# Change in vertical wind intensity in atmospheric modeling

I am a beginner to atmospheric modeling. I want to know about the change in vertical wind intensity in modeling studies.

In general, if I initiate a simulation,I will get the real vertical wind velocity of that place, or winds with weaker intensity calculated as per the model equations intensifying with each timestep? What are the factors which control it?

I am asking this because I made several setups to study a real time event and I am getting the winds with different intensity. I want to know which of them is right. if I am wrong anywhere, what could be the associated factor that caused it.

• Are you using a hydrostatic model or a non-hydrostatic model? – BarocliniCplusplus Oct 31 '17 at 17:44
• I am using a non hydrostatic model – Agni Nov 1 '17 at 1:18
• You will need to provide more details: What model are you using? What kind of situation are you trying to simulate? What resolution are you working on? What kind of data are you using for comparison? How do you perform the comparison?. Most of the situations where vertical wind is interesting are highly complex with short predictability ranges, so all these factors are relevant. – Christoph Nov 2 '17 at 17:48
• I am using RAMS to simulate TC at 20km resolution. I want to know the general tendency of vertical winds, like how they emerge from the model equations. I believe that if the first guess data is obtained, the winds may get their initial values and they should provide realistic values approximately. I want to confirm this. – Agni Nov 3 '17 at 15:44

It really depends on whether you're model is hydrostatic or not.

If your model is hydrostatic, then the vertical velocity is found diagnostically. The diagnostic algorithm is called the Richardson Equation.

If your model is nonhydrostatic, often it is presumed that the vertical velocity is 0. The vertical velocity is presumed to be 0 (unless you do some spin-up or model restart, or some other special initialization), and the prognostic equation for vertical velocity is found.

• The nonhydrostatic model I am most familiar with is WRF, so I don't know if that applies to RAMS. – BarocliniCplusplus Feb 2 '18 at 19:47
• @BrocliniCplusplus Thank you for your answer. RAMS is also non hydrostatic and as you mentioned in your answer, I have observed the zero w at the model initialization time. But unlike horizontal velocity values I never got any source to verify how should these values change during the preconditioning or spin up time. – Agni Feb 3 '18 at 17:10

The vertical equation of motion can vary considerably from one model to another, however, in general for a non-hydrostatic model the predominant terms are: advection, vertical pressure gradient and buoyancy. The order of importance of the previous terms depends on the phenomenon that is being modeled. The classic formulation of this equation, on a Cartesian coordinate system and without considering the effect of air humidity, reads:

$$\frac{\partial w}{\partial t} = - (u\frac{\partial w}{\partial x}+v\frac{\partial w}{\partial y}+w\frac{\partial w}{\partial z})-\frac{1}{\rho}\frac{\delta p^\prime}{\delta z}-g\frac{\rho^\prime}{\rho}$$

where the state variables are defined as the sums of base-state variables and the deviations from the base state as $p=\bar{p}+p^\prime$ and $\rho=\bar{\rho}+\rho^\prime$. The base state is assumed to be horizontally homogeneous, time invariant and hydrostatically balanced. Note that, in the fully compressible model the linearization with the reference atmosphere is not employed.

• This equation will always need an initial value, so the model will provide realistic winds just from the beginning? Kindly clarify this. – Agni Nov 3 '17 at 15:47