class: inverse, middle, left, my-title-slide, title-slide .title[ # Loss of lake ice cover in northern hemisphere lakes ] .author[ ### Gavin Simpson & Stefano Mezzini ] .institute[ ### Aarhus University · University of British Columbia ] .date[ ### June 6, 2023 ] --- ### Land acknowledgment * This work was done at URegina on Treaty 4 lands ### Funding .row[ .col-6[ .center[] ] .col-6[ .center[] ] ] ### Data .row[ .col-8[ * Lake ice data from [Global Lake and River Ice Phenology Database](http://nsidc.org/data/G01377.html) * Lake ice study joint work with Stefano Mezzini * [bit.ly/circle-u-2023](https://bit.ly/circle-u-2023) ] .col-4[ .center[ <img src="resources/bit.ly_circle-u-2023.png" width="90%" style="display: block; margin: auto;" /> ] ] ] <!-- ### Slides * HTML Slide deck [bit.ly/circle-u-2023](http://bit.ly/circle-u-2023) © Simpson & Mezzini (2023) [](http://creativecommons.org/licenses/by/4.0/) --> ??? This research was conducted while we were at the University of Regina, which is situated on the territories of the nay-hi-yuh-wuk (Cree; nêhiyawak), uh-nish-i-naa-payk (Salteaux; Anihšināpēk), Dakota, Lakota, and Nakoda, and the homeland of the Métis/Michif Nation. --- # Lake Suwa ice record <br /> .row[ .col-8[ <img src="resources/180205_Lake_Suwa_omiwatari_01_straightened.jpg" width="1600" /> ] .col-4[ <img src="resources/建御名方神_-_Takeminakata.jpg" width="1144" /> ] ] ??? The ice record at Lake Suwa, Nagano Prefecture, Japan, is the oldest known human-observed climate record in the world, ice formation dates from 1443 Omiwatari or ice ridges form on the lake as pressure ridges that arise due to vertical thermal gradients in the lake Local Shinto tradition holds that these Omiwatari — or God's Crossing — are formed by God's crossing Lake Suwa to move between the buildings of the Suwa Grand Shrine Folklore has it that the Omiwatari are formed when the Guardian God of Suwa, Takeminakata-no-kami, leaves his sanctuary to visit his wife the goddess Yasakotame --- # Lake ice records .row[ .col-7[ * Collected for *economical*, *recreational*, & *religious* purposes * Support a range of activities * Winter transportation * Fishing * Social activities * Spiritual ceremonies * Excellent climate indicators * Lake ice cover is key control on many lake processes ] .col-5[ <img src="resources/wired-article-screen-grab.png" width="1121" /> ] ] ??? Such records have been collected globally, principally in the Northern hemisphere, for decades to centuries for a host of economical, recreational, and religious reasons This is because lake and river ice supports a wide range of activities Lake ice is very sensitive to changes in climate (esp. temperature) and as such they are excellent indicators of climate change --- # Trends in lake ice phenology Magnuson *et al* (2000) — seminal study of trends in lake ice phenology Confirmed by multiple follow-up studies Long-term records of lake ice phenology demonstrated that many Northern Hemisphere lakes experienced earlier ice breakup, later ice freeze-up, and shorter ice duration within a warming world <br /> [Magnuson *et al* (2000) Science 289, 1743–1746](https://doi.org/10.1126/science.289.5485.1743) ??? Magnuson et al. (2000) observed long-term changes in lake ice cover in 20 spatially and morphologically heterogeneous lakes from 1855 to 1995. These long-term records of lake ice phenology demonstrated that many Northern Hemisphere lakes experienced earlier ice breakup, later ice freeze-up, and shorter ice duration within a warming world --- # Global Lake and River Ice Phenology .center[ <img src="resources/animated-map.gif" width="550" height="550" /> ] ??? Global Lake and River Ice Phenology Database We worked with 568 lakes & 628 observational records with data post 1950 --- # Problems .row[ .col-6[ * time to ice-on or ice-off positive, continuous, skewed * linear trends to estimate shifts in phenology * interest has turned to asking whether rates of change in lake ice phenology have changed ] .col-6[ .center[ <img src="resources/dates.svg" width="550" height="550" /> ] ] ] ??? Original analyses grappled with the problem that the day of year of freezing spanned the start/end of the calendar year A solution is to turn the data into time (days) to event (freezing) Such data are necessarily positive, continuous, and skewed Additionally, trends have been represented as linear models, which while perhaps OK for shorter time series are not useful for capturing the non-linear trends typically present in longer records or for asking more nuanced questions as to whether rates of change in ice loss are themselves changing --- # Time-to-event — Event history models Follow-up times `->` Survival analysis model Piece-wise exponential model is essentially a Poisson GLM on transformed data Piece-wise exponential additive mixed model — PAMM *pammtools* 📦 (Bender, Groll, Scheipl, 2018 *Statistical Modelling*) ??? hazard rate is piece-wise constant within time intervals but we estimate it semi-parametrically --- # PAMMs — Lake Mendota .center[ <!-- --> ] ??? Example is for Lake Mendota, with the days post June 30th of lake freezing shown in the upper left panel, superimposed is the estimated day of freezing from the PAMM To fit the PAMM we convert the data to Piece-wise exponential form by breaking the follow-up period within lake ice season (year) into essentially daily steps based on events in record We model `tend` for within season hazard, and the longer-term trend is modelled as a smooth of year, the effects of which are allowed to smoothly interact, using GAMs and splines --- # Splines formed from basis functions <!-- --> ??? Splines are built up from basis functions Here I'm showing a cubic regression spline basis with 10 knots/functions We weight each basis function to get a spline. Here all the basis functions have the same weight so they would fit a horizontal line --- # Weight basis functions ⇨ spline .center[] ??? But if we choose different weights we get more wiggly spline Each of the splines I showed you earlier are all generated from the same basis functions but using different weights --- # Maximise penalised log-likelihood ⇨ β .center[] ??? Fitting a GAM involves finding the weights for the basis functions that produce a spline that fits the data best, subject to some constraints --- # Model ```r pamm(ped_status ~ s(tend, bs = 'cr', k = 10) + s(year, bs = 'cr', k = 10) + s(tend, lake, bs = 'fs', k = 10) + s(Year, lake, bs = 'fs', k = 10) + s(long, lat, bs = 'ds', k = 20) + ti(tend, Year, bs = 'cr', k = c(5, 5)) + ti(tend, long, lat, bs = c('cr', 'ds'), d = c(1, 2), k = c(5, 5)) + ti(Year, long, lat, bs = c('cr', 'ds'), d = c(1, 2), k = c(5, 5)), data = freeze.na, method = 'fREML', # fast restricted marginal likelihood engine = 'bam', # use mgcv::bam() for faster fitting discrete = TRUE) # discretize the covariates for faster fitting ``` Fit North American and Eurasian lakes in separate models --- # Results _Eurasian_ lakes froze 17 days later and thawed 3 days earlier in 2010 than 1950 _North American_ lakes froze 25 days later and thawed 10 days earlier in 2010 than 1950 Most of that change happened post 1995 --- .center[ <img src="resources/p-freeze-thaw.svg" width="80%" /> ] --- # Change in freeze dates .row[ .col-12[ <img src="resources/hpam-change-in-freeze-dates-map.png" width="90%" style="display: block; margin: auto;" /> ] ] --- # Change in thaw dates .row[ .col-12[ <img src="resources/hpam-change-in-thaw-dates-map.png" width="90%" style="display: block; margin: auto;" /> ] ] --- # Summary * Time-to-event models are an appropriate way to model lake ice phenology data * PAMMs are a flexible way to model data with non-linear trends in freeze/thaw dates * Avoids *ad hoc* choices regarding change points * Eurasian lakes froze 17 days later and thawed 3 days earlier (1950 vs 2010) * North America lakes froze 25 days later and thawed 10 days earlier (1950 vs 2010) * Most of that change occured after 1995 --- # Future work * Update our models to the latest database release * Estimate rates of change using derivatives of smooths * Extending models to include explanatory factors --- # Thank you & More 📷 Mail: gavin@anivet.au.dk [github.com/gavinsimpson/circle-u-lake-ice-phenology](https://github.com/gavinsimpson/circle-u-lake-ice-phenology) .center[ <img src="resources/bit.ly_circle-u-2023.png" width="45%" style="display: block; margin: auto;" /> ]