Changes in extreme temperatures of the Earth's desert regions over the next 100 years

Using Bayesian inference and generalised extreme value regression on five CMIP6 models, this study projects that extreme temperatures in Earth's desert regions will significantly increase over the next century, with the most pronounced rises in annual maximums under severe forcing scenarios.

The Gist

Imagine the Earth's climate as a massive, complex orchestra. For a long time, we've been listening to the average volume of the music (the average temperature). But scientists are increasingly worried about the loudest, most jarring notes (the extreme heatwaves) and the deepest, most chilling silences (the record cold snaps).

This paper is like a team of detectives trying to predict how much louder those jarring notes and deeper silences will get in the Earth's deserts over the next 100 years. Here is the story of their investigation, broken down into simple parts.

1. The Mystery: What Happens to the Extremes?

The researchers focused on five of the world's hottest, driest places (like the Sahara and the Mojave) plus a "control group" in the UK. They wanted to know: If we keep burning fossil fuels at different rates, how much will the "100-year record" for heat and cold change by the year 2125?

Think of a "100-year return value" like a "century record." It's the temperature you'd expect to see only once every 100 years. The question is: Will that "once-in-a-century" heatwave become a "once-in-a-decade" event?

2. The Tools: The "Statistical Crystal Ball"

To make these predictions, they used data from five different super-computer climate models (CMIP6). But raw computer data is messy, like a radio with static. To clean it up, they used a special statistical tool called GEV Regression.

• The Analogy: Imagine you are trying to predict the height of the next giant wave in the ocean. You don't just look at the average wave; you look at the shape of the biggest waves. The GEV model is like a specialized ruler that measures the "shape" of these extreme waves (temperature spikes) to see how they are stretching or shrinking over time.

3. The Dilemma: Which Rulebook is Best?

Here was the tricky part. The researchers had to decide how to write the rules for their ruler. Should the temperature rise in a straight line? A curve? Or maybe it levels off like a cup filling with water?

They had 11 different "rulebooks" (models) to choose from. To pick the best one, they used something called Information Criteria.

• The Analogy: Imagine you are trying to guess the winner of a horse race. You have 11 different experts giving you advice.
  • Some experts say, "Keep it simple! The horse will win because it's fast." (Simple models).
  • Others say, "Look at the jockey's shoe size, the wind speed, and the color of the sky!" (Complex models).
  • The problem is, if you pick a model that is too complex, it might just be "overthinking" the noise (like blaming the horse's shoe size). If it's too simple, it misses the real story.

The team ran a simulation test (a practice race) to see which "expert" (Information Criterion) actually picked the right model most often. They found that the Bayesian Information Criterion (BIC) was the best detective. It was the expert who knew exactly when to stop looking for tiny details and stick to the big picture.

4. The Findings: The Heat is Turning Up the Volume

Once they picked the best rulebook (BIC), they ran the numbers for the next 100 years under three different future scenarios:

• The "Green" Scenario (SSP126): We fix the climate quickly.
• The "Middle" Scenario (SSP245): We do okay, but not great.
• The "Red" Scenario (SSP585): We keep burning everything and ignore the problem.

The Results:

• The Heat is Getting Hotter: In the "Middle" and "Red" scenarios, the "100-year record" for heat is going to get significantly hotter. In some deserts, the record-breaking heat of 2125 could be 11°C (20°F) hotter than the record-breaking heat of 2025. That's a massive jump.
• The Cold is Getting Warmer (Too): Even the "coldest" days are getting warmer, but the change is less dramatic and harder to predict than the heat.
• The "Warming Gap": Interestingly, in most places, the hottest days are getting hotter faster than the coldest days are getting warmer. It's like the thermostat is being cranked up on the "High" setting, but the "Low" setting is only being nudged up slightly.
  • Exception: In Antarctica, the opposite happened! The coldest days there are warming up faster than the hottest days.

5. The Takeaway

The paper concludes that if we don't change our path (the "Red" scenario), the extremes in our deserts will become truly extreme. The "once-in-a-century" heatwaves will become common occurrences.

The Simple Summary:
The Earth's deserts are like a pressure cooker. The researchers used a smart, tested method to figure out how much the pressure will rise. They found that if we keep the heat on high, the "pressure valve" (the extreme temperatures) will blow off much harder and much more often than we thought. The best way to predict this was to keep our statistical models simple and honest, avoiding over-complication.

In a nutshell: The extremes are getting worse, the heat is the biggest worry, and we have a very clear statistical map of where we are heading if we don't act.

Technical Summary

Here is a detailed technical summary of the paper "Changes in extreme temperatures of the Earth's desert regions over the next 100 years."

1. Problem Statement

The study addresses the critical need to quantify changes in extreme near-surface atmospheric temperatures ($tas$) in Earth's desert regions over the coming century (2025–2125). While Global Climate Models (GCMs) project rising mean temperatures, there is significant uncertainty regarding the behavior of extremes (annual maxima and minima) at local scales.

Key challenges identified include:

• Non-stationarity: The statistical distribution of temperature extremes is changing over time due to climate forcing.
• Model Selection: Selecting the appropriate functional form for how Generalized Extreme Value (GEV) parameters (location, scale, shape) vary with time is difficult, especially with limited data samples.
• Scenario Coupling: Different climate scenarios (SSP126, SSP245, SSP585) share a common historical baseline (2015), yet many analyses treat them independently, potentially introducing inconsistencies.
• Bias vs. Variance: Downscaling GCM output to regional scales introduces uncertainty; the authors chose to work directly with GCM output to avoid downscaling errors, accepting potential bias in exchange for reduced variance in the difference estimates.

2. Methodology

Data

• Source: Five CMIP6 GCMs (ACCESS-CM2, CESM2, EC-Earth3, MRI-ESM2-0, UKESM1-0-LL).
• Regions: Five major desert regions (Antarctic, Dasht-e Lut, Mojave, Sahara, Simpson) and a temperate UK control region.
• Scenarios: Three Shared Socioeconomic Pathways (SSP126, SSP245, SSP585) combined with Representative Concentration Pathways (RCPs).
• Data Structure: Annual spatial maxima and minima of $tas$ for the period 2015–2100, with up to 5 ensemble members per GCM/scenario combination.

Statistical Framework

• Modeling: The authors employ parametric Generalized Extreme Value (GEV) regression. The GEV parameters (location $\mu$, scale $\sigma$, shape $\xi$) are modeled as functions of time ($t$) and climate scenario ($j$).
• Coupling: A key innovation is the coupled model approach. All three scenarios are constrained to share the same GEV tail distribution in the baseline year (2015), ensuring physical consistency across scenarios.
• Parameterization: The study tests 11 candidate models with varying complexities (Constant, Linear, Quadratic, and Asymptotic) for the GEV parameters. For example, "QLC" denotes a Quadratic trend for location, Linear for scale, and Constant for shape.
• Inference: Bayesian inference using Markov Chain Monte Carlo (MCMC) is used to estimate the full joint posterior distribution of parameters, allowing for rigorous uncertainty quantification.
• Target Metric: The primary metric is $\Delta Q$, the difference in the 100-year return value between the years 2025 and 2125 ($\Delta Q = Q_{2125} - Q_{2025}$).

Model Selection Strategy

• Information Criteria: The study evaluates four standard criteria (AIC, BIC, DIC, WAIC) and several variants (e.g., BIC3, AIC3) that utilize posterior means instead of maximum likelihood estimates.
• Simulation Study: To determine which criterion performs best for this specific problem type, the authors conducted a simulation study. They generated synthetic data from the 11 candidate models and tested which information criterion minimized the Root Mean Square Error (RMSE) in predicting $\Delta Q$.
• Bayesian Model Averaging (BMA): As an alternative to selecting a single "best" model, the authors explored BMA using a stacking approach to weight all candidate models based on predictive performance.

3. Key Contributions

1. Coupled GEV Regression: Introduction of a framework that forces a common extreme value tail across different climate scenarios at the start of the projection period, improving physical consistency.
2. Empirical Model Selection: Instead of assuming a specific functional form (e.g., linear) for parameter trends, the study uses a simulation-based approach to identify that the Bayesian Information Criterion (BIC) outperforms AIC, DIC, and WAIC for this specific small-sample, extreme-value prediction task.
3. Direct GCM Analysis: A methodological choice to analyze raw GCM output directly to estimate changes in return values, avoiding the introduction of additional uncertainty from downscaling and bias correction procedures.
4. Comprehensive Uncertainty Quantification: Utilization of Bayesian inference to provide full posterior distributions for $\Delta Q$, rather than point estimates.

4. Key Results

Model Selection Performance

• The simulation study revealed that BIC (specifically variant BIC3) provided the best predictive performance (lowest RMSE) for estimating $\Delta Q$.
• BIC consistently selected more parsimonious models compared to AIC.
• DIC and WAIC performed poorly, likely due to overfitting in the context of small sample sizes (86 years $\times$ 3 scenarios).
• Model Complexity: The optimal models selected by BIC were predominantly LCC (Linear location, Constant scale, Constant shape) or QCC (Quadratic location). Complex variations in scale and shape were rarely selected, suggesting that the primary driver of non-stationarity in these datasets is the shift in the location parameter.

Temperature Extremes Trends (2025–2125)

• Regional Annual Maxima:
  • There is a consistent trend of increasing $\Delta Q$ (warming) across all desert regions as climate forcing increases.
  • Under SSP245 and SSP585, there is statistically significant evidence (95% credible intervals exclude zero) of substantial increases in the 100-year return value for annual maxima in all desert regions.
  • The magnitude of increase is generally higher in Dasht-e Lut, Sahara, and Simpson regions compared to the Antarctic.
• Regional Annual Minima:
  • Similar warming trends are observed for annual minima, but the signal is weaker and less significant. Many 95% credible intervals include zero, even under high-emission scenarios.
• Maxima vs. Minima:
  • In most regions, the rate of warming for extreme maxima is slightly higher than for extreme minima.
  • Antarctic Exception: In the Antarctic, the trend reverses under the SSP585 scenario; the 100-year return value for annual minima is increasing faster than for maxima (median $\Delta \Delta Q \approx -3K$).

Bayesian Model Averaging (BMA)

• Preliminary results suggest that the stacking BMA approach favors slightly more complex models than BIC (similar to AIC).
• In the simulation study, BMA resulted in a higher RMSE (3.98) compared to BIC-selected models (3.06), suggesting that for this specific problem, selecting a single parsimonious model via BIC is more effective than averaging.

5. Significance

This paper provides a robust statistical framework for assessing future climate risks in extreme environments. By demonstrating that BIC is the superior criterion for model selection in this context, the study offers a practical guide for future extreme value analyses using CMIP6 data.

The findings confirm that desert regions will experience significant intensification of heat extremes over the next century, particularly under moderate to high emission scenarios (SSP245/SSP585). The identification of the Antarctic as a region where minimum temperatures may warm faster than maximum temperatures highlights unique regional climate dynamics that require specific attention. The methodology avoids the pitfalls of downscaling uncertainty, providing a "best estimate" of the change in extremes directly from the climate models, which is crucial for infrastructure planning and risk assessment in arid zones.