Table 1.
Explanation of the four scales of novelty and how each was calculated.
‘Hyper’ is hypervolume, ‘ExDet’ is extrapolation detection.
Fig 1.
Schematic of how novel conditions were identified.
This is a simplified example with two covariates (SST and Latitude), and calculating novelty in the CCS climate envelope in July 2100 compared to historical Julys using the IPSL projection. a) Historical conditions in the CCS are extracted from projections for the desired environment and spatial covariates, and for the temporal span of interest (annual or monthly; Table 1). b) The hypervolume method creates a hypervolume (orange line an alpha hull approximation) surrounding these historical values (in as many dimensions as covariates), and then tests whether future values of the covariates (at every location in the domain) lie within the historical hypervolume. Locations that lie within the historical hypervolume (grey dots) have future conditions analogous to historical, and those that lie outside the hypervolume (purple dots) have novel future conditions. Brown dots are a subset of historical observations and orange dots are random points (used for hypervolume creation) guaranteed to be in the hypervolume. c) The ExDet method detects univariate novelty by identifying locations with conditions that lie outside the range of historical values for single variables (dashed box; red dots), and calculates the Mahalanobis distance to detect combinatorial novelty (dashed oval; S4 Fig), i.e. locations ‘outside’ the maximum of this distance have novel combinations of variable values (blue dots). Locations are otherwise considered to have future conditions analogous to historical (grey dots). d) For each of these methods, novelty for any future month is calculated as the percentage of locations in the CCS domain experiencing novel conditions compared to historical. This map shows the result of the ExDet method, with 75% of the CCS in July 2100 experiencing novel conditions (grey area) and 25% analog conditions (green area). In this example (essentially a local-monthly scale, but lacking longitude), novelty represents SSTs warmer than experienced historically in July anywhere in the CCS, plus SSTs warmer than experienced at specific latitudes. The black line is the exclusive economic zone (EEZ). The coastline data are sourced from https://naturalearthdata.com/downloads/110m-physical-vectors/110m-coastline, and the EEZ from https://nauticalcharts.noaa.gov/data/us-maritime-limits-and-boundaries.html.
Fig 2.
Projected percentage of the CCS experiencing novel conditions.
Novelty is shown at the four scales (regional, regional-monthly, local, local-monthly), from 2010 to 2100 (compared to the 1980–2009 period). In a) we show novelty in August under Hadley, and both the yearly percentages (jagged lines) and a GAM smoothed trend, as estimated by hypervolumes (black line) and ExDet (red line). Coupled climate models are not intended to be used to forecast what happens in specific years, so while the frequency and magnitude of spikes in novelty will likely reflect reality, the exact years in which they happen will not. In b) we show just the smoothed trends for all three projections (line type) for three representative months. As a visual aid, the dashed grey line indicates 50% novelty.
Fig 3.
Maps of locations with novel or analog climates.
Maps are shown for three example months at the end of five decades, under IPSL. Colors represent an analog climate (green), or climate novel to the region (red), novel to a given location or month of the year (orange), or novel at a given location and month of the year (yellow). The maps show each pixel’s majority classification over a 5-year period ending in the specified year (e.g. 2016–2020). These maps use the hypervolume method, and the ExDet method is shown S6 Fig. The black line is the exclusive economic zone (EEZ). The coastline data are sourced from https://naturalearthdata.com/downloads/110m-physical-vectors/110m-coastline, and the EEZ from https://nauticalcharts.noaa.gov/data/us-maritime-limits-and-boundaries.html.
Fig 4.
Historical and future end-of-century hypervolumes visualized as pair plots.
These hypervolumes respectively represent 30 years and 10 years of August climate conditions combined. This is for the IPSL projection and at the local-monthly scale; results are similar across months. Filled circles are hypervolume centroids. Overlap metrics of the two hypervolumes are given, i.e. 94% of each six-dimensional hypervolume is unique to that period, with very low similarity measures. Mean historical values for each variable are indicated in red font.
Fig 5.
Maps of MIC (most influential covariate) values estimated by the ExDet method for the GFDL and IPSL projections.
These are based on 2091–2100 July values at the local-monthly scale. Values are the proportion of months (n = 10) that each cell identified each variable as the MIC. This was calculated as the mean of the pixel-level proportions inside each of the 14 grid cells. Note the different color scale for SST (0–1) and the other covariates (0–0.12). Hadley is not shown because it was almost exclusively SST. A mid-century version showing a similar pattern is presented in S7 Fig. The coastline data are sourced from https://naturalearthdata.com/downloads/110m-physical-vectors/110m-coastline, and the EEZ from https://nauticalcharts.noaa.gov/data/us-maritime-limits-and-boundaries.html.