You have not informed in the question which level of knowledge of climate science books you are referring to, so I have arranged them with respect to their difficulties.

Beginner Level:

"Climate Change: What Everyone Needs to Know" by Joseph Romm This book provides a comprehensive introduction to the basics of climate change, covering the science, impacts, and potential solutions in an accessible and easy-to-understand manner.

"The Thinking Person's Guide to Climate Change" by Robert Henson Geared towards those new to the subject, this book breaks down the complex science of climate change into clear explanations and also addresses common misconceptions.

Intermediate Level:

"Dire Predictions: Understanding Climate Change" by Michael E. Mann and Lee R. Kump This book offers a more in-depth exploration of climate science, including discussions on climate modeling, historical climate data, and predictions for the future.

"The Sixth Extinction: An Unnatural History" by Elizabeth Kolbert While not exclusively focused on climate science, this Pulitzer Prize-winning book delves into the interconnectedness of species extinction and climate change, providing a deeper understanding of their effects.

Advanced Level:

"The Physics of Climate Change" by Lawrence M. Krauss This book delves into the physics behind climate change, explaining the scientific principles that underpin the climate system. It's recommended for readers with a strong background in physics and science.

"Climate Change Science: A Modern Synthesis" edited by G. Thomas Farmer and John Cook This comprehensive book provides an overview of climate science from various perspectives, making it suitable for those looking for an in-depth exploration of the subject.

Remember that climate science is a multidisciplinary field, and books on the topic often touch on aspects of physics, chemistry, biology, and more. Choose a book that matches your current knowledge level and interests, and don't hesitate to further explore specific areas that intrigue you.

Here are options for a Physics Grad student like you, you might like these:

Intermediate Level:

"Dire Predictions: Understanding Climate Change" by Michael E. Mann and Lee R. Kump This book offers a more in-depth exploration of climate science, including discussions on climate modeling, historical climate data, and predictions for the future.

"The Sixth Extinction: An Unnatural History" by Elizabeth Kolbert While not exclusively focused on climate science, this Pulitzer Prize-winning book delves into the interconnectedness of species extinction and climate change, providing a deeper understanding of their effects.

Advanced Level:

"The Physics of Climate Change" by Lawrence M. Krauss This book delves into the physics behind climate change, explaining the scientific principles that underpin the climate system. It's recommended for readers with a strong background in physics and science.

"Climate Change Science: A Modern Synthesis" edited by G. Thomas Farmer and John Cook This comprehensive book provides an overview of climate science from various perspectives, making it suitable for those looking for an in-depth exploration of the subject.

Remember that climate science is a multidisciplinary field, and books on the topic often touch on aspects of physics, chemistry, biology, and more. Choose a book that matches your current knowledge level and interests, and don't hesitate to further explore specific areas that intrigue you.