The volumetric budget after running modflow model has the terms storage in out, recharge in and recharge out, river leakage in and out, and constant head in and out. What does storage in and out mean in this?
Recharge in may be useful component in the ground water flow where as recharge out may be a horizontal flow going out of the system, may be otherwise called as negative recharge.
"Flow into and out of storage is also considered part of the overall budget inasmuch as accumulation in storage effectively removes water from the flow system and storage release effectively adds water to the flow—even though neither process, in itself, involves the transfer of water into or out of the ground-water regime." It's been awhile since I looked at model files, but I think "accumulation of storage" is equal to storage in, and "storage release" is equal to storage out. It's always been a tricky concept for me to understand.
"Storage in" is the volume of water stored in the porous media during the associated time step under transient groundwater dynamics. "Storage out" is the volume of water drained from the pores to the mobile water.
To help you understand this, you can imagine the porous media or the aquifer as a sponge absorbing and releasing/draining water depending on the time-dependent stresses (i.e. such as boundary conditions) applied to the system.
If you consider the groundwater flow equation as written in https://en.wikipedia.org/wiki/MODFLOW, the mass balance you get out as MODFLOW output is just a discrete numerical form of this equation. The storage term is the first on the right-hand side of that equation. It is nothing more than the net difference between groundwater leaving the system through outflowing boundaries (including sinks) and the inflowing groundwater (including sources). This is how it is calculated by the model, and the mass balance quantifies that and is, therefore, a meaningful way to check the model's accuracy and adequacy with the initially drafted conceptual model.
If you don't understand the basic concepts of groundwater storage, I recommend reading a classic textbook on groundwater hydrology. Bear (1972) & Bear and Cheng (2011) are highly recommended.
I realize this question was asked quite a while ago, but just for anyone interested in the future, the definition in the MODFLOW volumetric budget of STORAGE IN is actually the volume of water that is released from storage (i.e. added to the simulation). While STORAGE OUT is the volume of water that is partitioned into storage. Below is a direct quote from Applied Groundwater Modelling by Anderson, Woessner, and Hunt (2015) "Release of water from storage is counted as inflow and uptake is counted as outflow" (p. 99).