# Energy Balance Climate Models

Wiley Series in Atmospheric Physics and Remote Sensing

1. Edition September 2017

XVI, 369 Pages, Hardcover

100 Pictures*Monograph*

**978-3-527-41132-0**

### Short Description

This book covers all major aspects of Energy Balance Models, starting from the most simple zero-dimensional models and then proceeding to horizontally and vertically resolved models.

Written by renowned experts in the field, this first book to focus exclusively on energy balance climate models provides a concise overview of the topic. It covers all major aspects, from the simplest zero-dimensional models, proceeding to horizontally and vertically resolved models.

The text begins with global average models, which are explored in terms of their elementary forms yielding the global average temperature, right up to the incorporation of feedback mechanisms and some analytical properties of interest. The effect of stochastic forcing is then used to introduce natural variability in the models before turning to the concept of stability theory. Other one dimensional or zonally averaged models are subsequently presented, along with various applications, including chapters on paleoclimatology, the inception of continental glaciations, detection of signals in the climate system, and optimal estimation of large scale quantities from point scale data. Throughout the book, the authors work on two mathematical levels: qualitative physical expositions of the subject material plus optional mathematical sections that include derivations and treatments of the equations along with some proofs of stability theorems.

A must-have introduction for policy makers, environmental agencies, and NGOs, as well as climatologists, molecular physicists, and meteorologists.

CLIMATE AND CLIMATE MODELS

Defining Climate

Elementary Climate System Anatomy

Radiation and Climate

Hiercharchy of Climate Models

Greenhouse Effect and Modern Climate Change

Reading this Book

Cautionary Note and Disclaimer

Notes on Further Reading

GLOBAL AVERAGE MODELS

Temperature and Heat Balance

Time Dependence

Spectral Analysis

Nonlinear Global Model

Summary

RADIATION AND VERTICAL STRUCTURE

Radiance and Radiation Flux Density

Equation of Transfer

Gray Atmosphere

Plane Parallel Atmosphere

Radiative Equilibrium

Simplified Model for Water Vapor Absorber

Cooling Rates

Solutions for Uniform-Slab Absorbers

Vertical Heat Conduction

Convective Adjustment Models

Lessons from Simple Radiation Models

Criticism of the Gray Spectrum

Aerosol Particles

GREENHOUSE EFFECT AND CLIMATE FEEDBACKS

Greenhouse Effect without Feedbacks

Infrared Spectra of Outgoing Radiation

Summary of Assumptions and Simplifications

Log Dependence of the CO2 Forcing

Runaway Greenhouse Effect

Climate Feedbacks and Climate Sensitivity

Water Vapor Feedback

Ice Feedback for the Global Model

Probability Density of Climate Sensitivity

Middle Atmosphere Temperature Profile

Conclusion

Notes for Further Reading

LATITUDE DEPENDENCE

Spherical Coordinates

Incoming Solar Radiation

Extreme Heat Transport Cases

Heat Transport Across Latitude Circles

Diffusive Heat Transport

Deriving the Legendre Polynomials

Solution of the Linear Model with Constant Coefficients

The Two-Mode Approximation

Poleward Transport of Heat

Budyko's Transport Model

Ring Heat Source

Advanced Topic: Formal Solution for More General Transports

Ice Feedback in the 2-Mode Model

Polar Amplification through Icecap Feedback

Chapter Summary

TIME DEPENDENCE IN THE 1-D MODEL

Differential Equation for Time Dependence

Decay of Anomalies

Seasonal Cycle on a Homogeneous Planet

Spread of Diffused Heat

Random Winds and Diffusion

Numerical Methods

Spectral Methods

Chapter Summary

Appendix: Solar Heating Distribution

NONLINEAR PHENOMENA IN EBMS

Formulation of the Nonlinear Feedback Model

Stürm-Liouville Modes

Linear Stability Analysis

Finite Perturbation Analysis and Potential Function

Small Ice Cap Instability

Snow Caps and the Seasonal Cycle

Mengel's Land Cap Model

Chapter Summary

TWO HORIZONTAL DIMENSIONS AND SEASONALITY

Beach Ball Seasonal Cycle

Eigenfunctions in the Bounded Plane

Eigenfunctions on the Sphere

Spherical Harmonics

Solutions of the EBM with Constant Coefficients

Introducing Geography

Global Sinusoidal Forcing

Two Dimensional Linear Seasonal Model

Present Seasonal Cycle Comparison

Chapter Summary

PERTURBATION BY NOISE

Time-Independent Case for Uniform Planet

Time-Dependent Noise Forcing for Uniform Planet

Green's Function on the Sphere: f=0

Apportionment of Variance at a Point

Stochastic Model with Realistic Geography

Thermal Decay Modes with Geography

TIME-DEPENDENT RESPONSE AND THE OCEAN

Single-Slab Ocean

Penetration of a Periodic Heating at the Surface

Two-Slab Ocean

Box-Diffusion Ocean Model

Steady State of Upwelling-Diffusion Ocean

Upwelling Diffusion with (and without) Geography

Influence of Initial Conditions

Response to Periodic Forcing with Upwelling Diffusion Ocean

Summary and Conclusions

APPLICATIONS OF EBSM: OPTIMAL ESTIMATION

Introduction

Independet Estimators

Estimating Global Average Temperature

Deterministic Signals in the Climate System

APPLICATIONS OF EBMS: PALEOCLIMATE

Paleoclimatology

Precambrian Earth

Glaciations in the Permian

Glacial Inception on Antarctica

Clacial Inception on Greenland

Pleistocene Glaciations and Milankovic

Kwang-Yul Kim is a professor in climatology and physical oceanography at Seoul National University. Upon graduation from Texas A&M with his Ph.D. degree in physical oceanography he was inducted into the Phi Kappa Phi Honor Society. He authored two books: Fundamentals of Fluid Dynamics and Cyclostationary EOF Analysis. He programmed several new energy balance models.