Earth Energy Balance Calculator
Free Earth energy balance Calculator for planetary & earth system science. Enter variables to compute results with formulas and detailed steps.
Formula
T_eff = (S(1-a)/4sigma)^(1/4); T_surface = ((S(1-a)/4 + dF)/(eps*sigma))^(1/4)
Where S is solar constant, a is albedo, sigma is Stefan-Boltzmann constant, eps is effective emissivity, dF is additional radiative forcing.
Worked Examples
Example 1: Present-Day Earth Energy Balance
Problem: Calculate Earth energy balance with solar constant 1361 W/m2, albedo 0.30, effective emissivity 0.612.
Solution: Absorbed solar = (1361/4) * (1 - 0.30) = 238.18 W/m2\nT_eff = (238.18 / 5.67e-8)^0.25 = 254.8 K\nT_surface = (238.18 / (0.612 * 5.67e-8))^0.25 = 288.4 K\nGreenhouse warming = 288.4 - 254.8 = 33.6 K
Result: T_eff: 254.8 K | T_surface: 288.4 K (15.3 C) | Greenhouse warming: 33.6 K
Example 2: Doubled CO2 Forcing Scenario
Problem: Add 3.7 W/m2 radiative forcing (CO2 doubling) to present Earth energy balance.
Solution: Absorbed + forcing = 238.18 + 3.7 = 241.88 W/m2\nNew T_surface = (241.88 / (0.612 * 5.67e-8))^0.25 = 289.5 K\nWarming = 289.5 - 288.4 = 1.1 K (without feedbacks)
Result: New T_surface: 289.5 K | Direct warming: 1.1 K | Climate sensitivity: 0.30 K/(W/m2)
Frequently Asked Questions
What is Earth energy balance?
Earth energy balance is the accounting of incoming solar energy versus outgoing energy, which determines the planet temperature. The Sun delivers approximately 1361 watts per square meter at Earth distance, but only about 240 watts per square meter is absorbed on average after accounting for the spherical geometry and albedo reflection of about 30 percent. In equilibrium, Earth must radiate the same amount of energy back to space as outgoing longwave infrared radiation. Any persistent imbalance between absorbed and emitted energy causes the planet to warm or cool until a new equilibrium is reached.
What causes Earth energy imbalance?
Earth energy imbalance occurs when the planet absorbs more solar energy than it radiates to space, or vice versa. The current imbalance is approximately 0.5 to 1.0 watts per square meter, meaning Earth is absorbing slightly more energy than it emits due to increasing greenhouse gas concentrations. This excess energy is primarily stored in the ocean, which absorbs over 90 percent of the additional heat. The imbalance drives ongoing global warming and will persist until either greenhouse gas concentrations stabilize and temperatures rise enough to restore equilibrium.
How do clouds affect Earth energy balance?
Clouds have a dual effect on Earth energy balance that makes them one of the largest sources of uncertainty in climate projections. On one hand clouds reflect incoming solar radiation back to space with high albedo which has a cooling effect of roughly minus 50 watts per square meter globally. On the other hand clouds also absorb and re-emit outgoing longwave radiation like greenhouse gases producing a warming effect of about plus 30 watts per square meter. The net cloud radiative effect is currently about minus 20 watts per square meter of cooling.
What role does ocean heat storage play in energy balance?
The ocean stores over 90 percent of the excess energy from Earth current radiative imbalance due to its enormous heat capacity compared to the atmosphere and land surfaces. One meter depth of ocean has the same heat capacity as the entire atmospheric column above it. This thermal inertia means that surface temperatures lag behind changes in radiative forcing by decades to centuries. The ocean mixed layer of about 100 meters depth responds on timescales of years to decades while the deep ocean takes centuries to millennia to equilibrate.
How is Earth energy balance measured from space?
Earth energy balance is measured from space using broadband radiometers aboard satellites such as the Clouds and Earth Radiant Energy System (CERES) instruments on NASA Terra and Aqua satellites. CERES measures both reflected shortwave solar radiation and emitted longwave infrared radiation at the top of the atmosphere with accuracy approaching 0.5 watts per square meter. The Earth Radiation Budget Experiment (ERBE) provided earlier measurements starting in 1984. Combining these top-of-atmosphere measurements with ocean heat content data from the Argo network provides independent verification of the energy imbalance.
How do plate tectonics shape the Earth's surface?
Earth's lithosphere is divided into tectonic plates that move on the asthenosphere. Divergent boundaries create new crust (mid-ocean ridges), convergent boundaries destroy crust (subduction zones) or build mountains, and transform boundaries cause earthquakes. Plates move 1-10 cm per year, driven by mantle convection.