After years of looking at I don't know how many weather related web pages, I have put a few of my favorites here.

I have developed the ASP (Atmosphere-Surface forecast Prediction) model since about 2007 in my free time. The model is under continuous development and it must be noted that it is simpler and uses slightly more coarse vertical and horizontal resolutions than operational models (although it is comparable to some such models)... but it has baseline physics and a solid dynamical core and thus can produce reasonable forecasts. I have developed all the code and scripts using free sotware and literature from the web under the Linux operating system.

ASP is a hybrid-mass coordinate primitive equation model with equations expressed in flux form. It can be run in hydrostatic or non-hydrostatic mode using an add-on non-hydrostatic module (2 additional prognostic equations). The non-hydrostatic equations are fully compressible (this option is usally activated for resolutions below 10 km, although it can be run seamlessly at any spatial resolution). The model baseline physics consist in: bulk microphysics, broadband longwave and two-stream shortwave radiation models with clouds, a mass-flux convection scheme, vertical diffusion/turbulence with non-local diffusivities (K) based on a prognostic 1.5 order TKE scheme and an EDMF scheme within the PBL and a a fully implicit coupling between the atmosphere and three sub-grid surface tiles (continental surface, liquid water surfaces and sea ice). The four prognostic dynamic (atmospheric) variables consist in the u and v wind components, the dry or moist (density, the current default) air potential temperature, and the dry surface hydrostatic pressure. The mass coordinates and associated coordinate metrics use dry hydrostatic mass. Note that in non-hydrostatic mode, the 2 additional prognostic variables are the vertical velocity, w, and the geopotential.

There are 5 moist (microphysical) prognostic variables expressed as mixing ratios: water vapor, cloud liquid water content, cloud ice content, and 2 precipitation variables (rainfall and snowfall). There are 6 prognostic variables for the land surface; the soil temperature, moisture and ice content for N-layers (the current default is 5), snow density, SWE and albedo (currently a 2 layer snow scheme). The frozen water tile uses a single prognostic variables for ice temperature (2 layers). Finally, the surface water scheme (lakes and oceans/seas), uses a cool-skin prognostic temperature (with a relaxation to SSTs provided from an external source). Heat transfer in the soil and ice uses diffusion, while soil moisture transfer is modeled using Richard's equation. The time integration schemes use linearized fluxes and are implicit (soil, water and water-ice temperatures are implicitly coupled with the atmospheric temperature profiles).

The numerical schemes are fairly standard compared to research and operational models. The vertical resolution is variable and is greatest near the surface: terrain following pressure (dry mass) coordinates are used in the lower atmosphere, while constant pressure surfaces are used in the upper atmosphere. The vertical discretization uses a Lorenz staggered grid, and horizontal discreization is on an Arakawa C-grid. The model has options for Lambert and Mercator map projections for limited area applications, and a Plate Carree projection over the globe. Horizontal resolution for all 3 projections is a user option. For the Plate Carree projection, Fourier filtering of certain mass variables is used above a critical latitude for this application to optimize the balance between model time step and CPUs. The model has options for high order diffusion, divergence damping, and advection finite differences (including a 5th order WENO scheme). Note that scalar variables (water vapor and hydrometeors, TKE and a passive tracer used for testing) are currently advected using a standard 5th order horizontal scheme for the first 2 RK steps, and a 5th order WENO scheme for the third and last RK step. Vertical advection uses a 3rd order scheme for the first 2 RK steps, and a 3rd order WENO scheme for the last RK step. The numerical integration includes 3 time steps (from largest to smallest): i) large/physics time step, ii) Runge-Kutta (RK) time integration methods for advection and coriolis terms, and iii) foward-backward time splitting for gavity and sound wave terms. Note that there are options to use implicit second-order vertical advection of certain variables within the RK loop (the default, however, is currently RK vertical advection). In non-hydrostatic mode, the model uses the HEVI (horizontally-explicit, vertically implicit) approach to simultaneously solve for w, geopotential and the pressure during the time split using a tridiagonal matrix solver. Finally, there is fully implicit vertical turbulence-coupling with surface (on large/physics model time step) in which the dynamics tendencies are source terms. Finally, radiation and the convection schemes are generally called at a lower frequency than the large time step (depending on size of large time step).

The model is initialized either using a "cold-start" (NWP analysis interpolated to the ASP grid, followed by a digital filter using short forward and backward dry-adiabtic integrations), or a simple data assimilation scheme in which a previous forecast is nudged to the NWP provided initial state. Finally, a "big-brother" data-assimilation option exists in which certain variables can be nudged using large scale variables (from an NWP model which is also providing the time varying lateral boundary conditions) during the early part of the forecast to potentially improve the trajectory (a simple economical way to benefit from a NWP models likely better early forecast period owing to a more elaborate data assimilation scheme).