The United States Department of Agriculture classifies plant hardiness zones based on mean annual minimum temperatures over some past period (currently 1976–2005). Since temperatures are changing, these values may benefit from updating. I outline a multistep methodology involving imputation of missing station values, geostatistical interpolation, and time series smoothing to update a climate variable’s expected value compared to a climatology period and apply it to estimating annual minimum temperature change over the coterminous United States. I show using hindcast experiments that trend estimation gives more accurate predictions of minimum temperatures 1-2 years in advance compared to the previous 30 years’ mean alone. I find that annual minimum temperature increased roughly 2.5 times faster than mean temperature (

Expected values of various climate variables at particular locations are used for decision making in many sectors. Traditionally, these have been estimated based on the average over some past period. If the variable is statistically stationary, averaging over a long period should result in an accurate estimate of its expected value; however, in the presence of trends, such as those associated with global warming, such averages will not be optimal estimates for the expected value going forward [

In this paper, the climate variable considered is the annual minimum temperature, an important determinant of the range over which particular varieties of perennial plants and overwintering insects may thrive. The United States Department of Agriculture (USDA) first released maps of plant hardiness zones for the coterminous United States (USA) and southern Canada in 1960, where each zone corresponded to a particular range of mean annual minimum temperature; similar maps, with different numbering of hardiness zones, were published as early as 1938 by Harvard University's Arnold Arboretum [

There have been few systematic studies of observed changes in annual minimum temperature, compared to many studies of trends in mean temperatures. Karl et al. [

In this study, I sought to quantify trends in annual minimum temperature since the early 20th century and evaluate how currently mapped hardiness zones might be adjusted to account for these trends. My interest here was in trends (i.e., systematic shifts between time periods, including nonlinear change patterns), rather than in actual annual minimum temperature at a given location. While temperatures show pronounced differences over small spatial scales, as captured by the latest USDA map, trends in mean temperature tend to have spatial scales of hundreds to thousands of km [

The source of temperature observations was a current version of the Daily Global Historical Climatology Network (GHCN-Daily,

Annual minimum temperature over a year was calculated as the lowest daily minimum temperature for that year in a given station record. The annual minimum temperature was considered missing if minimum temperature for any day during the year was missing from a given station record. Years were defined to begin in March because in the northern midlatitudes, the annual minimum temperature almost always occurs between December and February. (Thus, the official record minimum temperatures in each of the 48 contiguous states (

Only stations with at least 30 years of annual minimum temperature data were used. This gave 2733 available stations, of which 1065 were in the coterminous USA (Figure

Locations of GHCN-Daily stations used.

GHCN-Daily stations with annual minimum temperature data per year.

While GHCN has developed an homogeneity-adjusted monthly temperature product [

For the selected stations, missing annual mean temperature values were imputed, producing complete time series of annual minimum temperature; this was done to minimize the impact of changing station coverage over time on the estimated regional trends. I chose an imputation method based on singular value decomposition (SVD), variants of which have been tested in genomics and data mining applications [

Construct an

Center

Fill in missing values in

Find the thin SVD [

For each year index

Compute

Compute the iteration increment

Set

Iterate steps (4)–(8) until

The limiting in step (6) prevents occasional divergence of the iterations. Presumably, it could be replaced by a suitable regularization constraint in the regression step (5). It may also be possible to refine the procedure by using only a geographically nearby station subset to fill in each value, analogous to the implementation of locality in data assimilation for numerical weather prediction [

The empirical correlation of annual minimum temperatures between pairs of stations (using only years for which both stations have data) was plotted as a function of interstation distance (Figure

Correlation of annual minimum temperature time series between pairs of stations as a function of the distance between them.

Ordinary Kriging [

For the annual minimum temperature time series

In order to check whether the results were sensitive to the trend estimation method, an alternative smoothing approach tried was a local linear regression estimator [

Do the trend estimates obtained on a

Hindcast values were obtained for all coterminous USA stations with available observations for comparison and for all years since 1980, for a total of 11,465 hindcast opportunities at 1-year lag and 10,854 at 2-year lag. For both hindcast methods, the root mean square, mean absolute value, and mean (bias) of the error (hindcast minus actual value) were computed.

Figure

Annual minimum temperature anomaly (relative to the 1976–2005 mean) averaged across the coterminous USA, along with a fitted trend curve. Dashed curves show a 1-

(a) Gridded annual minimum temperature trend as that of 2011-2012, relative to the 1976–2005 mean, over the coterminous USA. (b) Change in trend annual minimum temperature between 1970-1971 and 2011-2012. Units are K; pointwise 1-

It is also possible to look at annual minimum temperature anomalies for particular years, in addition to the trend. Averaged across the coterminous USA, 2011-2012 seems to have been the warmest since 1900 (in terms of annual minimum temperature), at 3.8 K above the 1976–2005 mean; the next warmest years were 1999-2000 (+3.2 K), 1930-1931 (+3.1 K), and 1991-1992 (+3.0 K) (Figure

Gridded annual minimum temperature (K), relative to the 1976–2005 mean, over the coterminous USA, for individual cold and warm winters: (a) 1962-1963, (b) 2011-2012.

The obtained increases in annual mean temperature since 1970 and since the 1976–2005 base period are very similar if only the USHCN stations are used, at 2.1 K and 1.4 K, respectively, compared to 2.0 K and 1.2 K when all HCDN-Daily stations are used (Figure

Annual minimum temperature trend (anomaly relative to the 1976–2005 mean) over the coterminous USA, compared to

Coterminous USA mean annual minimum temperature anomalies plotted against annual mean temperature anomalies, relative to the 1976–2005, over years since 1900. The least-squares regression line shown has the equation

Averaged over the years since 1980, the climatology hindcasts of station minimum temperatures as the average of the past 30 years have been biased low by

Results of hindcasts of station annual minimum temperature.

1 year ahead | 2 years ahead | |||
---|---|---|---|---|

Climatology | Trend | Climatology | Trend | |

RMSE | 3.97 | 3.88 | 3.99 | 3.85 |

MAE | 3.15 | 3.03 | 3.17 | 3.00 |

Bias | −1.05 | +0.11 | −1.13 | +0.01 |

RMSE: root mean square error; MAE: mean absolute error; units are K.

Annual minimum temperatures since 1980 at sample stations, compared to climatology and trend hindcasts (see Section

The approach outlined here to estimate trends from relatively sparse, temporally incomplete station data should be of general applicability to other climate variables such as maximum temperature or precipitation, though some details such as the form of the falloff in interstation covariance with distance may need adjusting when different climate variables are considered. My approach may be useful in updating climate-based quantities such as growing season length and heating degree days which find a variety of applications and which are also changing [

This approach compares favorably in generality to others proposed for reducing the bias of climatology estimates of expected values in a changing climate. Compared to the “optimal climate normals” approach for finding expected values, where the climatology averaging period is shortened to reduce the trend-induced bias [

In order to gauge how much confidence can be placed on climate model simulations of future changes in derived climate quantities of interest, such as hardiness zones and species-specific climate envelopes [

The physical explanation for the fast rise in annual minimum temperature requires detailed investigation. Certainly snow albedo feedback is a likely contributing factor to winter amplification of warming in parts of the USA that have had significant winter snow cover [

In terms of the specific application of delineating USA plant hardiness zones, I found that annual minimum temperatures are already on average some 1.2 K higher than at the 1976–2005 base period used in the most recent release. Given that hardiness half-zones are defined at 2.8 K intervals [

In order to enable adoption and modification of the procedures proposed here, the computer programs used for downloading data, imputation of missing data, interpolation, and smoothing, written in the computer language Octave [

I have shown that the expected values of annual minimum temperature over the coterminous USA have changed substantially over the past century, that interannual variability and trends in annual minimum temperature can be mapped from available daily station data, and that accounting for estimated trends improves hindcasts of observed annual minimum temperatures. This trend estimation procedure may be used to provide yearly updates to hardiness zone maps based on expected annual minimum temperature. Similar or identical methods could be used to improve forecasts of many other climatically derived quantities, compared to the alternative of using statistics from some past baseline period without adjustment for trends.

This work benefited from discussions with Alan Betts, Pierre Gentine, and Alessandra Giannini. Soni Pradhanang, Boris Shmagin, Alexander Stine, and Brian Tkatch reviewed and commented on drafts of the paper. This study was supported by NOAA under Grant NA11SEC4810004. Statements made are the views of the author and are not the opinions of the funding agency or the US Government.