February 22, 2008
Numerical Weather Forecasting (Chapter 9)
n I will present a quick overview of how weather forecasting is done today and why forecast accuracy decreases the further the forecast moves into the future. Much of this is found on the supplemental reading page, labeled “Numerical Weather Forecasting” on the assigned reading link for today.
n Go over what is shown in first part of the supplemental reading
o We rely on computer forecast models
o Complexity required of the computer models
o Draw a simple block diagram for numerical forecasting
n Show (using figures in the supplemental reading) how the atmospheric state is specified in numerical models with grid boxes
n Continue on with supplemental reading page up to errors in the forecast
n Why is it so difficult to make exact forecasts?
o Model is not perfect. Some equations are only approximations. Also have model representation problems since some processes in the atmosphere happen at scales smaller than a grid box.
o Initial conditions are not perfect. There are errors in measurements. In addition, not all areas of the Earth have observations available (Oceans, remote areas). This reason is discussed more fully in the reading.
§ Go over figure of what happens to model forecasts over time
n Read over material under section “Dilemma for forecasters”
n The atmosphere is a chaotic system …
o Often a chaotic system is entirely predictable in that the equations governing how the system will change with time are well known, thus if you know the initial state exactly, you can in theory predict the future exactly
o But a chaotic system is very sensitive to knowing the initial state exactly. Slight variations in the initial state can lead to wildly different forecasts, especially the longer you go out in time.
n Read through the analogy at the bottom of the page.
o Thus there is a fundamental limit to how accurately weather can be predicted in the future. Current forecasts are generally good out to 3 days, still decent out to 5 or 6 days, but degrade very quickly beyond that.
n Ensemble forecasting provides a method to test the confidence in model forecasting.
o In ensemble forecasting, several forecasts are made for a given model, each beginning with slightly different initial conditions. The difference in initial conditions for each forecast are based on the expected uncertainty in the measurement and processing of the initial data.
o The level of confidence for a specific forecast time is based on how well the individual models agree (or disagree) with each other.
o Show link (on lecture summary page) to a “spaghetti diagram” of ensemble members predictions of the 500 mb pattern with time. You will see that the individual forecasts are quite similar for short forecasts, but spread apart significantly for longer range forecasts.
Temperature, temperature scales (Chapter 2)
n Temperature is a measure of the average speed of the atoms and molecules in a substance. The higher the temperature, the faster they move.
o For solids and liquids, it is a measure of the average vibrational speed of individual molecules, since molecules are chemically bonded together.
o For gases, it is the average speed at which individual gas molecules are moving. Keep in mind the Kinetic model for gases, where we consider each molecule as a tiny sphere. Individual molecules (spheres) are not chemically bonded together and move about randomly with frequent collisions between molecules (spheres).
§ At 0° C, average speed of individual gas molecules is ~1100 miles per hour. This is called thermal motion or kinetic motion. We sense this motion to say that air “feels” warm or cold.
§ Kinetic motion is not wind. In kinetic motion, individual molecules move about in random directions. Wind is ordered movement of the fluid (air). If we put an imaginary box around some air and all the molecules in the box move together in a certain direction, that is wind. If there is no wind the molecules in the box do not move together in a specific direction. Thermal or kinetic motion is always happening whether there is a wind or not. The average speed of this motion is what determines air temperature.
n
The three most common temperature scales are
Fahrenheit (°F), Celsius (°C), and Kelvin (K).
Most of the world uses the Celsius scale. In the
o Formula for converting from Fahrenheit to Celsius
§ °C = (5/9) x (°F - 32°) = 1.8 x (°F - 32°)
o Formula for converting from Celsius to Fahrenheit
§ °F = [(9/5) x (°C)] + 32° = [1.8 x °C] + 32°
o Formula for converting from Celsius to Kelvin
§ K = °C + 273
o Boiling point of water at sea level is 212° F = 100° C = 373 K
o Freezing point of water at sea level is 32° F = 0° C = 273 K
o 0 K is called absolute zero, since at that temperature, the molecules of a substance have no thermal motion. As temperature increases, thermal motion increases.
Phase Changes of Water, Latent heat
n In general, the three phases of matter are solid, liquid, and gas. We will specifically talk about the substance water. Water commonly changes phases in the environment of Earth. For water to change phase, energy must be either added to or removed from the water. This exchange of energy is critical in understanding how the Earth’s climate works and how and why clouds, thunderstorms, and hurricanes form. Thus, we will spend enough time on this subject for you to understand the physics of phase changes or water.
n In the gaseous state, water is called water vapor. Water vapor is an invisible gas. If you are able to see something (e.g., clouds, steam, etc.), you are seeing tiny droplets of liquid water suspended in the air, not water vapor. Note that figure 2.3 in the textbook is very misleading because it makes it seem that water vapor is visible and actually looks like a cloud.
n Water in the gas phase (water vapor) contains more internal energy per gram of water than water in the liquid or solid phase. Water in the liquid phase (often just called water) contains more internal energy per gram of water than water in the solid phase (ice).
o Draw a diagram to show this and point out:
§ To go from a lower energy phase to a higher energy phase, energy needs to be added to the water
§ To go from a higher energy phase to a lower energy phase, energy must be removed from the water
n Latent Heat is the energy added to or removed from water as it changes phases … there is no measureable change in the temperature of the water. Latent literally means “hidden” in that even though energy was added to or removed from water, there is no way to measure (or sense) this using a thermometer.
n Sensible Heat is the energy added to or removed from water that results in a temperature change of the water, but no phase change. Sensible literally refers to a change that can be easily sensed using a thermometer.
n The calorie is a unit for measuring energy. We will use it in this discussion.
o One calorie is equal to the amount of energy required to raise the temperature of one gram of water by 1° C.
o In dietary science 1 Calorie = 1000 calories. In relation to the food, Calories give the maximum amount of energy that your body can extract by breaking down the food, so it is a measure of the energy content of food.
n Draw a diagram showing the amount of energy involved in moving from one gram of ice at a temperature of -100° C to one gram of water vapor at a temperature of 100° C and back again. We will come to the following important conclusions:
o There is a lot of energy involved in phase changes of water, especially phase changes between liquid and gas.
o For water to evaporate (liquid à gas), energy must be added to the water. For climate and weather processes, this energy is supplied by the surrounding environment (where the water is evaporating), thus the surrounding environment gives up some of its energy and cools (temperature of surrounding environment goes down).
§ Example: evaporation of sweat cools the body
o For water to condense (gas à liquid), energy must be removed from the water. For climate and weather processes, this energy must be taken up by the surrounding environment (where water is condensing), thus the surrounding environment gains energy and warms (temperature of the surrounding environment goes up)
§ Example: the formation of clouds heats (or warms) the air