# Presentation: 073750

## How Models and Data Assimilation of Observations Work

- Without The Models
- Weather Prediction Is Not Possible!

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-  Originally prepared for HCC METO 111 and presented as a starting point of a script for NCEP video. 					9/06/2002

**Notes:**
Draft of a Script for a Video on how the models (NWP) work.  
Most bullets in the following should be an animated segment.

## To look at a current satellite or radar loop is to view a collection of observations, not a prediction.

**Nowcasts **can be used to make short time forecasts of up to 12 hours, but often they are not accurate beyond a few hours.
- Over a beer, weather forecasters will admit and proclaim that to go beyond **Nowcasts** they need a model to forecast the weather accurately.
- It is the combination of the model and the **MANual **forecasts that makes NWS forecasts as good as they are.

**Notes:**
Observations such as Radar and satellite loops are often taken as predictions.  In our minds we extrapolate the movements of patterns projecting future events.  We do this officially with mathematical and statistical algorithms, for example, built in the WSR88D radar are extrapolation algorithms for the future movement of storm cells.  This form of prediction can be used from 0-18 hours (usually 18 hours is a stretch) and is called a Nowcast.  A video animation of a squall line with extrapolation arrows provided by the WSR88D algorithm can replace the picture in the above slide.  When atmosphere conditions are changing rapidly as in severe weather regimes, Nowcasts and extrapolations do not work as well as they would under normal conditions.  A video short of the conversation occurring between forecasters proclaiming they could not make a 2 day forecast from a 500 mb observe chart.  Quite a few beers would be spent on the table.   Jargon in the business was to say “the MAN adds value to the
Model product by correcting model biases” but some thought that it was wrong to
Exclude women from the equation.  They did not know that MAN was short for
Manual vs the machine models.

## Predicting The FutureModels are based on the idea that the atmosphere is capable of analysis and being understood in terms of the basic laws and concepts of physics.

- How do prediction models determine the future state of the atmosphere?
- Start with a simple physical system containing an object subject to forces.
- Think of an accelerating piano, a car, or a parcel (a 3-dimensional cube) of air.

- A parcel of air

## A Prediction PrescriptionNewton’s Law						

- Acceleration = change in speed divided by change in time = force on the object times the mass of the object.
- The speed change = the speed some time in the future minus the initial speed.
- The time change = the time some time in the future minus the time initially.
- Putting it together

*a *= *V*/*t = F / M*
-  *V = V**f**  –  V**i** *
* **t = t**f**  –  t**i*
*(V**f **– V**i**)** **= F / M*
*     **(t**f** – t**i**)*

## A Prescription for Predicting the Future

- Rewrite and get a prediction equation by isolating the “Speed in the future” term on the left hand side of the equation and everything else on the right hand side.
*Speed**future** = Speed**initially** +  (mass X Forces) X the time change desired*.

- In the short hand of math:
-  ***V****f ** = ****V****i** + (****F / ****M*) X *(t**f** – t**i**)*
*We know the mass, initial time and the desired time in the future for the prediction.  We can also measure the initial speed, ****V****i*.* *
*We need only know the forces, ****F****, that are acting now to give the future speed, ****V****f **!*

**Notes:**
A video of the equations being formed in animation can be done here.  Starting from Newtons law each term can move to the eq in the slide above Vf = ....

## Our Prediction equation: Vf  = Vi + (F / M ) X (tf – ti)

- This will do for an auto or moving a piano, but what about predicting the state of future weather?
- A whole science has grown up around the methods used to engineer the prediction equation.

- Apply the above equation to each parcel or cube of air!
- Divide up the atmosphere into vertical and horizontal rows and columns of “air cubes” or parcels over the entire globe!
**Then apply the above equation over and over again in small time steps [***(t**f** – t**i**) is small*** ] to predict further and further into the future.**

**Notes:**
For example: Lagrangian and Eulerian, Grid and Spectral.  
Answer the question why is [(tf – ti) is small ].  Image of cubes on the Globe needed – my MSWord at home can make cubes in color but the one on my PC can’t.  An Image of the equations repeatedly applied is needed as well.

## How to we find the Forces that are acting on the atmosphere initially?

- The Forces can be calculated from the state variables of our earth’s observing system.  Temperature, Moisture, Wind, Surface Pressure and tracers like liquid water content, ozone, etc...

* **We measure the state variables with observing instruments.*

**Notes:**
There should be a slide that talks about the fact that in these terms the parcels or cubes of air do not remain shaped like a cube but are distorted by the movement of the air of neighboring parcels.  The distortion stress and strain the shape of the parcels into filaments which intertwine with each other causing the prediction equation to be resolved over smaller and smaller distance (scales) to catch the necessary action and continue to define the parcels of air. 
The model has equations for the physics in the biology of plant leaves in the jungle where at high sun angles, the leaves turn away from the sun and decrease their release of moisture.   Known as Stomata plant resistance, such calculation must be included to get the right amount of evaporation and precipitation if the model is to be accurate.  This is in addition to many other physical processes.

## The prediction equation is “solved” or integrated forward in time.

- The prediction equation is applied to each of the vertically stacked and horizontally distributed air parcels over the globe.
- Each time resulting in a new set of parcel future speeds.
- There is a similar prediction equation for temperature, moisture, surface pressure and “tracers”, like liquid water and Ozone.

- We diagnose from the predictions of these  basic variables other quantities, such as clouds, rain amount, ... that comprise the NWS products that are delivered to the public - - with adjustments made MANually by weather service professional forecasters.

**Notes:**
Picture of 3-D cubes or parcels stacked...
There is a separate prediction equation like the one above for the speed in one direction.  Wind is a vector with 2 directional components or a magnitude and direction so there are two equation for the components of the wind, u,v.  The temperature has a thermodynamic equation, and (gas) equation of state, and so do the other state variables have a predictive equation for their quantities.
In addition, there are external or fixed fields such as the mountain description, location of water bodies, land, ice, the vegetation index, soil index and type, etc...
The equations can get clever and complex in terms of the physics and physical processes.  This is on top of the complex interaction between each parcel o  air and its neighboring parcel.  Each parcel drives its neighbor by its own flows which changes the neighbors flow which changes the values of the state variables which changes and distorts the movement of the original parcel.

## The state variables of our earth’s observing system are measured from the Global Observing System

_**Number of Observations per day:**_
- 2,765,278 (April,2002)
- RAOBS (8,964)
-               (717,120)*
- AIRCFT & ACARS (111,726)
- *RAOBS contain many measurements

- Polar Orbiting Satellite (1,582,954)
- GOES Satellite (1,182,684)
- Radar and Profiler (6,459 & 746)
- Ship-Buoy (15,769)

**Notes:**
Show the table (Table 1) of the observing system.

Each RAOB has about 20 vertical levels and gives wind direction and speed, temperature and moisture for a total of 717,120 independent pieces of data per day.  The satellite and Radar observations do not deliver independent pieces of information.  In the case of the Radar, “Super-Ob”-ing the data 
Improves the information content for modeling. 

## Space and Time Scales in the AtmosphereThe weather telescopes from Planetary to phenomena resulting from city heat islands and river beds.

- The atmosphere appears to have distinct spatial and time domains:
- Some weather has components of many scales at once, for example, a hurricane spans most scales from tornados to interactions between tropics and mid-latitudes.

*Planetary scale determines the *
*climate, monthly and longer, *
*e.g., El Nino*

*Continental scales drive *
*“**weather systems”,  *
*e.g., 500mb waves*.

- Weather systems ,
- e.g., Lows and Highs

- Meso-scale, e.g., low
- level jets and severe
- weather

-  Micro-scale, e.g., Zephyrs,  Tornados

- Long Lived                          Short Lived

- Large Area

- Small area

**Notes:**
Each of the images is a vedio.  The meso-scale is already 
In animation (divergence with Low Level Jet conduit during time of Georgia tornado), on lnx73 web page (recently turned off).

## Big whirls have little whirls that feed on their velocity,Little whirls have lesser whirls and so on to viscosity.  (L.. F. Richardson)

- Planetary scale determines the climate, monthly and longer
- Synoptic scale encompass the cyclones and anti-cyclones (Lows and Highs) from days to weeks.
- Meso-scale has meso-cyclones thunderstorm supercells and squall lines which last from hours to a day and ...
- Micro-Scale are phemomena smaller than 10 km such as a tornado or a zephyr which last from minutes to hours.

## The Numerical Weather Prediction System takes account of the influence of large (small) scale phenomena on small (large) scales

- Computers are very good at keeping track of the millions of calculations that need to be accomplished each time the prediction equation is iterated.
- All the scales of motion and phenomena interact non-linearly according to the basic laws of physics.
- The smallest size or minimum time that can be resolved is determined by the number of calculations that the computer can provide to resolve the phenomena.

**Notes:**
Discuss the question of predictability and non-linearity.

## The problem is the earths observations are not delivered from equally spaced locations or at the same time.Clever mathematical and statistical calculations are made to interpolate the observations to an equally spaced grid.

- To start the integration of the prediction equation an analysis of the observations is done to interpolate the information to the model grid of parcels.
- Quality control of the observations to minimize errors is done.
- The models previous run is used as a guess and error statistics of the observations play an important role in creating optimal interpolation systems.

## .

- 29,412 (32,385) complex numbers representing each predicting vertical level, 3-dimensional variable, T, U, V, q, and tracers like liquid water and Ozone.  Two–dimensional Surface Pressure as well as other diagnosed and fixed fields like sea surface temperature, snow, Ice,... are part of the observing system initial files and read in at the beginning of each integration.
- The model diagnoses precipitation type and amount, clouds, convection and radiation.

**NWS Operational Model Suite**
- Global forecast System is a spectral model used for aviation, medium range forecasting and climate with ...

## NWS Operational Model SuiteThe Eta Model (Meso-Eta) 

- Is a regional model convering North America with higher resolution resolving meso-scale phenomenon at 12 km and 50 levels.
- The meso-scale regional Eta model starts with boundary and initial conditions from a global model run and then uses all the observations in its domain to make is own analysis and improved high resolution forecast.
**Telescoping regional models from the global model is a cost effective way to get more details where they are needed.**
- The Eta model gives the best precipitation predictions and is the primary forecasters tool for making quantitative precipitation forecasts.

## Higher resolution models will enable more accurate prediction of meso-scale and large scale phenomena including severe weather and special quantities like aerosol and pollutants.

- Models can target cities and associated weather events, watching and warning against loss of property and injury, distilling the interactions between the largest and smallest scales for predicting climate, weather and ocean phenomena.
- Accuracy improvements  in modeling are rewarded by decreasing the risk to population and commerce.
- The prediction system success is proven by past verification that they are up to the job, for example, in tropical cyclone and hurricane track prediction.

**Notes:**
Not all models are mentioned here