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28

All numerical atmospheric models are built around calculations derived from primitive equations that describe atmospheric flow. Vilhelm Bjerknes discovered the relationships and thereby became the father of numerical weather prediction. Conceptually, the equations can be thought of as describing how a parcel of air would move in relationship to its ...


20

Weather models (or, as they are more commonly called in the field, atmospheric models) are computer programs that read in input data (initial conditions) and solve partial differential equations to produce a future state of the atmosphere. Although @JonEricson provides an overall good but anecdotal summary of what models do, here I describe the exact steps ...


15

The hydrostatic approximation begins with the full 3-D momentum equation (Navier-Stokes) and through scale analysis the vertical momentum equation reduces to: $$\dfrac{\partial p}{\partial z} = -\rho g$$ This is a balance between the vertical pressure gradient force and gravity with no net acceleration. This tends to hold for atmospheric phenomena that ...


13

Your premise is incorrect. Numerical models normally have: A full temperature profile A specific field for the 2 metre temperature A specific field for the skin temperature For example, see ERA-40 daily fields, which both 2 metre temperature and Skin temperature, or CFS reanalysis 6-hour fields, which has Air temperature, Skin temperature, and Surface air ...


12

This is not a complete answer. One aspect of weather models consists of Data assimilation or 4D-var. I agree that they are amazing, and the question how do they work is too broad to be answered. So I recommend you read up on data assimilation and in particular 4D-Var. Concepts are somewhat similar in inverse theory, but of much higher dimensionality. In ...


11

This is my favorite example of the difference between a hydrostatic and a non-hydrostatic code. The simulation depicts a lock exchange which you can picture as opening your window if you live in a cold place and it is winter. Inside your house, presumably, the air is warmer than the outside. So when you open the window, the cooler (heavier) air will ...


11

The Barotropic vorticity equation is insufficient to model rain. Part of this is due to the word 'Barotropic,' which indicates a lack of thermal gradient. The other reason is that while vorticity is a useful quantity, it lacks explicit information on the atmospheric state. The primitive equations are a system of partial differential equations that are used ...


10

The resources you want will vary on what level of understanding you are seeking. For example, knowing the math means you can solve equations or transform them, but it doesn't mean you understand the physics involved. Some topics you'll want an understanding of to understand the process: Physics At the heart of any weather model are our primitive ...


10

There are lots of articles that assess global models both locally and globally. They usually focus on a few parameters that are easily comparable with observations (e.g., temperature, wind, surface pressure). A couple of examples of the many available: for ECMWF: Roberto Buizza, 1997: Potential Forecast Skill of Ensemble Prediction and Spread and Skill ...


9

Everything. Parametrizations Spatial (horizontal and vertical) and temporal resolution Initialization Dynamical core Handling of some complex non-linear physical processes (i.e. snow) Topography representation How the mathematical equations are numerically implemented The computer used etc... These are some of the main differences between 2 given numerical ...


8

Weather models and forecasts are governed by systems of differential equations. One starts with the current levels or values of causal variables: temperature, humidity, atmospheric pressure etc. One also has to factor in the "derivatives," or rates of change of these variables. Hence the need for differential equations, which incorporate both variables and ...


7

Presume that the atmosphere can be modeled with waves of different frequencies. Therefore, the atmosphere can be written as a series of sine and cosine functions with different frequencies and coefficients. Consider the linear advection equation: $$\frac{\partial u}{\partial t}= -c \frac{\partial u}{\partial x}$$ Consider the assumption that $u$ can be ...


7

TL;DR: Global NWP models such as NCEP's GFS (free access) and ECMWF's IFS (restricted access) provide forecasts at a horizontal scale of a few tens of kilometers every few hours. Starting from global NWP data, NCAR's WRF (free) can be used to produce results at a resolution of a few kilometers and stored every few minutes in time. I felt I could give some ...


7

Schmidt-Appleman criterion (SAC) is used to model contrail formation. I advise reading in full Ulrich Schumann's article "A contrail cirrus prediction model" (http://www.geosci-model-dev.net/5/543/2012/gmd-5-543-2012.pdf) to get all the relevant formulae and literature references. While it is possible to transcribe the formulae here, the reference cited ...


7

The answer by @IsopycnalOscillation explains some implications of using explicit and implicit schemes and in what applications one is preferred over the other. Here, I describe how these two methods actually work, and how does the implicit scheme uses knowledge of the later state. Take the ordinary differential equation: $$ \dfrac{\partial u}{\partial t} = ...


6

Implicit and explicit methods have the same differences no matter what context. The building blocks from which these methods are constructed are the same, they all use Taylor series expansion of a function. Of course, there are many different numerical methods, explicit and implicit, with different degrees of numerical accuracy, consistency and stability. ...


6

The answer to this question depends on what process one is interested in simulating well. As you know, short/mid-range weather prediction models and climate models have very different applications and goals. Because the short range weather prediction model is typically of much higher resolution than climate models (~1-10 km versus ~50-200 km), it is almost ...


6

A difference of accuracy between weather models can be due to different factors, one of these is certainly the availability of "good" initialization data. As pointed out in Bradley Ballish (NOAA/NCEP) in his AMS presentation the accuracy of GFS has improved drastically when ECMWf initaliziation data have been used. Furthermore, I think there is a big ...


6

Bifurcation is relevant to the atmosphere because it effects the predictability of the evolution of the atmosphere. I can't speak to its merits with climate models, but with weather it is quite important. As Lorenz discovered, the atmosphere is chaotic and numerical prediction is very sensitive to the initial conditions. If the initial conditions are ...


5

One of the issues with ARGO data is that in most cases it does not provide data from the real surface of the ocean. When they ascend from their drifting depth (usually at 1000 or 2000 meters) to the surface, most of them stop recording at a depth of around 5 meters from the surface. From SeaBird (the company that provides the CTD sensors in most ARGO floats, ...


4

Europe is looking nicer and nicer every year (source): This is a little bit out of date, since AR5 is already out - the dates for the first 4 IPCC reports were: IPCC First Assessment Report, 1990 IPCC Second Assessment Report, 1995 IPCC Third Assessment Report, 2001 IPCC Fourth Assessment Report, 2007 IPCC Fifth Assessment Report, 2014 And an updated ...


4

You could look further into how currently used weather models actually work. If you want to do a prediction you will have to run a model which is not just as simple as your question would imply. There are actually many equations in parallel and that describe how motions in a grid behave. Sub grid phenomena like rain are parametrized also. Rain depends e.g. ...


4

It is also challenging to get clouds, rain etc. right in weather forecasts. Compared to climate applications the advantage in weather forecasts is that cloud information from the initial conditions can improve the cloud representation in the model. Unfortunately that information does not last that long in the model due to the limited lifetimes of clouds. ...


4

Bifurcation is a characteristic of chaotic systems. To quote the Wikipedia article on chaos theory Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions—a paradigm popularly referred to as the butterfly effect. Small differences in initial conditions (such as those due to rounding errors in numerical ...


2

Here are some excerpts from my answer here at scicomp ... "You have to solve a linear system of the type Ax=b in the implicit scheme where as in the explicit scheme you do not, Your time step in the explicit scheme is limited by the CFL criteria for stability. Implicit schemes are unconditionally stable (though in practice you still need a reasonable time ...


2

I don't have a mathematical illustration at the moment (though I might edit this answer if I come across something in my notes). But the basic problem is sound waves. If you make a numerical model of the full Navier-Stokes equations, that model has to allow sound waves to propagate. That implies that the time step used has to be incredibly short -- under 5 ...


2

A good rule of thumb for down-scaling with WRF is not to interpolate down more than 3 or 4 times; with 3 being the standard recommendation. So while 18 km is probably overkill for an outer domain (this is a personal opinion, there are some operational models like HWRF that start at 18km), 2km would definitely be too fine for a parent domain. The main reason ...


1

The answer before me is correct, but that is not the only reason why digital filters are used. After the data assimilation procedure occurs, the resulting model state may not be in equilibrium. For example, if geopotential height (or surface pressure) is updated in the assimilation procedure, but wind is not (or vice versa), then the assimilated fields are ...


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