Climate variability: statistics and observation based simulations

Characterizing potential future changes in temperature variability across frequencies: 

The impacts of climate change on human societies may arise not just from changes in climate means but from changes in climate variability. Many agricultural crops, for example, are highly sensitive to even brief periods of stress temperatures, particularly at certain times of the growing cycle. Crop yields can be strongly affected by changes in temperature variability even in the absence of a change in mean. Understanding potential changes in temperature variability has therefore been a research priority in climate science.

Impacts of climate variability depend on not only the magnitude but also the frequency of variations: day-to-day temperature fluctuations have different consequences than year-by-year differences. We therefore study variability using spectral methods that allow distinguishing timescales of fluctuations. Current projects address climate variability in a number of ways

  • comparing variability changes in present-day or preindustrial and and future equilibrated climates
  • developing methodologies to characterize variability changes in transient climates
  • evaluating the effect of model spatial resolution on temperature variability

In our study of equilibrated climates, we compare pre-industrial and future climate scenarios in two different climate models, CCSM3 and GISS-E2-R, with millennial runs so that each climate state is stationary. Following techniques developed in Leeds et al (2015),  we compute integrated variability in distinct frequency bands and show changes over time as the future/present ratio. spectral ratios to explore the temperature variability changes in increased radiative forcing based on climate models. Within CCSM3, we also compare variability changes when warming is driven by two different forcing agents (CO2 and solar radiation).

Figure 1: Changes in summertime (JJA) temperature variability in three frequency bands from pre-industrial to future climates states, for Two models: (LEft) CCSM3 (289 ppm → 1400 ppm); (Right) GISS-E2-R (285 ppm → 1140 ppm). Variability changes are shown as ratios of the standard deviation, Values below 1 mean temperature variability decreases. GISS-E2-R model outputs are regrided to T31 resolution as CCSM3 using area-conserving remapping. Patterns In both models are similar: variability tends to increase slightly over land and decrease over the ocean. (In wintertime, variability tends to decrease everywhere other than tropical land.)

Figure 1: Changes in summertime (JJA) temperature variability in three frequency bands from pre-industrial to future climates states, for Two models: (LEft) CCSM3 (289 ppm → 1400 ppm); (Right) GISS-E2-R (285 ppm → 1140 ppm). Variability changes are shown as ratios of the standard deviation, Values below 1 mean temperature variability decreases. GISS-E2-R model outputs are regrided to T31 resolution as CCSM3 using area-conserving remapping. Patterns In both models are similar: variability tends to increase slightly over land and decrease over the ocean. (In wintertime, variability tends to decrease everywhere other than tropical land.)

Characterizing and emulating variability in a transient climate:

Characterizing climate variability is easier in stationary conditions, but the Earth for the foreseeable future will be in a changing or "transient" state, in which temperatures are evolving in response to changed CO2 concentrations. Most archived climate model output also simulates transient states. We therefore seek to statistically describe how variability changes in a transient climate. This statistical exploration also serves our overall research goal is also to use model information to produce "data-driven simulations" for use in impacts assessments.  GCM output should not be used directly in impacts assessments, because GCMs do not fully reproduce present-day temperature distributions. Instead we develop methods of generating simulations of future temperatures that combine observational records with GCM projections of changes in variability (covariances). (See Figure 2 for cartoon, also description of emulation research.) 

Figure 2: Cartoon illustration comparing strategies for simulating temperatures that combine information from a model and the observational record. Columns compare simple bias correction (left), the Delta method (center), and our proposed method (right). Top row, the model predicts changes in mean temperature but no changes in variability; in this case, our proposed method is equivalent to the Delta method. Bottom row, the model predicts changes in both mean and covariance. Simple bias correction does not retain the higher order properties of the observations, whereas the Delta method does not account for model changes in covariance; our proposed method does both. FROM POPPICK ET AL, 2015.

Figure 2: Cartoon illustration comparing strategies for simulating temperatures that combine information from a model and the observational record. Columns compare simple bias correction (left), the Delta method (center), and our proposed method (right). Top row, the model predicts changes in mean temperature but no changes in variability; in this case, our proposed method is equivalent to the Delta method. Bottom row, the model predicts changes in both mean and covariance. Simple bias correction does not retain the higher order properties of the observations, whereas the Delta method does not account for model changes in covariance; our proposed method does both. FROM POPPICK ET AL, 2015.

Again using the CCSM3 model, but now an ensemble of transient simulations rather than a single stationary run, we describe a statistical model for the evolution of temporal covariances in a GCM in response to altered CO2 levels. We find that, at least in CCSM3, changes in the local covariance structure can be explained largely as a function of the regional mean change in temperature, with a small term related to the rate of change of warming. (A warming climate will have slightly greater variability than an equilibrium climate at the same temperature.)

The statistical model can then be used to emulate the evolving covariance structure of temperatures, and therefore used to create in data-driven simulations that account for the projections of changes while still retaining fidelity with the observational record. We demonstrate the emulation of variability changes below, training the statistical model on model runs of several CO2 scenarios and using it to emulate changes under another scenario. Variability changes can indeed be described and emulated with a simple statistical model.

Figure 3: (Left): ESTIMATES OF CHANGES IN VARIABILITY IN Future (year 2100) RELATIVE TO PREINDUSTRIAL CLIMATEs, UNDER A MONOTONICALLY INCREASING CO2 CONCENTRATION SCENARIO IN CCSM3. RED INDICATES AN INCREASE IN VARIABILITY AND BLUE A DECREASE IN VARIABILITY. THE ASSOCIATED TIMESCALE OF VARIATION FOR WHICH THE CHANGES IN VARIABILITY ARE DISPLAYED IS GIVEN ABOVE ON THE Y-AXIS OF THE  MAP.  (RighT):, emulation of The Estimates on the LEFT. Locations are marked with “.” (or “x”) when the difference between the emulator and the fitted model is more than two (or three) standard errors away from zero. The patterns are similar under both schemes, with most of the differences at locations where our model would not be expected to be a good description of changes in variability (e.g., at ice margins). From Poppick et al, 2015.

Figure 3: (Left): ESTIMATES OF CHANGES IN VARIABILITY IN Future (year 2100) RELATIVE TO PREINDUSTRIAL CLIMATEs, UNDER A MONOTONICALLY INCREASING CO2 CONCENTRATION SCENARIO IN CCSM3. RED INDICATES AN INCREASE IN VARIABILITY AND BLUE A DECREASE IN VARIABILITY. THE ASSOCIATED TIMESCALE OF VARIATION FOR WHICH THE CHANGES IN VARIABILITY ARE DISPLAYED IS GIVEN ABOVE ON THE Y-AXIS OF THE  MAP.  (RighT):, emulation of The Estimates on the LEFT. Locations are marked with “.” (or “x”) when the difference between the emulator and the fitted model is more than two (or three) standard errors away from zero. The patterns are similar under both schemes, with most of the differences at locations where our model would not be expected to be a good description of changes in variability (e.g., at ice margins). From Poppick et al, 2015.