OVERVIEW:

We will introduce and the discuss the use of numerical weather prediction (NWP) products.

OUTLINE:

1. A historical anecdote on the origin of "chaos." Ed Lorenz -- Massachusetts Institute of Technology (MIT) mathematician and former U.S. Army Air Corp meteorologist:

1.1. 1960: Created the first sophisticated numerical weather model. Simultaneous solutions to twelve equations, running on a Royal McBee computer. (The computer was an ungainly, tube-operated device that occupied a large portion of his office and broke down frequently.) His simple model reproduced two important features of terrestrial weather: the repetition of patterns, with disturbances. Lorenz called this kind of system "Deterministic Nonperiodic Flow."

1.2. 1961: Discovered one of the fundamental limitations of numerical weather models: Chaos.

1.2.1. Computer models begin with a detailed picture of the state of the atmosphere at a given moment -- this is called initialization or setting the initial condition. The more complete the initialization, the better the prognoses will be.

1.2.2. Computer models calculate prognoses (the state of the atmosphere at some point in the future) by applying the laws of physics to the initial condition.

1.2.3. Because the exact initial condition can never be known, and because the physical limitations of the computer require the simplification of the laws of physics used in the model, error will inevitably creep into the model's prognoses. The error -- the difference between the actual state of the atmosphere in the future and the model's prediction of the future state -- usually starts out fairly small, but grows larger and larger as the difference between the initialization time and prognosis time gets larger and larger.

1.3. Chaos is often called Complex Determinism. In popular literature, chaos has been called The Butterfly Effect.

1.3.1. Complex Determinism implies that, although each molecule in the atmosphere is obeying deterministic (Newtonian) laws of physics, the interactions between the uncountable billions of particles are so complex that predicting each particle's future velocity and position is only possible in a statistical sense. It also implies that each departure of reality from the model's prediction could have been predicted, had a more complete initilization been achieved and a more complete model physics been applied.

1.3.2. The Butterfly Effect implies that the inevitably incomplete initilization will lead to inevitably growing error in the model's prognoses, even if the model physics is perfectly complete. This inevitable initialization error may cause catastrophic failures in the model's ability to predict future states -- e.g. because the initialization failed to account for the flapping of a butterfly's wings on one side of the planet, the model physics subsequently failed to predict the formation of a cyclonic storm on the other side of the planet.

2.1. The model begins by creating an initial condition.

2.1.1. The initial condition is created by assimilating surface and upper-air (UA) observational data. After a quality-control routine, these data are interpolated from their irregular horizontal distribution to a regularly-spaced set of gridpoints. The data are also interpolated to a fixed number of vertical layers. This sets the model's horizontal and vertical resolution.

2.1.2. The interpolated data are then analyzed for several different physical quantities, such as temperature, moisture content, and wind components (u, v, and w).

2.2. Next, the model's physics are applied to the analyzed fields.

2.2.1. Model physics are derived by applying scaling arguments to the equations of motion and the gas laws. Scaling arguments remove terms from the equations that are either too large, too small, too short-term, or too slow to be of importance to the domain of the model. E.g. A model covering a region of the Earth's surface less than 10 miles across for periods of less than 12 hours need not include the coriolis terms. Scaling increases the efficiency of the model, but does so by sacrificing accuracy.

2.2.2. The equations are simultaneously solved for every gridpoint in the model (at all vertical levels) for each time-step. The length of a time-step is determinined by the model resolution, the mathematical methods employed to solve the equations, and the available computer power. The current time-step's gridpoint solutions become the "initial condition" for the next time-step. In this way, the model can time-step its way an arbitrary amount of time into the future. Of course, error inevitably creeps in, rendering the solutions essentially useless after a certain number of time-steps.

2.3. A certain set of time-step solutions are saved.

2.3.1. A given time-step may only represent a 10-minute jump into the future. Practical limitations on computer storage space prohibit "saving" each time-step's complete solution in digital form in the computer's memory. For the global-scale, operational weather models, there is no demand for complete solutions saved at such a high frequency. Instead, a set of regularly-spaced time-step complete solutions are saved -- usually once every 12 hours for the operational weather models. (For the hypothetical 10-minute time-steps, this means that one out of every 72 time-steps are saved to disk.) Partial solutions (i.e. containing only a few gridpoints and/or variables) are often saved at a higher frequency.

2.3.2. An array of graphical and tabular products are then derived from the saved time-steps. For the operational weather models run by NOAA and WMO, the graphical output resembles the surface and UA charts we have analyzed up 'til now, without the data plots, which are observational data. The tabular output often contain forecasts of specific meteorological quantities at specific locations -- such as the vertical velocity at 700 millibars above Portsmouth, New Hampshire, at 6-hour intervals over the next 48 hours.

2.4. Two models that are currently used operationally by NOAA are the Nested Grid Model (NGM) (late 1980's) and the Eta model (1990's). (There are others, but we will focus on these two.) For North America and the adjacent Pacific and Atlantic waters, the NGM has a horizontal resolution of 65 kilometers (1/2 of a degree of latitude), and over the rest of the northern hemisphere, it has a broader resolution (thus the name nested grid). The NGM represents a significant improvement over the earlier Limited Fine Mesh (LFM), which had a broader resolution and didn't cover the entire northern hemisphere. The Eta model represents additional improvments over the NGM.

3.1. The NGM and the Eta (both are now run operationally) create graphical output for points in time 0, 12, 24, 36, and 48 hours after the initialization point. These graphics are extremely useful tools for forecasters, and often are a significant improvement over continuity and other forms of non-numerical prognoses. Graphical Eta-model output from the latest model run can be viewed here. Text-format NGM "model output statistics" (MOS) for a user-selected location can be viewed here.

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A computer model should be used as a tool, not a crutch.
It is very bad practice to blindly forecast for the model's solution. Be sure you have sound meteorological reasons for your forecast, and can honestly justify your decisions to yourself and other meteorologists.

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3.2. Some of the graphics output by the model are:

3.2.1. Surface isobars and 1000-500 millibar thickness. We are already familiar with surface isobars, but 1000-500 millibar thickness is new. Thickness is simply the vertical distance, in linear distance units such as meters, between the 1000-millibar (or the Earth's surface, if the surface pressure is less than 1000 millibars) and the 500-millibar surfaces.

3.2.1.1. Larger thicknesses are associated lower density air, and smaller thicknesses are associated with higher density air. Put another way (and ignoring the role of water vapor in the density of air), larger thicknesses are associated with warmer air, and smaller thicknesses are associated with colder air.

3.2.1.2. Because thickness is a measure of the mean density of the air between 1000 and 500 millibars, it is very useful for locating transition zones and airmasses. The presence of closely packed thickness lines in a pressure trough is a good indicator of a frontal position.

3.2.1.3. Another use for this is the location 5460-meter thickness line -- which often represents the dividing line between rain and snow in the winter.

3.2.2. 700-millibar heights and relative humidity. We already know what both of these represent. Use the 700-mb relative humidity to forecast mid-level cloud cover:

.lt. 50 %	Insignificant cloudiness.
50 - 70 %	Scattered cloudiness.
70 - 90 %	Broken cloudiness.
.gt. 90 %	Overcast cloudiness.

Use the height contours to forecast mid-level wind direction.

3.2.3. Precipitation/700-millibar vertical velocity. This is the model's projection of precipitation areas (hatched) as well the direction and amplitude of vertical motion in the middle troposphere.

3.2.4. 500-millibar heights and vorticity. We already know what the 500-mb heights are, but vorticity is new.

3.2.4.1. Vorticity (also known as the curl of the velocity field) is a mathematically-derived quantity that describes the "spin" of a parcel of air. Positive vorticity indicates cyclonic spin (counter-clockwise in the northern hemisphere), and negative vorticity indicates anti-cyclonic spin (clockwise in the northern hemisphere).

3.2.4.2. Parcels with positive vorticity will move upward, and parcels with negative vorticity will move downward. (Remember the right-hand rule.)

3.1.4.3. The model graphics should be analyzed for Vorticity advection. (Use the 500-mb heights, the implied geostrophic flow, and the vorticity isopleths.) Regions of Positive Vorticity Advection (PVA) are undergoing an upward acceleration, and regions of Negative Vorticity Advection (NVA) are undergoing a downward acceleration

LAB:

Divide up into groups of three -- these should be the same groups you were in last week. Using no more than one hour of time, each group should jointly:

1. Review the pre-analyzed UA package, surface charts, and skew-t, as well as the available GOES photographs and radar summaries.

2. Using continuity, basic meteorological principles and the ETA model output, forecast the following weather elements for Portsmouth, New Hampshire for (a) 12 hours after the latest chart valid time and (b) 24 hours after the latest chart valid time:

2.1. Surface wind speed [knots] and direction [degrees true].

2.2. Surface air temperature [degrees C] and sea-level pressure [millibars].

2.3. Surface prevailing visibility (0 to 1 mile/1 to 3 miles/3 to 7 miles/greater than 7 miles).

2.4. Whether or not precipitation will be occurring.

2.5. The amount (none, partly cloudly, mostly cloudy, or overcast) and type (cumuliform or stratiform) of clouds that will be seen by the weather observer on the ground.

HOMEWORK:

1. Read Lutgens and Tarbuck chapter 14 and skim chapter 15.

2. Read the AGU Position Statement on Climate Change and Greenhouse Gases, and skim Climate Change and Greenhouse Gases (EOS, 1999).

3. Study notes and labs from meetings 1 through 9.