Hottest Year on Record and Accelerating Global Warming

The year 2023 was officially the hottest in human history. However, 2024 has already surpassed that milestone. The following graph compares daily global temperatures of 2024 (blue points) with 2023(green points). On average, 2024 was hotter than 2023 by 0.113°C – a significant jump compared to the average warming rate of 0.02°C per since 1975. Only 118 days of 2023 were warmer than their 2024 counterparts. Before 2023, the hottest year was 2016, but only 40 days in 2016 were hotter than in 2024. No year before 2014 had days that surpassed 2024’s temperatures. Thus, we now have a new hottest year in recorded history.

Global Warming Trends Since 2015

Despite worldwide efforts to reduce warming under the Paris Agreement, global temperatures have continued to rise at an accelerating pace. Since 2015, the average rate of warming has been faster than during the preceding 40 years. This trend is visible when global temperatures are averaged over different time periods, as shown in the following graph:

• Blue lines: Ten-year averages.
• Green lines: Five-year averages.
• Red lines: Two-year averages.

From 1945 to 1975, the blue lines are close together, indicating slow warming. Between 1975 and 2015, the blue lines are evenly spaced, showing a steady warming of about 0.17°C per decade. However, the most recent step (2015-2025) shows a larger temperature increase of 0.357°C – more than double the previous rate. One step alone does not provide sufficient evidence of an accelerating warming rate unless the cause of the warming is increasing.

Understanding Energy Imbalance and Global Warming

The root cause of global warming is Earth’s energy imbalance (EEIMB): the difference between absorbed solar radiation (ASR) and emitted thermal radiation (ETR). When EEIMB is positive, the planet absorbs more energy than it emits, leading to warming. Conversely, a negative EEIMB results in cooling.

If the energy imbalance remains constant, global temperature would rise at a steady rate. However, a growing EEIMB implies an accelerating rate of warming. Since 2000, NASA has been monitoring radiation fluxes at the top of the atmosphere, making it possible to track this imbalance alongside temperature changes.

Seasonal variations in EEIMB are driven by Earth’s elliptical orbit, which causes a 6.5% fluctuation in incoming solar radiation from January to July. Although seasonal variations in EEIMB explain the 4.2°C swing in global temperature each year, the response of average global temperature to changes in EEIMB is counterintuitive. As seen in the first graph, the Earth’s surface is warmest in July when the planet is farthest from the sun and it is coolest in January when the planet is closest.

Plotted together below, for a typical year, is the rate of temperature change, i.e. the first derivative, – black line and smoother blue line – and the energy imbalance, EEIMB – red line.   

 

There is a noticeable phase lag: the fastest warming occurs about 61 days after the maximum positive imbalance, and the fastest cooling occurs about 116 days after the maximum negative imbalance.  This must be due to a thermal inertia of Earth’s systems, particularly the oceans, which absorb and release heat over extended periods. Remarkably, the planet can warm or cool at rates as high as 10°C per year – an astonishingly rapid change compared to the long-term warming of just 2°C over a century.

Increasing Energy Imbalance and Accelerating Warming

If the positive and negative swings of the energy imbalance remained equal year over year, there would still be a seasonal swing to global temperature, but there would be no year-to-year warming. Since 2000, however, the 12-month running average of EEIMB has been a net positive. If the EEIMB net positive were stable, global warming would follow a linear trajectory. In fact, a 12-month running average of EEIMB shows a steady increase, indicating that the imbalance is not stabilizing.

  

Global temperature increase depends on cumulative retained energy, the integral (ΔQ) of the EEIMB. In the 12-month running average of the integral of the energy imbalance, shown below, the parabolic shape is visibly evident. 

The cumulative retained energy over the past 25 years is equivalent to the energy of a 20-watt bulb shining on every square meter of the Earth’s surface for 20 years. In the following graph a one year running average of temperature is compared with the cumulative energy (ΔQ). The scaling for the cumulative energy is adjusted to fit the temperature in the least squares sense. It shows that global temperature has risen in proportion to cumulative energy, following the same parabolic trajectory.  

Three potential future scenarios are shown in the graph below:

1. Accelerating (parabolic) path: If current trends continue, temperatures will rise even faster.
2. Linear path: Temperature increase at a constant rate.
3. Equilibrium path: Temperatures stabilize if greenhouse gas and albedo effects stop changing.

Currently we are on an accelerating path. In all scenarios, global temperatures will exceed the critical 1.5°C threshold in fewer than 10 years.

The Drivers of Increasing Energy Imbalance

The increase in EEIMB is not due to changes in incoming solar radiation, which has remained constant at 340.2 W/m² +/-0.03% over the past 25-years. Instead, the widening gap between ASR and ETR is the driver:

• ASR (Absorbed Solar Radiation): Reflectivity (albedo, α) has decreased, allowing more solar energy to be absorbed.
• ETR (Emitted Thermal Radiation): While ETR has increased in response to warming, it has not kept pace with ASR. This disparity is partly or completely due to the greenhouse effect, which reduces Earth’s effective emissivity (ε).

  The energy balance, EEIMB, is the difference between absorbed solar radiation, ASR, and emitted thermal radiation, ETR. The following graph shows 12-month running averages of ASR and ETR. It is the same graph as in Berkeley Earth Global Temperature Report for 2024, but I have added two additional curves.

Both ASR and ETR have been increasing, but not at the same rate, so the gap between them is widening. ASR, the fraction of incoming solar radiation not reflected into space, is increasing because the earth is reflecting less radiation. Earth’s reflectivity, α, dropped from 0.621 in 2000 to 0.615 in 2025 (see graph for albedo below). ETR, the emitted thermal radiation is also increasing, but not keeping up with the ASR. A definition of Earth’s effective emissivity, ε, is that ETR should equal εσT⁴, where σ is the Stefan-Boltzmann constant. The quantity εσT⁴ closely tracks ETR only if ε is a gradually decreasing quantity. The emissivity of the earth is affected by the greenhouse gas effect, so I modeled ε using atmospheric CO₂ as a proxy for all greenhouse gasses. From that model, emissivity decreased from 0.621 in 2000 to 0.618 in 2025 (see graph for emissivity below). This change aligns with rising CO2 levels, 369.7ppm in 2000 to 425.9ppm in 2025.

Conclusion

The accelerating rate of global warming is driven by a persistent and growing energy imbalance. Both albedo and emissivity have been decreasing, exacerbating this imbalance. Without immediate and effective action, the planet will continue a path of accelerating warming, with consequences for ecosystems, economies, and human well-being.