AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |
Back to Blog
Earthnet webmail4/28/2023 ![]() Our equation for steady state solutions independent of longitude, writing out the divergence of the diffusive flux in spherical coordinates, is now Finally, we can use the simplest possible albedo formulation that provides some ice-albedo feedback: for and for. We can define a non-dimensional temperature,, diffusivity, and mean incident solar flux or total solar irradiance. We can just set (and think of it as the freezing temperature when we set the albedo). is the outgoing infrared flux linearized about the reference temperature, is a heat capacity, and is a kinematic diffusivity. The form, with the second Legendre polynomial is a pretty good fit to the annual mean incident solar flux as a function of latitude. We set, where is the global mean incident flux = total solar irradiance/4 so that averages to unity over the sphere. Is the absorbed solar flux, where is the co-albedo. Playing with this kind of “toy” model is valuable pedagogically - I certainly learned a lot by building and elaborating this kind of model - and can even lead to some nuggets of insight about the climate system. At about the same time, Jerry North had simplified this kind of model to its bare essence: linear diffusion on the sphere with constant diffusivity, outgoing infrared flux that is a linear function of surface temperature, and absorbed solar flux equal to a specified function of latitude multiplied by a co-albedo that is itself a function of temperature to capture the different planetary albedos for ice-free and ice-covered areas. When we were first starting out as graduate students, Max Suarez and I became interested in ice age theories and found it very helpful as a starting point to think about energy balance models for the latitudinal structure of the surface temperature. Stable states are indicated by a thicker line. Latitude of ice margin as a function of a non-dimensional total solar irradiance in the diffusive energy balance climate model described by North 1975, for different values of the non-dimensional diffusion. Posted on August 8th, 2013 in Isaac Held's Blog
0 Comments
Read More
Leave a Reply. |