How Models and Data Assimilation of Observations Work

1. logo logo How Models and Data Assimilation of Observations Work Without The Models Weather Prediction Is Not Possible! Originally prepared for HCC METO 111 and presented as a starting point of a script for NCEP video. 9/06/2002

2. 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.

3. 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. Predicting The FutureModels 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. A parcel of air

4. 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 = DV/Dt = F / M DV = Vf – Vi Dt = tf – ti (Vf – Vi)= F / M (tf – ti) A Prediction PrescriptionNewton’s Law

5. 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. Speedfuture = Speedinitially + (mass X Forces) X the time change desired. In the short hand of math: Vf = Vi + (F / M) X(tf – ti) We know the mass, initial time and the desired time in the future for the prediction. We can also measure the initial speed, Vi. We need only know the forces, F, that are acting now to give the future speed, Vf ! A Prescription for Predicting the Future

6. 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 [(tf – ti) is small ] to predict further and further into the future. Our Prediction equation: Vf = Vi + (F / M ) X(tf – ti)

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

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

9. Number of Observations per day: 1.3 billion (June 2008) RAOBS (1409) AIRCFT & ACARS (147,228) Polar Orbiting Satellite (1,224,115,502 ) GOES Satellite (37,591,953 ) Radar and Profiler (6,842 & 813) Ship-Buoy (66,035) The state variables of our earth’s observing system are measured from the Global Observing System

10. 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. Micro-scale, e.g., Zephyrs, Tornados Space and Time Scales in the AtmosphereThe weather telescopes from Planetary to phenomena resulting from city heat islands and river beds. Small area Meso-scale, e.g., low level jets and severe weather Weather systems , e.g., Lows and Highs Continental scales drive “weather systems”, e.g., 500mb waves. Planetary scale determines the climate, monthly and longer, e.g., El Nino Large Area Long Lived Short Lived

11. 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.

12. 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.

13. 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.

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

15. NWS Operational Model SuiteThe Eta Model (Meso-Eta) • Is a regional model covering 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.

16. 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.