582665
3:R Squared:      0.615067

 6:R Squared:      0.194422
9:R Squared:      0.355412
10:R Squared:      0.330671
11:R Squared:      0.558928
12:R Squared:      0.231059
17:R Squared:      0.460555
18:R Squared:      0.214937


In each of the first three cases, March temperatures were significant (the only significant factor in the first, one of two temperatures in the second (March and July from the previous year), and one of two in the third (March and February). Newfoundland ice extent[\cite{Hill}] was significant in only one of the first three factors. Factor 2 took advantage of it, which was also the only factor to take advantage of a summer temperature:

factor 1:
Linear Regression:        Estimate            SE              Prob
Constant                 0.210527       (1.289806E-3)       0.00000
MarTemp                  -1.527643E-3   (4.827093E-4)       0.00487
R Squared:               0.333677

factor 2:
Linear Regression:        Estimate            SE              Prob
Constant                 0.935345       (0.272097)          0.00294
JulTemp                  -5.405931E-2   (1.677388E-2)       0.00472
MarchIce                 4.345671E-7    (1.550018E-7)       0.01175
MarTemp                  -1.475162E-2   (6.740209E-3)       0.04205
R Squared:               0.582665

factor 3:
Linear Regression:        Estimate            SE              Prob
Constant                 -0.373015      (9.447744E-2)       0.00086
MarTemp                  -4.940990E-2   (1.722101E-2)       0.00982
FebTemp                  -3.822118E-2   (1.640365E-2)       0.03098
R Squared:               0.615067


So we can characterize

1. the major "mean" rank-one tensor as sensitive to March temperatures;
2. the second major rank-one tensor as sensitive to March temperatures, but also dormancy from the fall before, and March Ice (which may be a surrogate for the type of winter); and
3. the third major rank-one tensor as sensitive to early spring (February/March) temperatures.

Decomposing the Decomposition

The structure of the tensor singular vectors ${\displaystyle {\underline {w}}_{i}}$ is interesting. When I did an SVD on the three of them, I obtain the following:

• Singular values: 1.395 1.002 0.225
• Singular vectors (U)
-0.145658     -0.156489     -0.382019
-0.176774     -0.559444     -0.173804
-0.217054     -0.261788       3.879101E-2
-0.200465       6.522980E-2  -8.423445E-2
-0.198576      -3.649047E-3 -0.130389
-0.179559      -3.448744E-2 -0.247755
-0.235425      0.126207       4.986251E-2
-0.230699      0.126017       6.089306E-2
-0.206660     -0.150835      -7.416663E-2
-0.154223      0.343064     -0.367731
-0.174673       8.004928E-2 -0.243651
-0.244992     -0.234865      0.229653
-0.236732      0.362089       9.217535E-2
-0.247393     -0.154076      0.184025
-0.273549      0.159440      0.327968
-0.279200     -0.113246      0.343448
-0.196513      0.265561     -0.119672
-0.245407      -9.387621E-2  0.208803
-0.187567      -5.402422E-2 -0.174432
-0.168491      -5.488184E-2 -0.225585
-0.174299      -9.546858E-3 -0.237683
-0.245094      0.276168      0.119300

• The Singular vectors (V). The ${\displaystyle i^{th}}$ row is the emphasis that each of the original columns places on the columns above. So
1. the first singular vector uses the first and third "exclusively";
2. the second uses the first and third "primarily", but a little of the second; and
3. the third the second almost exclusively.
-0.707853      -8.338669E-3 -0.706310
-0.687306      0.238812      0.685988
0.162955      0.971030     -0.174775


What is not readily apparent, however is that the third singular vector of ${\displaystyle U}$ is well expressed as a linear combination of the first:

             var0     var1     var2
var0       1.0000  -0.0935  -0.9884
var1      -0.0935   1.0000  -0.0029
var2      -0.9884  -0.0029   1.0000


which led me to do a regression:

Linear Regression:        Estimate            SE              Prob
Constant                 -1.21267       (4.098822E-2)       0.00000
Variable 0               -5.60133       (0.192252)          0.00000
R Squared:               0.976982
Sigma hat:               3.342032E-2


The important upshot of this is that the first three factors of the TSVD are really represented by just two "phenomena", which require modeling. If I can model vectors ${\displaystyle U_{1}}$ and ${\displaystyle U_{2}}$, then I can model the first three yearly vectors.

So what if we try to model the singular vectors with the usual suspects? I get this:

Singular Vector 1:
Linear Regression:        Estimate            SE              Prob
Constant                 -0.575638      (0.145608)          0.00078
JulTemp                  2.166527E-2    (8.616075E-3)       0.02058
R Squared:               0.240202

Singular Vector 2:
Linear Regression:        Estimate            SE              Prob
Constant                 -0.339790      (9.522331E-2)       0.00205
FebTemp                  -3.973373E-2   (1.653315E-2)       0.02662
MarTemp                  -5.146347E-2   (1.735696E-2)       0.00795
R Squared:               0.630118

Singular Vector 3:
Linear Regression:        Estimate            SE              Prob
Constant                 2.11176        (0.815337)          0.01750
JulTemp                  -0.127284      (4.824594E-2)       0.01576
R Squared:               0.258169


So ice no longer figures in the regressions -- but, while the second is higher, and seems to have just the spring temperatures, the first and third are lower and use only the July temperatures from the previous fall.

I find this odd: Factor 1 is composed primarily of SV1 and SV3, but they have July temp dependence, not March dependence.

Regressions on Tensor Region Vectors

Regression were performed on the region vectors against the tilted latitude/longitude coordinates.

Here is a summary of results for the first 28 singular values:

 Rank Singular Value Intercept Intercept p-value Minor(tlat) Coef Minor p-value Major(tlong) Coef Major p-value Adjusted R squared 1 4539.8676 0.319638 4.31e-13* -0.001460 0.5784 0.005152 1.64e-05* 0.9504 2 83.0595 -0.38230 0.000223* 0.36046 0.006295* 0.15987 3.45e-05* 0.9441 3 76.5755 0.419747 8.26e-09* -0.189612 3.01e-05* -0.026632 7.95 e-05* 0.964 4 46.6206 0.51195 0.01392* 0.06377 0.00545* 0.8028 5 37.8441 -0.43306 0.001098* -0.24640 0.114751 0.16828 0.000277* 0.8796

Mean Surface Models

These mean surfaces were computed via SVD: the matrix of means of each of the 45 1901-1923 time series (9 regions, 5 flowers) ${\displaystyle M_{5\times 9}}$ was decomposed via matrix SVD,

${\displaystyle M=U\Lambda V^{t}=\sum _{i=1}^{5}\lambda _{i}{\overline {u}}_{i}{\overline {v}}_{i}^{t}}$

The region singular vectors ${\displaystyle {\overline {v}}_{i}}$ (corresponding to the centroids of the nine regions) were regressed on a quadratic trend of the corresponding latitudes, longitudes, and their squares. The first three singular vectors were significantly correlated with geography, and the last two were not (and so were eliminated as "noise"). The vectors ${\displaystyle {\overline {v}}_{i}^{t}}$ become functions ${\displaystyle v_{i}(long,lat)}$, and hence the vector model for means of all species over these 23 years is thus defined by

${\displaystyle {\overline {M}}(long,lat)=\sum _{i=1}^{3}\lambda _{i}{\overline {u}}_{i}v_{i}(long,lat)}$

They are graphed below over Nova Scotia, along with the data from 1901. Earlier first arrival times are lighter, and larger. Of course our contours are not meant to be "taken seriously" when extrapolated far from Nova Scotia. We include them to emphasize the shape of the quadratic trend surface.

Conclusions

Expected Climate Change

"Although there are important micro- and meso-scale variations between the climate projections, there are some general patterns that emerge. The Maritime Provinces are projected to experience increases in both mean annual temperature and precipitation (Figures 4, 5). By 2050, there would be a 2 to 4 C ° increase in summer temperature, depending on model inputs and geographic location. Future warming of 1.5 to 6 C ° during winter can be anticipated. Coastal areas would see lesser changes in temperature than would interior Nova Scotia and western New Brunswick. Precipitation in Maritime Canada is anticipated to increase in the future, continuing the trend established since 1948, but seasonal and yearly variations will become more evident. Drier summer conditions may characterize inland regions. For these areas, the change in rainfall may not offset the increase in evapotranspiration caused by higher summer temperatures."

We suggest then, that a 4 degree change overall by 2050. We can run our model with a 4 degree C change across the board, and discover how our model suggests flowering might change.

Acknowledgements

We gratefully acknowledge the help we have received on this project, in terms of

• data (Adam Fenech, Brian T. Hill),
• thoughtful suggestions (Teresa Devor), and
• grant support (NKU Collaborative Faculty and Student Grant #)
• student research support from NKU's Department of Mathematics and Statistics (Dr. Roger Zarnowski, chair)

Long thanks Culbertson for inspiring this project in the first place.

Bibliography

Vasseur et al. (2001)

• Bibtex citation:
@article{10.2307/3858444,
ISSN = {10926194, 19385307},
URL = {http://www.jstor.org/stable/3858444},
abstract = {Since 1996, Nova Scotia Plantwatch has collected earliest flower dates for 12 plant species at 200 sites in Nova Scotia. The initial results for 1996-1998 are compared with records collected by MacKay between 1892 and 1923. Although the Mackay data were from a colder climatic interval in the Northern Hemisphere, most flowering dates are not significantly different from the present warmer (+0.5 - 0.7°C) period except during the 1998 season of record warmth. The only two species that showed significant differences are Epigaea repens and Syringa vulgaris. While E. repens showed significant later recent dates of first bloom, S. vulgaris showed earlier dates. Some of the variation within the province may be linked to oceanic influence; other variation reflects latitudinal gradients. These phenological results are compatible with other evidence that the average spring climate of the Atlantic Canada region has remained cool since 1948, but the early flowering in 1998 may be a response to a warming trend in the western part of the region.},
author = {Liette Vasseur, Robert L. Guscott, Peta J. Mudie},
journal = {Northeastern Naturalist},
number = {4},
pages = {393-402},
publisher = {Eagle Hill Institute},
title = {Monitoring of Spring Flower Phenology in Nova Scotia: Comparison over the Last Century},
volume = {8},
year = {2001}
}


Quotes:

• However, climate records for the Atlantic region of Canada (i.e., Nova Scotia, New Brunswick, Prince Edward Island, and Newfoundland) have shown a warming trend from 1885-1947 and a cooling trend (-0.7 °C) from 1948-1995
• merging of data from almost degrees of latitude (-43.5 - 52 N)
• in Nova Scotia alone, there is a steep gradient in mean annual temperature from 7.1 °C in the Southwest to 5.5°C in the Northeast
• Jackson (1966) established the sensitivity of spring flowering dates to air temperatures on a microcli- matic level in a small study area.
• Price and Wasser (1998) also showed that early season warming and snowmelt may advance flowering by 7 days.
• In 1998, however, all species except Epigaea repens flowered on average 12 days earlier. This extraordinary year was marked by an annual temperature increase in Nova Scotia of almost 1°C, with most of this increase occurring in spring and the fall (Environment Canada 1998). Flowering dates varied greatly between the different parts of Nova Scotia because of the east-west and north-south ranges in climatic conditions.
• This trend is consistent with the slight cooling reported for the Atlantic region (Nova Scotia to Newfoundland) as a whole and it may indicate major inter-regional differences between eastern and western Canada, where spring flowering is now 10 days earlier than it was 45 years ago
• Most species, such as red maple, exhibited more spatial variation in phenological dates within in the Nova Scotia study area than between the two periods of survey. These differences were most noticeable between coastal and interior sites. On the coast, cold nearshore currents and prolonged spring fog may have buff- ered effects of air warming; in the interior, conditions are more subject to rapid changes in response to warm, dry, continental air masses.
• while lilac bloomed significantly earlier over time [ael: I don't think that they made this case], Epigea repens did not seem as sensitive to change. Past phenology studies (Price and Wasser 1998, Sparks and Carey 1995) have shown that it is normal for the response to climate change to vary according to species. With regard to mayflower, this may reflect a lack of plastic response or the buffering conditions associated with its prostrate morphology. The sheltered conditions in which mayflower grows might have buffered its ability to respond to climatic changes.
• on the Northumberland Strait coast, where delay in sea ice break-up may slow the time of flowering.
• studies have suggested that recent winter cooling trends may be related to either high levels of atmospheric aerosols over Atlantic Canada, or to changes in ocean and sea ice patterns (e.g., Morgan et al. 1993). The semi-insular topography of Nova Scotia may further increase the impact of lowered coastal water temperature
• if global temperatures rise by more than 1°C over the next 50 years (Jones et al. 1999), the 1998 survey response may indicate that most species will flower earlier by about 4 days to two weeks. However, other factors such as the season of warming may also influence the level of response (Fitter et al. 1995). Warming in winters and early spring may advance flowering dates (Price and Wasser 1998
• it is also important to understand their means of adaptation to environmental variation. [ael: variability is important.]
• it is possible to monitor phenology with the help of volunteers. But, as pointed out by Klaveness and Wielgolaski (1996), analysis and interpretation of the data require a critical sense of data quality and sound judgement. [ael: why not cite MacKay himself? Every report had something about data quality in it, and its importance]
• there was a need for more detailed information on flowering morphology and the definition of the flowering stages. In MacKay's survey, training of the teachers was done on a regular basis to maintain a certain quality of the data.
• [ael: They've got one date wrong: they indicate that MacKay was using data from his schools from 1892, when in fact he began using that data in 1897 -- cite MacKay's report from 1897 or 98.]

Garbary and Taylor (2007)

Garbary, David J., and Barry R. Taylor. 2007. Flowering during January in Antigonish County, Nova Scotia. Canadian Field Naturalist 121(1): 76–80.
http://journals.sfu.ca/cfn/index.php/cfn/article/view/397
DOI: http://dx.doi.org/10.22621/cfn.v121i1.397


Garbary et al. (2012)

David J. Garbary, Jonathan Ferrier, Barry R. Taylor (2011). Late bLooming of pLants from Northern Nova Scotia: responses to a miLd faLL and winter. Proceedings of the Nova Scotian Institute of Science (2011), Volume 46, Part 2, pp. 149-174
https://www.researchgate.net/publication/230646834_Late_blooming_of_plants_from_northern_Nova_Scotia_responses_to_a_mild_fall_and_winter



Houle (2007)

@article{doi:10.1139/X06-239,
author = {Gilles Houle},
title = {Spring-flowering herbaceous plant species of the deciduous forests of eastern Canada and 20th century climate warming},
journal = {Canadian Journal of Forest Research},
volume = {37},
number = {2},
pages = {505-512},
year = {2007},
doi = {10.1139/X06-239},
URL = {http://dx.doi.org/10.1139/X06-239},
abstract = {Increases in the emission of greenhouse gases, particularly during the second half of the 20th century, have been associated with climate warming at the global scale. High latitude areas have been reported to be particularly sensitive to such changes, with significant impacts on plant phenology. The objectives of the present study were to (i) estimate changes in the flowering dates of 18 spring-flowering herbaceous plant species typical of the deciduous forests of eastern North America in three areas of eastern Canada (Gatineau-Ottawa, Montreal, and Quebec) from 1900 to 2000 and (ii) associate these changes with those of annual and spring local temperatures. My results show a 2-6 day advance in flowering date over 100 years, depending on the region considered (corresponding to a ~2-3 advance per 1 degree C);  these values are somewhat lower than those published in other studies, but still support the increasing body of literature on the effects of climate warming on plant phenology. Shifts in flowering phenology were particularly evident for Montreal, a large metropolitan region; this suggests that global climate warming, and its effects on plant phenology, may be exacerbated by local conditions, particularly those associated with large urban areas. Furthermore, species-specific responses to climate warming, as those presented here, might lead to significant changes in community composition and ecosystem functions.
},
eprint = {http://dx.doi.org/10.1139/X06-239}
}


Astonishing stuff: This article was cited by Hill and Garbary. It seems to be a relatively straight-forward regression analysis of FAT data:

"My results show a 2-6 day advance in flowering date over 100 years, depending on the region considered (corresponding to a ~2-3 advance per 1 degree C); these values are somewhat lower than those published in other studies, but still support the increasing body of literature on the effects of climate warming on plant phenology."

p. 509: "... the species studied appeared to show different sensitivity (i.e., intensity of response) to climate; such species-specific responses might cause significant changes in community composition and ecosystem functions with climate warming...."

Hill and Garbary (2013)

@Article{Hill-n-Garbary2013,
author =      "Nicholas M. Hill and David J. Garbary",
title =       "Early spring flowering in Nova Scotia: an extreme spring is reflected in advanced flowering",
journal =     "Proceedings of the Nova Scotian Institute of Science",
year =        "2013",
volume =      "47",
number =      "2",
pages =       "211--220",
OPTmonth =    "",
abstract = "Twenty species of herbaceous plants and four non-amentiferous shrubs were found in flower in March-April in Nova Scotia during the spring of 2012. Plants were observed primarily in Kings and Antigonish Counties, with several observations from Inverness County. The precocious flowering is attributed to an abnormally warm late winter and spring (February-March) in which climate normals for monthly average temperature were exceeded by a minimum of 1.2Â°C in February (Tracadie) to a maximum of 8.5Â°C in March (Kentville). Flowering was an average of 17 days earlier than herbarium records in the largest regional herbaria (ACAD, NSAC). Proportional contribution to the early flowering guild was greater for exotic species which featured weedy families not represented in the native group. These observations of spring climate conditions and flowering phenology are consistent with regional climate change associated with milder and earlier springs.",
URL =        "https://ojs.library.dal.ca/nsis/article/view/nsis47-2hillgarbary/3921"
}

• "As shown by the climate normals, February through April are not particularly conducive to plant growth and flowering in Nova Scotia (Table 1). There is typically extensive snowfall, and considerable snowpack remaining at the end of each month. While the data for Antigonish Co. are not available, the lower temperatures would suggest even greater snowpack than for the Annapolis Valley. The mild winter of 2012 was characterized by an 88% reduction in snowpack at the end of February and 100% reduction in March and April."
• Climate data for Nova Scotia were obtained from the internet (http://www.climate.weatheroffice.gc.ca/Welcome_e.html). Kentville (45Â°04'N, 64Â°29'W, Kings Co.) was used as the reference site for South Berwick (45Â°1.4'N, 64Â°42.6â'W) where most of the observations were made by NMH. Tracadie (45Â°36'N, 61Â°40'W, Antigonish Co.) was used as the reference site for Antigonish town and environs (45Â°37.4 N, 61Â°59.5'W) where most of the observations were made by DJG.
• The link to the climate data above is dead. http://www.climate.weatheroffice.gc.ca/ is live, however, but the best link might be http://climate.weather.gc.ca/historical_data/search_historic_data_e.html
• Flowering onset in the temperate region is determined mainly by temperature (Miller-Rushing and Primack 2008); soil moisture levels and precipitation do not appear to be limiting factors in most years.
• Native and exotic taxa were equally represented among the 24 early flowering species. Since exotic species are a minority of the total flora, a weighted analysis was required. Exotics account for more than a third of the flora in Nova Scotia (Hill and Blaney 2010) but even this overestimates their real frequency, since many of these exotics are transitory and fail to become established in the regional flora. When a Chi-square analysis is performed using only the common native and exotic species, (i.e., subtracting the rare and transient species from both groups), exotic species are significantly (p<0.05) overrepresented in the early spring flowering guild. In addition to a greater proportional representation of exotics among the early flowering plants, their seasonal shift in flowering time, from the earliest records in herbaria, was significantly earlier than that of native plants (see Table 2). The average shift in flowering time was two weeks earlier for the group of exotic plants than the natives (2012 flowering time shifts= 24.5 Â± 16.7 versus 10.6 Â±15.7 days for exotics and natives respectively). Many of the exotic species are ruderals, plants adapted to frequently disturbed habitats through fast growth rate and early and often lethal reproduction (Grime 1979). The evolution of this set of ruderal traits is pronounced in several highly successful families which are also those best represented among the world's worst weeds (Huston 1994). Early flowering exotic representatives in Nova Scotia were with one exception all short-lived herbs representing three of the top weedy families (3 species of Asteraceae, 2 Brassicaceae, and 1 Lamiaceae) that contribute 10 or more species to the World's Worst Weeds (Holm et al. 1979, cited in Huston 1994). Although herbs were best represented among the early flowering native plants, this group shared only one family with the exotics (Violaceae) and it represented only one of the common weedy families (viz. the Rosaceae, 2 represented in native groups). Based on the above differences in their relative contribution to the early flowering records, their 2012 flowering shift, and their phylogenetic origins, these exotics are clearly the group poised to expand, given a fundamental change in spring climate.
• these records average 17 days earlier than the earliest of these specimens. While it is tempting to conclude that we have shown an advancement of 17 days in average flowering, such a conclusion is moderated by the fact that our records are based on haphazard observations in 2012 rather than systematic observations over many years.

We used our model to attempt to reproduce their results for the anomolous year 2012. We computed estimated FATs for Mayflower and Strawberry -- the two members of our five species that they also collected -- and compared our results to their data.

Our results (with their data in parentheses):
Antigonish: Mayflower: April 10 (April 15)
Antigonish: Strawberry: April 25 (April 28)
Annapolis : Strawberry: April 17 (April 16)


Compare those dates to the dates we estimate for the two adjacent years. We find that FATS are six or seven days earlier in 2012 than in these other years:

2011:
Antigonish: Mayflower: April 16
Antigonish: Strawberry: May 1
Annapolis : Strawberry: April 21

2013:
Antigonish: Mayflower: April 17
Antigonish: Strawberry: May 2
Annapolis : Strawberry: April 23


Hence our model suggests, as does the article, that 2012 was exceptional -- and our model also does a remarkable job of estimating the FATs, nearly 100 years after the data used to create our model.

The Extraordinary SVD

@ARTICLE{2011arXiv1103.2338M,
author = {{Martin}, C.~D. and {Porter}, M.~A.},
title = "{The Extraordinary SVD}",
journal = {ArXiv e-prints},
archivePrefix = "arXiv",
eprint = {1103.2338},
primaryClass = "math.NA",
keywords = {Mathematics - Numerical Analysis, Computer Science - Numerical Analysis, Physics - Computational Physics, Physics - Data Analysis, Statistics and Probability},
year = 2011,
month = mar,
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}


This article makes the claim that no natural analogy for the SVD exists in the tensor case, and discusses two alternatives.

Pictonians at Home (1914)

SKETCHES OF PROFESSIONAL MEN AND WOMEN OF PICTOU COUNTY - ITS HISTORY AND INSTITUTIONS

By Rev. J. P. MacPhie, M. A. Author of "The Homeland of the Bible"

Pinkham Press

Boston, Massachusetts U.S.A.

Copyright 1914, by J. P. MacPhie

Wood (1994)

@Article{Wood-1994,
author =      "B. Anne Wood",
title =       "Constructing Nova Scotia's 'Scotchness': the Centenary Celebrations of Pictou Academy in 1916",
journal =     "Historical Studies in Education",
year =        "1994",
volume =      "6",
number =      "2",
pages =       "281--302",
OPTmonth =    "",
note =        "http://historicalstudiesineducation.ca/index.php/edu_hse-rhe/article/view/1206"
}


Wood (1999)

@Article{Wood-Schooled,
author =      "B. Anne Wood",
Promoting 'Schooled Subjectivities' in 19th-Century Nova Scotia",
year =        "1999",
volume =      "28",
number =      "2",
pages =       "41--57",
OPTmonth =    "",
OPTnote =     "Description of 'Little Goosey' -- Wood not fond of MacKay"
}


Scobie (1997)

@book{scobie1997contribution,
title={Contribution of Presbyterianism to the
author={Scobie, C.H.H. and Rawlyk, G.A.},
isbn={9780773516007},
lccn={97222710},
series={McGill-Queen's Studies in the History of
Religion},
year={1997},
ceremony, from Wood, B. Anne. 'Schooling /
credentials for professional advancement: a case
study of Pictou Presbyterians.' In The Contribution
of Presbyterianism to the Maritime Provinces of
Canada, ed. Charles H. H. Scobie and George
A. Rawlyk. Montreal and Kingston: McGill-Queen's
University Press, 1997, 54-72.",
publisher={MQUP}
}


Nilsson (2013)

@article {Nilsson566,
author = {Nilsson, Ove},
title = {A Pathway to Flowering{\textemdash}Why Staying Cool Matters},
volume = {342},
number = {6158},
pages = {566--567},
year = {2013},
doi = {10.1126/science.1245861},
publisher = {American Association for the Advancement of Science},
issn = {0036-8075},
URL = {http://science.sciencemag.org/content/342/6158/566},
eprint = {http://science.sciencemag.org/content/342/6158/566.full.pdf},
journal = {Science}
}


"Temperature is one of the most important cues that plants use to flower at the right time of year -- a process crucial for adaptation and reproductive success."

I found an article (566, attached) quite by accident yesterday, but which we can mine for a quote, perhaps: it starts off with "Temperature is one of the most important cues that plants use to flower at the right time of year -- a process crucial for adaptation and reproductive success."

And there are some other really nice tidbits. As we reflect back on how we ended up modeling the climate piece, we also ended up including ice -- as a sort of integral of the winter temps -- more ice, means it was a tougher winter? (also a function of precipitation, of course, but...:)

At any rate, they say that "Many plants ... require an extended period of cold during winter before they can respond to the increasing temperatures and day lengths during spring that will trigger flowering. This process, called vernalization...." I've thought since we introduced ice, that it is a proxy for "an extended period of cold".

Lee, et al. (2013)

@article {Lee628,
author = {Lee, Jeong Hwan and Ryu, Hak-Seung and Chung, Kyung Sook and Pos{\'e}, David and Kim, Soonkap and Schmid, Markus and Ahn, Ji Hoon},
title = {Regulation of Temperature-Responsive Flowering by MADS-Box Transcription Factor Repressors},
volume = {342},
number = {6158},
pages = {628--632},
year = {2013},
doi = {10.1126/science.1241097},
publisher = {American Association for the Advancement of Science},
abstract = {In a cool spring, flowering might be delayed compared to a warm spring, even though the change in day length marches on regardless of temperature. Lee et al. (p. 628, published online 12 September; see the Perspective by Nilsson) now show that this delay in flowering is a regulated process, not simply a consequence of sluggish metabolism. In the model plant Arabidopsis, transcription of the gene encoding the regulator SHORT VEGETATIVE PHASE (SVP) is unaffected by temperature, but the stability of the SVP protein is decreased at higher temperatures. Its regulatory partner, FLOWERING LOCUS M (FLM)-β, is the product of alternative splicing of transcripts from the gene encoding FLM that favors the β form at lower temperatures. SVP and FLM-β form a complex that represses flowering. At lower temperatures, more of the repressive complex is present and flowering is delayed. At higher temperatures, SVP tends to degrade and FLM-β tends not to be produced, yielding reduced levels of the repressive complex, which allows flowering to proceed.Changes in ambient temperature affect flowering time in plants; understanding this phenomenon will be crucial for buffering agricultural systems from the effects of climate change. Here, we show that levels of FLM-β, an alternatively spliced form of the flowering repressor FLOWERING LOCUS M, increase at lower temperatures, repressing flowering. FLM-β interacts with SHORT VEGETATIVE PHASE (SVP); SVP is degraded at high temperatures, reducing the abundance of the SVP{\textendash}FLM-β repressor complex and, thus, allowing the plant to flower. The svp and flm mutants show temperature-insensitive flowering in different temperature ranges. Control of SVP{\textendash}FLM-β repressor complex abundance via transcriptional and splicing regulation of FLM and posttranslational regulation of SVP protein stability provides an efficient, rapid mechanism for plants to respond to ambient temperature changes.},
issn = {0036-8075},
URL = {http://science.sciencemag.org/content/342/6158/628},
eprint = {http://science.sciencemag.org/content/342/6158/628.full.pdf},
journal = {Science}
}


In the next paper (Lee), which I found from the references in 566 (it was in the same issue of Science, by the way), is the quote "Because day length and temperature vary with latitude, flowering responses condition the global distribution of plant species." This ties in with the regional modeling, and our surprise at discovering the necessity of the tilted coordinates (related, no doubt, to coastal/ocean effects, which we attempt to account for by using the quadratic long/lat models).

Pose, et al. (2013)

TY  - JOUR
AU  - Pose, David
AU  - Verhage, Leonie
AU  - Ott, Felix
AU  - Yant, Levi
AU  - Mathieu, Johannes
AU  - Angenent, Gerco C.
AU  - Immink, Richard G. H.
AU  - Schmid, Markus
TI  - Temperature-dependent regulation of flowering by antagonistic FLM variants
JA  - Nature
PY  - 2013/11/21/print
VL  - 503
IS  - 7476
SP  - 414
EP  - 417
SN  - 0028-0836
UR  - http://dx.doi.org/10.1038/nature12633
L3  - 10.1038/nature12633
M3  - Letter
L3  - http://www.nature.com/nature/journal/v503/n7476/abs/nature12633.html#supplementary-information
ER  -


General Index

"The phenological data, collected over 31 years by Dr. A.H. MacKay is a major contribution to Canadian science...."

%%% New Entry: Mon Nov 28 22:18:23 EST 2016 %%%

@Article{ProceedingsGeneralIndex,
author = 	"",
title = 	"Cumulative Author and Subject Indices to Proceedings of the Nova Scotian Institute of Science Volumes 1-39 (1863 to 2008) inclusive",
journal = 	"Proceedings of the Nova Scotia Institute of Science",
year = 	"1992",
volume = 	"39",
number = 	"4",
pages = 	"149--247",
OPTnote = 	"http://nsis.chebucto.org/cumulative-author-and-subject-indices-to-proceedings-of-the-nova-scotian-institute-of-science-volumes-1-39-1863-to-1992-inclusive/"
}


Proceedings1901

%%% New Entry: Mon Nov 28 22:18:23 EST 2016 %%%

@Article{Proceedings1901,
author = 	"Alexander H. MacKay",
title = 	"Phenological Observations in Nova Scotia and Canada, 1901",
journal = 	"Proceedings and Transactions of the Royal Society of Canada",
year = 	"1901",
volume = 	"10",
number = 	"4",
pages = 	"485--501",
OPTmonth = 	"May",
OPTnote = 	""
}


ProceedingsMay1911

%%% New Entry: Mon Nov 28 22:18:23 EST 2016 %%%

@Article{ProceedingsMay1911,
author = 	"Alexander H. MacKay",
title = 	"Phenological Phenomena, Canada, 1910",
journal = 	"Proceedings and Transactions of the Royal Society of Canada",
year = 	"1911",
volume = 	"5",
number = 	"3",
OPTpages = 	"",
month = 	"May",
OPTnote = 	"At the meeting of The Royal Society on the 28th of September,
1910, Dr. A. H. Mackay, F.R.S.C., General Secretary of the Botanical
Club of Canada, gave notice of the dissolution of this club, the chief
work of which was the collection and publishing phenological statistics.
The necessity for this decision is to be regretted, more especially by
those interested in phenological phenomena, and it is to be hoped
that Dr. Mackay and his phenological staff will still be able to carry on in
Nova Scotia the excellent work they have been doing for so many years.
In the various European countries the work of collecting and publishing phenological statistics is undertaken by the different Weather
Bureaus, and the Meteorological Service of Canada, which for some
years past has also published statistics prepared by Mr. F. F. Payne,
of the Central Office, Toronto, will extend this work. It is also hoped
that we may be able to enlist the services of the provincial Boards of
Education, as has been done in the Province of Nova Scotia.
The chief use of phenological statistics from a meteorological point
of view is the graphic indication they give of the climate and the varying seasons. To those familiar with the dates of the flowering of
common plants, etc., in their own district, a mental picture of the
climate of another district can more readily be formed by comparing
such dates than would be formed by consulting meteorological statistics.
Included in schedules accompanying this report are dates from
twenty-five selected stations in Nova Scotia, which have been kindly
suppliai, and, subject to the approval of Dr. Mackay and his staff,
the average dates (phenochrons) for that province will be added for publication as soon as they have time to prepare them. The reports from
other portions of Canada include six from British Columbia, six from
Alberta, five from Saskatchewan, ten from Manitoba, nine from Ontario, two from Quebec and one from New Brunswick. Much fuller
reports were supplied from Nova Scotia than are included in the
Meteorological Service schedules and doubtless they will be published
elsewhere."
}


Sheehan (1974)

@article{sheehan1974alexander,
title={Alexander H. MacKay, social and educational reformer},
author={Sheehan, Nancy M},
journal={Profiles of Canadian Educators (np, 1974)},
pages={253--70},
url={http://norsemathology.org/wiki/images/b/b0/MacKayStory.pdf}
year={1974}
}


A.H. MacKay, whose career as Superintendent of Education might be summed up in his claim that "nothing has been left undone...to inculcate into youth a sense of the privileges and responsibilities of citizenship", called for the introduction of compulsory military drill -- a programme he had established in Halifax in 1892 -- into the province's schools as an aid to personal and civic discipline and, ultimately, as a preparation for war.

Austen

Austen, I. (2000). Grassroots science. Canadian Geographic. May/June: 76.

@Article{Austen2000,
author =      "I. Austen",
title =       "Grassroots Science",
year =        "2000",
OPTvolume =   "",
OPTnumber =   "",
pages =       "76",
month =       "May/June",
OPTnote =     ""
}


Zeller, 2015

@article{zeller2015reflections,
title={Reflections on time and place: The Nova Scotian Institute of Science in its first 150 years},
author={Zeller, Suzanne},
journal={Proceedings of the Nova Scotian Institute of Science (NSIS)},
volume={48},
number={1},
year={2015}
}

• This is an extraordinary document that gives some of the background information on how MacKay may have come to do his citizen science, prompted by people such as George Lawson and James Gordon MacGregor (1852-1913): "As the NSIS delegate to the RSC meeting the following year, MacGregor proposed an RSC committee to design a centralized programme of 'simultaneous observations over the whole country' of various periodic natural phenomena, including bird migrations (MacGregor 1886b). As NSIS president in 1888, he reiterated his call for an RSC-administered programme of â'collective investigation,' citing a list of relevant subjects for which the NSIS could, in turn, serve as a regional coordinator."
• While Lawson and MacGregor lent their broader scientific vision to this Humboldtian project, it was the Botanical Club's first secretary, the Nova Scotia-born Alexander Howard MacKay (1848-1929), whose Herculean efforts lent it longevity with increasing analytical sophistication.

Fenech, et al.

%%% New Entry: Tue Nov 22 19:26:10 EST 2016 %%%

@InBook{Fenech2005,
author =      "",
title =       "Integrated Mapping Assessment",
chapter =     "Impact of climate on changes in the seasonal timing of life cycle events of eastern Canada from 1901 to 1923",
year =        "2005",
editor =   "A. Fenech, D. MacIver, H. Auld and R. Hansell",
pages =    "186",
OPTvolume =   "",
OPTseries =   "",
OPTedition =  "",
OPTmonth =    "",
OPTnote =     "access"
}


Citizen Scientists (2013)

%%% New Entry: Sat Oct 8 20:58:30 EDT 2016 %%%

@Article{Williams2013,
author = 	"A. R. Williams",
title = 	"Citizen Scientists",
journal = 	"National Geographic",
year = 	"2013",
volume = 	"223",
number = 	"3",
pages = 	"p. 118",
month = 	"March",
OPTnote = 	""
}


As early as 17002 European bird surveys included reports from backyard birders.

Vincent, et al. (2012)

@article {JGRD:JGRD18070,
author = {Vincent, Lucie A. and Wang, Xiaolan L. and Milewska, Ewa J. and Wan, Hui and Yang, Feng and Swail, Val},
title = {A second generation of homogenized Canadian monthly surface air temperature for climate trend analysis},
journal = {Journal of Geophysical Research: Atmospheres},
volume = {117},
number = {D18},
issn = {2156-2202},
url = {http://dx.doi.org/10.1029/2012JD017859},
doi = {10.1029/2012JD017859},
pages = {n/a--n/a},
keywords = {Climate change and variability, Climatology, General or miscellaneous, Canada, adjustment, discontinuity, homogeneity, temperature, trends},
year = {2012},
note = {D18110},
}


This study presents a second generation of homogenized monthly mean surface air temperature data set for Canadian climate trend analysis. Monthly means of daily maximum and of daily minimum temperatures were examined at 338 Canadian locations. Data from co-located observing sites were sometimes combined to create longer time series for use in trend analysis. Time series of observations were then adjusted to account for nation-wide change in observing time in July 1961, affecting daily minimum temperatures recorded at 120 synoptic stations; these were adjusted using hourly temperatures at the same sites. Next, homogeneity testing was performed to detect and adjust for other discontinuities. Two techniques were used to detect non-climatic shifts in de-seasonalized monthly mean temperatures: a multiple linear regression based test and a penalized maximal t test. These discontinuities were adjusted using a recently developed quantile-matching algorithm: the adjustments were estimated with the use of a reference series. Based on this new homogenized temperature data set, annual and seasonal temperature trends were estimated for Canada for 1950–2010 and Southern Canada for 1900–2010. Overall, temperature has increased at most locations. For 1950–2010, the annual mean temperature averaged over the country shows a positive trend of 1.5�C for the past 61 years. This warming is slightly more pronounced in the minimum temperature than in the maximum temperature; seasonally, the greatest warming occurs in winter and spring. The results are similar for Southern Canada although the warming is considerably greater in the minimum temperature compared to the maximum temperature over the period 1900–2010.

Webb and Marshall (1999)

%%% New Entry: Fri Oct 7 21:00:52 EDT 2016 %%%

@TechReport{Webb1999,
author = "K.T. Webb and I.B. Marshall",
title = "Ecoregions and Ecodistricts of Nova Scotia",
institution =	"Agriculture and Agri-Food Canada, Crops and Livestock Research Centre",
year = 	"1999",
OPTtype = 	"",
OPTnumber = 	"",
note = 	"http://sis.agr.gc.ca/cansis/publications/surveys/ns/nsee/nsee_report.pdf"
}


Morgan, et al. (1993)

%%% New Entry: Fri Oct 7 20:26:16 EDT 2016 %%%

@Article{Morgan1993,
author = 	"M. R. Morgan and K. F. Drinkwater and R. Pocklington",
title = 	"Temperature trends at coastal stations in Eastern Canada",
journal = 	"Climatological Bulletin",
year = 	"1993",
volume = 	"27",
number = 	"3",
OPTpages = 	"",
OPTmonth = 	"",
note = 	"http://geoprodig.cnrs.fr/items/show/81768"
}


Annual air temperature anomalies (relative to the 1900-90 mean) for a composite record derived from the average of the annual means of data from Charlottetown (P.E.I.), Sydney and Sable Island (N.S.), are shown in Figure 2A. Data from the three stations were similar with correlation coefficients (r) between any two sites exceeding 0.85 (p<.01).

A cooling trend from 1900 to 1923 was followed by a rapid rise of about l.O°C by 1930.

Monahan, et al. (2016)

• BibTex citation:
@article {ECS2:ECS21465,
author = {Monahan, William B. and Rosemartin, Alyssa and Gerst, Katharine L. and Fisichelli, Nicholas A. and Ault, Toby and Schwartz, Mark D. and Gross, John E. and Weltzin, Jake F.},
title = {Climate change is advancing spring onset across the U.S. national park system},
journal = {Ecosphere},
volume = {7},
number = {10},
issn = {2150-8925},
url = {http://dx.doi.org/10.1002/ecs2.1465},
doi = {10.1002/ecs2.1465},
pages = {n/a--n/a},
keywords = {climate change, landscape context, monitoring, national parks, phenology, protected areas, Special Feature: Science for Our National Parks' Second Century, spring index, United States},
year = {2016},
}


The “Spring indices” are climate-based empirical models of phenological events—developed from a 60-yr data set of in situ lilac and honeysuckle phenology—that predict leaf and bloom dates for a suite of species and provide insight into historical patterns of spring warming (Schwartz 1997, Rosemartin et al. 2015). The models used day of year, chilling hours, heat accumulation, and number of high-energy synoptic events (i.e., large-scale warm spells) to develop indices of first leaf (FLi) and first bloom (FBi) dates for a cloned lilac cultivar (Syringa x chinensis “Red Rothomagensis”) and two cloned honeysuckle species (Lonicera tatarica “Arnold Red” and L. korolkowii “Zabeli”) (Schwartz 1997, Schwartz et al. 2006). Recent work has extended these indices across the continental United States, from high-latitude regions to subtropical environments, by removing the chilling requirement and leveraging gridded climate products (Schwartz et al. 2013, Ault et al. 2015a).

Nova Scotia: the Stormiest Region of Canada (1990)

Nova Scotia: the Stormiest Region of Canada. Pages 77-81, in Phillips, David. The Climates of Canada. 1990. 176 pages. Canadian Government Publishing Centre, Supply and Services Canada.

HillNFIce

This study is an attempt to create representative historic ice charts off the east coast of Newfoundland for the winter months, January to April, on an annual basis for as long as records exist. Earlier work (Hill & Jones, 1990) had suggested a possible correlation between solar activity and the March ice extent for the years 1920 to 1988. No such correlation could be found for the years 1860 to 1920 and this left some doubt as to the veracity and consistency of the older ice records. While established ice records had been used since 1920, ice indices from a variety of sources and authors had been used prior to that year. The search for ice information from original sources, therefore, was begun with emphasis on the years preceding 1920. As one might expect, the further one goes back in history, the scantier the records become. Although the earliest recorded sighting of ice found so far is from 1527, it is only from 1810 that we have mention of ice on an annual basis, and even then there are years with little information.

%%% New Entry: Mon Nov 28 23:01:58 EST 2016 %%%

@PROCEEDINGS{hill1999
author = 	"Brian T. Hill",
title = 	"Historical sea ice extent for the Gulf of St. Lawrence and the Scotian Shelf from 1817 to 1962",
booktitle = {18th International Conference on Offshore Mechanics and Arctic Engineering - OMAE99},
year = {1999}
}


Weckström (2013)

• BibTex citation:
@article{Weckström201353,
title = "Evaluation of the sea ice proxy \{IP25\} against observational and diatom proxy data in the \{SW\} Labrador Sea ",
journal = "Quaternary Science Reviews ",
volume = "79",
number = "",
pages = "53 - 62",
year = "2013",
note = "Sea Ice in the Paleoclimate System: the Challenge of Reconstructing Sea Ice from Proxies ",
issn = "0277-3791",
doi = "http://dx.doi.org/10.1016/j.quascirev.2013.02.012",
url = "http://www.sciencedirect.com/science/article/pii/S0277379113000668",
author = "Kaarina Weckström and Guillaume Massé and Lewis G. Collins and Sami Hanhijärvi and Ioanna Bouloubassi and Marie-Alexandrine Sicre and Marit-Solveig Seidenkrantz and Sabine Schmidt and Thorbjørn J. Andersen and Morten L. Andersen and Brian Hill and Antoon Kuijpers",
keywords = "IP25",
keywords = "Diatoms",
keywords = "PIP25",
keywords = "Sea ice",
keywords = "NAO",
abstract = "The recent rapid decline in Arctic sea ice cover has increased the need to improve the accuracy of the sea ice component in climate models and to provide detailed long-term sea ice concentration records, which are only available via proxy data. Recently, the highly branched isoprenoid IP25, identified in marine sediments underlying seasonal sea ice, has emerged as a potential sea ice specific proxy for past sea ice cover. We tested the reliability of this biomarker as a sea ice proxy against observational sea ice data (sea ice concentrations from the global HadISST1 database) and against a more established sea ice proxy (sea ice diatom abundance in sediments) in the South-West (SW) Labrador Sea. Furthermore, our study location at the southern margin of Arctic sea ice drift provided a new environmental setting in which to further test the novel \{PIP25\} index. Our two study sites are located North-East (NE) and South-East (SE) of Newfoundland where box cores covering the last ca 100–150 years were collected. \{IP25\} concentrations are nearly an order of magnitude higher and sea ice diatoms more abundant in sediments from \{NE\} of Newfoundland, where sea ice prevails 2–4 months per year compared to the sediments \{SE\} of Newfoundland, where conditions are generally ice-free year round. The \{IP25\} fluxes \{NE\} of Newfoundland agree well with multi-decadal North Atlantic Oscillation (NAO) trends in the study area, which in previous studies have been shown to affect the climatic and sea ice conditions in the region. When assessed against observational sea ice data, \{IP25\} appears to be a more sensitive indicator of sea ice variability in this setting compared to sea ice diatoms and proved to be a robust and reliable proxy for reconstructing low-frequency variability in past sea ice concentrations. The \{PIP25\} index results clearly differ from the observed sea ice data underlining that caution needs to be exercised when using the index in different environmental settings. "
}


@article{doi:10.1137/07070111X,
author = {Tamara G. Kolda and Brett W. Bader},
title = {Tensor Decompositions and Applications},
journal = {SIAM Review},
volume = {51},
number = {3},
pages = {455-500},
year = {2009},
doi = {10.1137/07070111X},
URL = { http://dx.doi.org/10.1137/07070111X },
eprint = { http://dx.doi.org/10.1137/07070111X }
}


Fitter and Fitter (2002)

• BibTex citation:
@article {Fitter1689,
author = {Fitter, A. H. and Fitter, R. S. R.},
title = {Rapid Changes in Flowering Time in British Plants},
volume = {296},
number = {5573},
pages = {1689--1691},
year = {2002},
doi = {10.1126/science.1071617},
publisher = {American Association for the Advancement of Science},
abstract = {The average first flowering date of 385 British plant species has advanced by 4.5 days during the past decade compared with the previous four decades: 16\% of species flowered significantly earlier in the 1990s than previously, with an average advancement of 15 days in a decade. Ten species (3\%) flowered significantly later in the 1990s than previously. These data reveal the strongest biological signal yet of climatic change. Flowering is especially sensitive to the temperature in the previous month, and spring-flowering species are most responsive. However, large interspecific differences in this response will affect both the structure of plant communities and gene flow between species as climate warms. Annuals are more likely to flower early than congeneric perennials, and insect-pollinated species more than wind-pollinated ones.},
issn = {0036-8075},
URL = {http://science.sciencemag.org/content/296/5573/1689},
eprint = {http://science.sciencemag.org/content/296/5573/1689.full.pdf},
journal = {Science}}

• Flowering is especially sensitive to the temperature in the previous month, and spring-flowering species are most responsive.
• Flowering time also influences animals for which pollen, nectar, and seeds are important resources (9), and earlier flowering also implies earlier activity in other processes (leaf expansion, root growth, nutrient uptake) that are important for niche differentiation among coexisting species.... Large changes in flowering date will therefore disrupt ecosystem structure.
• FFD showed little variation in flowering time during the first four decades of the period studied (Fig. 1, inset), but there has been a major shift in FFD since the 1980s.
• Both pollination mechanism and geographical distribution explain part of the variation.
• insect-pollinated species that flowered early were much more sensitive to warming than those that flowered later (Fig. 2B).
• These data confirm studies (4, 13,28, 29) suggesting that FFD is sensitive to temperature. Some of those studies have shown a temporal trend, implying that climate warming is changing phenology progressively. In an analysis covering all of Germany in the period 1951–1996 (30), early spring phenophases advanced by up to 6 days in the second half of the period (1974–1996), a slower rate than we observed, whereas olive phenology in the Mediterranean has advanced by about 6 days per °C, comparable to our own findings
• There may also be evolutionary consequences: Table 3 lists six pairs of species, all of which form natural hybrids (33). Four of these are more likely to flower synchronously now than formerly, increasing the probability of hybridization, and two are less likely to, reducing it. These phenological changes, therefore, combined with more obvious consequences of climate change such as changes in geographic range (34), will alter population-level interactions (35) and community dynamics and have profound ecosystem and evolutionary consequences (36, 37).

Fitter, et al. (1995)

@article{10.2307/2390090,
ISSN = {02698463, 13652435},
URL = {http://www.jstor.org/stable/2390090},
abstract = {1. A data set of 36 years (1954-1989) of observations on first flowering dates (FFD) of 243 species of angiosperms and gymnosperms in one locality in southern central England is presented and analysed. 2. Individual FFDs ranged from 1 January to 17 August, and species varied considerably in the standard deviation of their FFD. The most variable species were mainly annuals and there was a negative relationship between mean FFD and variability, early-flowering species being the most variable. 3. For 219 of the 243 species, it was possible to fit regression equations for FFD to some set of monthly mean temperatures of the preceding months. These fits were generally best for woody plants and geophytes. February temperature was overall the most important determinant of flowering time. Sixty per cent of species flowering between January and April were affected by temperature 1-2 months before flowering; for summer (May onwards) flowering species, temperatures up to 4 months previously were important. 4. High spring temperatures advanced flowering by a mean of 4 days per degree. In contrast, both spring- and summer-flowering species were retarded in flowering by high temperatures in the previous autumn. 5. These relationships were used to simulate the effects of climatic warming: an overall increase of 1 ⚬C in each month would advance flowering in some species and retard others, by as much as 6 weeks. Retarded species were early-flowering, advanced species late-flowering. These results suggest a high degree of dependence of flowering time on temperature, and the variation between species implies that responses to climatic warming may be difficult to predict.},
author = {A. H. Fitter, R. S. R. Fitter, I. T. B. Harris, M. H. Williamson},
journal = {Functional Ecology},
number = {1},
pages = {55-60},
publisher = {[British Ecological Society, Wiley]},
title = {Relationships Between First Flowering Date and Temperature in the Flora of a Locality in Central England},
volume = {9},
year = {1995}
}

• Sixty per cent of species flowering between January and April were affected by temperature 1-2 months before flower- ing; for summer (May onwards) flowering species, temperatures up to 4 months previ- ously were important. 4. High spring temperatures advanced flowering by a mean of 4 days per degree. In contrast, both spring- and summer-flowering species were retarded in flowering by high temperatures in the previous autumn.
• These results suggest a high degree of dependence of flowering time on temperature, and the variation between species implies that responses to climatic warming may be difficult to predict.
• it is well known that variation in the first flowering time occurs from year to year for most species, with warm winters and springs bringing forward the date of first flowering, just as latitudinal gradients in first flowering date also reflect temperature gradient... flowering is also dependent on photoperiod in many species and this dependence may be absolute, such that the plant will not flower unless a particular day-length is exceeded, or relative, where flowering is delayed by short or shortening (or long or lengthening) day-length, but eventually occurs and may simultaneously be affected by temperature (Bernier 1988).
• February was a significant term for over 100 species, for example, but December rarely appeared (Fig. 2). After February, succeeding months entered progressively less often, until June which was a more frequent entrant than May.
• Nearly 60% of species flowering in spring (January-April) are strongly affected by the temperature 1 and 2 months earlier
• Figure 3 also shows a distinct bimodality, with spring-flowering species also being affected by temperature 7-9 months previously and summer-flowering species 10-11 months;
• These data demonstrate a very high degree of dependence of first flowering date on temperature in previous months: for only 24 out of 243 species (9.9%) was there no relationship between FFD and previous temperature.
• In 24% of the species, over half the variation in FFD could be accounted for by variation in mean monthly temperatures in the preceding year and for 54% of the species at least one-third was accountable
• Nevertheless, retardation was the general autumn effect (see Fig. 4) and seems not to have been widely noted previously
• This suggests that responses to warming will be complex, varying with species and conditions and their interaction.

Schwartz (1999)

• BibTex citation:
@Article{Schwartz1999,
author="Schwartz, D. M.",
title="Advancing to full bloom: planning phenological research for the 21st century",
journal="International Journal of Biometeorology",
year="1999",
volume="42",
number="3",
pages="113--118",
abstract="{\enspace}Phenology has emerged recently as an important focus for ecological research, primarily because of its considerable promise to address important questions in global modeling, monitoring, and climate change. Remote sensing technological developments have also contributed to phenology's resurgence, by generating extensive biosphere-related databases that require careful calibration and interpretation. This article reviews the major objectives, accomplishments, and challenges of contemporary phenological research, concentrating on papers presented in this thematic issue of the International Journal of Biometeorology and other recent venues relevant to global change. Strategies for the continued advancement toward global change-related goals are also presented. The crucial catalyst to this potential contribution will be the systematic development of observation networks on a national and global scale during the next decade and beyond.",
issn="1432-1254",
doi="10.1007/s004840050093",
url="http://dx.doi.org/10.1007/s004840050093"
}


Mohandass (2015)

• BibTex citation:
@article{Mohandass2015191,
title = "Increasing temperature causes flowering onset time changes of alpine ginger Roscoea in the Central Himalayas ",
journal = "Journal of Asia-Pacific Biodiversity ",
volume = "8",
number = "3",
pages = "191 - 198",
year = "2015",
note = "",
issn = "2287-884X",
doi = "http://dx.doi.org/10.1016/j.japb.2015.08.003",
url = "http://www.sciencedirect.com/science/article/pii/S2287884X15000576",
author = "Dharmalingam Mohandass and Jian-Li Zhao and Yong-Mei Xia and Mason J. Campbell and Qing-Jun Li",
keywords = "climate change",
keywords = "flowering phenology",
keywords = "global warming",
keywords = "herbarium-based phenology",
keywords = "Zingiberaceae ",
abstract = "Abstract Recent herbarium-based phenology assessments of many plant species have found significant responses to global climate change over the previous century. In this study, we investigate how the flowering phenology of three alpine ginger Roscoea species responses to climate change over the century from 1913 to 2011, by comparing between herbarium-based phenology records and direct flowering observations. According to the observations, flowering onset of the three alpine ginger species occurred either 22 days earlier or was delayed by 8–30 days when comparing the mean peak flowering date between herbarium-based phenology records and direct flowering observations. It is likely that this significant change in flowering onset is due to increased annual minimum and maximum temperatures and mean annual temperature by about 0.053°C per year. Our results also show that flowering time changes occurred due to an increasing winter–spring minimum temperature and monsoon minimum temperature, suggesting that these Roscoea species respond greatly to climate warming resulting in changes on flowering times. "
}


Ho (2006)

Earlier spring in Seoul, Korea

• BibTex citation:
@article {JOC:JOC1356,
author = {Ho, Chang-Hoi and Lee, E.-J. and Lee, I. and Jeong, S.-J.},
title = {Earlier spring in Seoul, Korea},
journal = {International Journal of Climatology},
volume = {26},
number = {14},
publisher = {John Wiley & Sons, Ltd.},
issn = {1097-0088},
url = {http://dx.doi.org/10.1002/joc.1356},
doi = {10.1002/joc.1356},
pages = {2117--2127},
keywords = {global warming, urbanization, flowering, growing degree-days, Seoul},
year = {2006},
}

• Where the initiation of blooming in most plants is cued by photoperiodism, actual blooming is triggered by an accumulation of warm temperature (Salisbury and Ross, 1992). Because the annual photoperiodic cycle has presumably not changed for the analysis period, long-term variations of phenological dates are almost certainly related to local warming. (p. 2119)

Clark (2010)

• BibTex citation:
@article {JOC:JOC2004,
author = {Clark, Robert Malcolm and Thompson, Roy},
title = {Predicting the impact of global warming on the timing of spring flowering},
journal = {International Journal of Climatology},
volume = {30},
number = {11},
publisher = {John Wiley & Sons, Ltd.},
issn = {1097-0088},
url = {http://dx.doi.org/10.1002/joc.2004},
doi = {10.1002/joc.2004},
pages = {1599--1613},
keywords = {global warming, climate change, onset of spring, phenology, first flowering, statistical model, growth degree-days},
year = {2010},
}


Titchner (2014)

• Titchner, H. A., and N. A. Rayner (2014), The Met Office Hadley Centre sea ice and sea surface temperature data set, version 2: 1. Sea ice concentrations, J. Geophys. Res. Atmos., 119, 2864-2889, doi: 10.1002/2013JD020316.

Walsh, et al. (2016)

• Bibtex citation:
@article {GERE:GERE12195,
author = {Walsh, John E. and Fetterer, Florence and Scott Stewart, J. and Chapman, William L.},
title = {A database for depicting Arctic sea ice variations back to 1850},
journal = {Geographical Review},
issn = {1931-0846},
url = {http://dx.doi.org/10.1111/j.1931-0846.2016.12195.x},
doi = {10.1111/j.1931-0846.2016.12195.x},
pages = {n/a--n/a},
keywords = {Arctic, climate change, ice extent, sea ice},
year = {2016},
}


Nova Scotia Plants (2014)

Nova Scotia Plants Marian C. Munro, Ruth E. Newell & Nicholas M. Hill Published 2014 https://ojs.library.dal.ca/NSM/pages/view/Plants

Natural History (1996)

• Citation:
• Davis, D., Browne, S. (Eds.) 1996. Natural history of Nova Scotia. Volume 1: topics and habitats. Halifax: Nimbus/Nova Scotia Museum

Natural History of Nova Scotia, Volumes 1 and 2. Derek S. Davis Sue Browne, Editors. Co-published with Nimbus Publishing. A product of the Nova Scotia Government Co-publishing Program.

Chang, et al. (1994)

• simple model of soil temperature as a function of air temperature and time of year (depth implied).
• Bibtex citation:
@article{chang1994air,
title={AIR AND SOIL TEMPERATURES UNDER 3 FOREST CONDITIONS IN EAST TEXAS},
author={CHANG, MT and Crowley, Christopher M and Juin, Eric and WATTERSTON, KG},
journal={Texas Journal of Science},
volume={46},
number={2},
pages={143--155},
year={1994},
publisher={TEXAS ACAD SCI TEXAS TECH UNIV, LUBBOCK, TX 79401}
}

• found the model in google books, Forest Hydrology: An Introduction to Water and Forests, Third Edition, By Mingteh Chang

Tufte (2004)

• Bibtex citation:
@Book{Tufte2004,
author =      "Edward R. Tufte",
title =       "The Visual Display of Quantitative Information (Second Edition)",
publisher =   "Graphics Press, Cheshire, Connecticut",
year =        "2004"
}


Thornley (1976)

• Chapter 12: A Biochemical Switch, Development, and Flower Initiation
• Thornley may have some ideas (certainly some basic models) about when things "first appear".
• Bibtex citation:
@Book{Thornley1976,
author =      "J. H. M. Thornley",
title =       "Mathematical Models in Plant Physiology",
year =        "1976"
}


Roweis (1998)

• Basic approach to PCA imputation
• Bibtex citation:
@INPROCEEDINGS{Roweis98emalgorithms,
author = {Sam Roweis},
title = {EM Algorithms for PCA and SPCA},
booktitle = {in Advances in Neural Information Processing Systems},
year = {1998},
pages = {626--632},
publisher = {MIT Press}
}


Piers (1930)

• Bibtex citation:
@INPROCEEDINGS{Piers1930,
author = {Harry Piers},
title = {Obituary Notice of Alexander Howard MacKay, B.A., B.Sc., LL.D., F.R.S.C. Educationish and Scientist, 1848-1929},
booktitle = {Proceedings of the Nova Scotian Institute of Science},
year = {1930},
volume = {XVII, Part IV},
pages = {xlvii-lii},
publisher = {Nova Scotian Institute of Science}
}


Devor (2014)

• “The Explanatory Power of Climate History for the 19th-Century Maritimes and Newfoundland: A Prospectus,” Acadiensis XLIII, no. 2 (Summer/Autumn 2014): 57-78.
• Bibtex citation:
@article{Devor2014,
title={The Explanatory Power of Climate History for the 19th-Century Maritimes and Newfoundland: A Prospectus},
author={Devor, Teresa},
volume={XLIII},
number={2},
pages={57-78},
year={2014}
}

• Received a copy from the author; on my Mac
• "Snow was a variable and precious resource in the winter and spring seasons. It surfaced the ground to permit some of the smoothest transportation of the year, and was used to insulate houses and cellars"
• "cold is then more intense, and cellars (the store houses and receptacles of the chief comforts) without their deep covering of snow, become penetrated by the frost, and their contents much injured, if not totally destroyed..."
• "In addition to temperature, factors including timely warmth, precipitation, and clear skies were central to the success of crops -- just as their absence posed challenges to colonial agriculture in other years and at particular times of the year."
• Colonel W.J. Myers observed that in 1865 "the rainy, foggy and unsettled weather of May, caused a serious interruption to agricultural operations, compensated, however, to some extent by the impulse given to the grass crop by the warm moisture. . . . In June . . . frost, which occurred in some parts of the Province, did much injury to fruit trees and gardens."
• They also lived further from water than their neighbours who farmed the rich riverbank or intervale soils, and hence from water's small though important moderating effects on the climate as well as its nutritive legacy in the soil.
• For more details of how the NAO and the AMO influence regional climates, see Devor, "Climate History of the Gulf of St. Lawrence Region," 16-17, 65-6, 69, 70, 77, 80, 81, 86, 87, 88, 90, 91, 102, 112, 133, as well as Stephen T. Gray et al., "A Tree-Ring Based Reconstruction of the Atlantic Multidecadal Oscillation Since 1567 A.D.," Geophysical Research Letters 31,no. 12 (June 2004): L12205, and J. Marshall et al., "North Atlantic Climate Variability: Phenomena, Impacts and Mechanisms," International Journal of Climatology 21, no. 15 (December 2001): 1863-98.
• While the overall trend in average annual temperatures was towards warming between 1873 and 1930, cold conditions continued on a sporadic basis throughout the period -- including several remarkably severe winter seasons between 1874 and the late 1890s as well as between 1904 and 1925.
• Growing seasons in Halifax and St. John's cooled between 1870 and around 1930, perhaps in relation to the specific phases of the AMO and the NAO -- the coupled ocean-atmospheric circulation systems that appear to have a degree of influence on the climates of all three cities.
• Climatic averages, however, gloss over the crucial elements of the timing of warm or cool weather, its correspondence with particular forms of precipitation, and daily minimum and maximum temperatures. Plants do not grow in average conditions; each has its own specific growing season requirements and associated vulnerabilities.

Skinner and Gullet (1993)

• Bibtex citation
@Article{Skinner1993,
author = 	"W. R. Skinner and D. W. Gullet",
title = 	"Trends of daily maximum and minimum temperature in Canada During the Past Century",
journal = 	"Climatological Bulletin",
year = 	"1993",
volume = 	"27",
number = 	"2",
pages = 	"63--76",
OPTmonth = 	"",
OPTnote = 	""


}

• obtained from http://www.cmosarchives.ca/CB/cb270203.pdf
• Mentions "Polar vortex" in 2001 -- during the Bush years! Proves that Obama isn't making it up!
• Gives overview of changes in Canadian climate: "...in the Atlantic region where a relatively larger increase in maximum temperatures and a smaller increase in minimum temperatures has resulted in a significan increase in temperature range of about 0.5oC per century."

Vincent and Gullet (1998)

@article {JOC:JOC427,
author = {Vincent, Lucie A. and Gullett, D.W.},
title = {Canadian historical and homogeneous temperature datasets for climate change analyses},
journal = {International Journal of Climatology},
volume = {19},
number = {12},
publisher = {John Wiley & Sons, Ltd.},
issn = {1097-0088},
url = {http://dx.doi.org/10.1002/(SICI)1097-0088(199910)19:12<1375::AID-JOC427>3.0.CO;2-0},
doi = {10.1002/(SICI)1097-0088(199910)19:12<1375::AID-JOC427>3.0.CO;2-0},
pages = {1375--1388},
keywords = {Canada, homogeneity, trends, time series, temperature, database},
year = {1999},
}


Abstract

Jackson (1966)

• Bibtex citation:
@article{10.2307/1932980,
ISSN = {00129658, 19399170},
URL = {http://www.jstor.org/stable/1932980},
abstract = {Sixteen microclimatic stations with differences in slope, exposure, vegetation cover, and seasonal change were established in a heavily dissected 180-acre Indiana tract. Correlations, based on cumulative air temperature duration-summations, were made between microclimatic differences and variation in phenological events. Nine widespread species of spring wildflowers had a collective mean range in dates of first flowering of 7.2 days for all stations. The maximum range for a single species was 11 days. Flowering dates of nine species of a large gorge were retarded an average of 6.0 days in the north-facing slope with respect to the opposing south-facing slope. This 6.0-day difference between gorge slopes 150 ft apart is equal to the expected to occur in about 110 miles of latitude, assuming standard exposures. Six species of the north-facing slope in a small gorge were retarded an average of 2.8 days with respect to the opposing south-facing slope. Flowering on north-facing gorge slopes was retarded more than in gorge bottoms, and upland stations had earlier than normal flowering dates. Mean flowering dates for the entire area were retarded more at cooler locations than warmer slopes were advanced. Air-temperature sums and flowering dates correlated well in a given microclimate. The results suggest that phenological research could be expedited by making observations in diverse microclimates during a few seasons rather than acquiring long-term phenological records.},
author = {Marion T. Jackson},
journal = {Ecology},
number = {3},
pages = {407-415},
publisher = {Ecological Society of America},
title = {Effects of Microclimate on Spring Flowering Phenology},
volume = {47},
year = {1966}
}

• Nine widespread species of spring wildflowers had a collective mean range in dates of first flowering of 7.2 days for all stations. The maximum range for a single species was 11 days. Flowering dates of nine species of a large gorge were retarded an average of 6.0 days on the north-facing slope with respect to the opposing south-facing slope. This 6.0-day difference between gorge slopes 150 ft apart is equal to the expected to occur in about 110 miles of latitude,
• Flowering on north-facing gorge slopes was retarded more than in gorge bottoms, and upland stations had earlier than normal flowering dates. Mean flowering dates for the entire area were retarded more at cooler locations than warmer slopes were advanced. Air-temperature sums and flowering dates correlated well in a given microclimate.
• A simplified form of temperature summation was used as early as 1915 by Lamb. Pearson (1924) suggested that the duration component should also be considered in temperature summation. Lindsey and Newman (1956) developed a novel method for arriving at duration-summation temperature sums, and constructed a master chart whereby the temperature sum in degree hours above a given threshold for a given day can be obtained if daily maximum and minimum temperatures are known.
• Recent comparative phenological and bioclimatic studies were done by Caprio (1957, 1961) on Syringa vulgaris L. in western United States and by Jeffree ( 1960) on an analysis of the long-term records of the Royal Meteorological Society
• The flowering sequence was bimodal with peak flowering times occurring in mid-April and early August. This same pattern was observed by Wolfe, Wareham, and Scofield (1949) and other bioclimatic workers. The early peak represented those woodland perennials that complete their flowering activity before the canopy closes
• In general, spring and early summer flowering species are most closely correlated with temperature, while late summer and fall species are most closely correlated with photoperiod.
• Early spring flowering during 1963 was both earlier than normal and telescoped into a somewhat shorter period than normal. The acceleration of flowering dates was largely a result of an abrupt temperature climb during an abnormally warm late-March and early-April.
• http://norsemathology.org/wiki/images/1/13/JacksonWow.png
• The excellent correlation between microclimatic deviations in flowering dates which were earlier or later than normal with above- or below-normal temperature sums, respectively (Fig. 4), indeed indicates that temperature sums exert a close control over flowering activity.
• Soil-temperature summation values were also computed, but they did not correlate with flowering data as well as did air-temperature sums.
• According to Hopkins' bioclimatic law (1938), this amount of variation is equivalent to that expected as a result of a geographical distance of about 125 miles northward or an elevational distance of 720 ft upward, assuming standard exposures at both locations

Lindsey and Newman (1956)

author = {Lindsey, Alton A. and Newman, James E.},
title = {Use of Official Weather Data in Spring Time--Temperature Analysis of an Indiana Phenological Record},
journal = {Ecology},
volume = {37},
number = {4},
publisher = {Ecological Society of America},
issn = {1939-9170},
url = {http://dx.doi.org/10.2307/1933072},
doi = {10.2307/1933072},
pages = {812--823},
year = {1956},
}


Lindsey (1963)

ISSN = {00129658, 19399170},
URL = {http://www.jstor.org/stable/1933190},
author = {Alton A. Lindsey},
journal = {Ecology},
number = {1},
pages = {149-151},
publisher = {Ecological Society of America},
title = {Accuracy of Duration Temperature Summing and Its Use for
Prunus serrulata},
volume = {44},
year = {1963}
}


Miller-Rushing (2012)

@article {FEE:FEE2012106285,
author = {Miller-Rushing, Abraham and Primack, Richard and Bonney, Rick},
title = {The history of public participation in ecological research},
journal = {Frontiers in Ecology and the Environment},
volume = {10},
number = {6},
publisher = {Ecological Society of America},
issn = {1540-9309},
url = {http://dx.doi.org/10.1890/110278},
doi = {10.1890/110278},
pages = {285--290},
year = {2012},
}


Walsh (2016), and Sea Ice Data, NSIDC

@article {GERE:GERE12195,
author = {Walsh, John E. and Fetterer, Florence and Scott Stewart, J. and Chapman, William L.},
title = {A database for depicting Arctic sea ice variations back to 1850},
journal = {Geographical Review},
issn = {1931-0846},
url = {http://dx.doi.org/10.1111/j.1931-0846.2016.12195.x},
doi = {10.1111/j.1931-0846.2016.12195.x},
pages = {n/a--n/a},
keywords = {Arctic, climate change, ice extent, sea ice},
year = {2016},
}


Hill, et al. (2002)

International Association of Hydraulic Engineering and Research

Provider: National Science Library - National Research Council Canada / Bibliothèque scientifique nationale - Conseil national de recherches Canada

TY  - JOUR
TI  - Historical record of the incidence of sea ice on the scotian shelf and the Gulf of St. Lawrence
AU  - Hill, B.
AU  - Ruffman, A.
AU  - Drinkwater, K.
T3  - 16th International Symposium on Ice, 2-6 December 2002, Dunedin, New Zealand
KW  - Scotian Shelf
KW  - Gulf of St. Lawrence
KW  - Cabot Strait
AB  - An historical record of the incidence of sea ice on the Scotian Shelf and the Gulf of St. Lawrence of Atlantic Canada has been compiled on an annual basis from the early 1800?s to 1962. A variety of data sources were used in the compilation of ice records including ice patrol and shipping reports, local newspapers, lighthouse records and other holdings in the U.S. and Canadian National Archives. In the order of 25,000 ice records were found and used in the plotting of monthly ice charts for the region. This current work was undertaken to lengthen an existing sea ice database covering the years from 1963 to near present. Natural gas development is well under way in the Sable Island area of the Scotian Shelf and while no ice has visited this island?s shores in recent memory, it is clear from the ice record that intrusions that far south are not unusual, historically.
DA  - 2002
PY  - 2002
C1  - Collection / Collection : NRC Publications Archive / Archives des publications du CNRC
C2  - Record identifier / Identificateur de l’enregistrement : ae2eb779-93fe-474d-bb01-2f881a133b25


@article{CaraDonna01042014,
author = {CaraDonna, Paul J. and Iler, Amy M. and Inouye, David W.},
title = {Shifts in flowering phenology reshape a subalpine plant community},
volume = {111},
number = {13},
pages = {4916-4921},
year = {2014},
doi = {10.1073/pnas.1323073111},
abstract ={Phenology—the timing of biological events—is highly sensitive to climate change. However, our general understanding of how phenology responds to climate change is based almost solely on incomplete assessments of phenology (such as first date of flowering) rather than on entire phenological distributions. Using a uniquely comprehensive 39-y flowering phenology dataset from the Colorado Rocky Mountains that contains more than 2 million flower counts, we reveal a diversity of species-level phenological shifts that bring into question the accuracy of previous estimates of long-term phenological change. For 60 species, we show that first, peak, and last flowering rarely shift uniformly and instead usually shift independently of one another, resulting in a diversity of phenological changes through time. Shifts in the timing of first flowering on average overestimate the magnitude of shifts in the timing of peak flowering, fail to predict shifts in the timing of last flowering, and underrepresent the number of species changing phenology in this plant community. Ultimately, this diversity of species-level phenological shifts contributes to altered coflowering patterns within the community, a redistribution of floral abundance across the season, and an expansion of the flowering season by more than I mo during the course of our study period. These results demonstrate the substantial reshaping of ecological communities that can be attributed to shifts in phenology.},
URL = {http://www.pnas.org/content/111/13/4916.abstract},
eprint = {http://www.pnas.org/content/111/13/4916.full.pdf},
journal = {Proceedings of the National Academy of Sciences}
}

• For 60 species, we show that first, peak, and last flowering rarely shift uniformly and instead usually shift independently of one another... Shifts in the timing of first flowering on average overestimate the magnitude of shifts in the timing of peak flowering, fail to predict shifts in the timing of last flowering, and underrepresent the number of species changing phenology in this plant community.
• an expansion of the flowering season by more than I mo during the course of our study period. These results demonstrate the substantial reshaping of ecological communities that can be attributed to shifts in phenology.
• Seasonal timing of biological events, phenology, is one of the strongest bioindicators of climate change.

Petrie, et al. (2004)

An Overview of Meteorological, Sea Ice and Sea-Surface Temperature Conditions off Eastern Canada during 2003: B. Petrie, R. G. Pettipas, W. M. Petrie and K. F. Drinkwater

Xie, et al. (2015)

@article{Xie03112015,
author = {Xie, Yingying and Wang, Xiaojing and Silander, John A.},
title = {Deciduous forest responses to temperature, precipitation, and drought imply complex climate change impacts},
volume = {112},
number = {44},
pages = {13585-13590},
year = {2015},
doi = {10.1073/pnas.1509991112},
abstract ={Changes in spring and autumn phenology of temperate plants in recent decades have become iconic bio-indicators of rapid climate change. These changes have substantial ecological and economic impacts. However, autumn phenology remains surprisingly little studied. Although the effects of unfavorable environmental conditions (e.g., frost, heat, wetness, and drought) on autumn phenology have been observed for over 60 y, how these factors interact to influence autumn phenological events remain poorly understood. Using remotely sensed phenology data from 2001 to 2012, this study identified and quantified significant effects of a suite of environmental factors on the timing of fall dormancy of deciduous forest communities in New England, United States. Cold, frost, and wet conditions, and high heat-stress tended to induce earlier dormancy of deciduous forests, whereas moderate heat- and drought-stress delayed dormancy. Deciduous forests in two eco-regions showed contrasting, nonlinear responses to variation in these explanatory factors. Based on future climate projection over two periods (2041–2050 and 2090–2099), later dormancy dates were predicted in northern areas. However, in coastal areas earlier dormancy dates were predicted. Our models suggest that besides warming in climate change, changes in frost and moisture conditions as well as extreme weather events (e.g., drought- and heat-stress, and flooding), should also be considered in future predictions of autumn phenology in temperate deciduous forests. This study improves our understanding of how multiple environmental variables interact to affect autumn phenology in temperate deciduous forest ecosystems, and points the way to building more mechanistic and predictive models.},
URL = {http://www.pnas.org/content/112/44/13585.abstract},
eprint = {http://www.pnas.org/content/112/44/13585.full.pdf},
journal = {Proceedings of the National Academy of Sciences}
}