Lecture Notes on Weather Forecasting and Analysis | CLIM 2000 | Study notes Meteorology

CLIM2000 (The Atmosphere and Weather)

Lecture Notes

Instructor: Dr. Esmaiel Malek (Associate Professor)

Chapter Thirteen: Weather Forecasting and Analysis

Knowing the weather in the future is vital to many human activities.

A summer forecast of extended heavy rain and cool weather:

→ Construction under protective cover,

→ Advertising of umbrellas rather than bathing suits,

→ Alert farmer to harvest their crops before their fields become too soggy,

→ To support the heavy machinery for the job,

→ Flooding.

A forecast calling for extended high temperature with low humidity:

→ Ice cream makers prepare for record sales,

→ Dairy farmers anticipate a decrease in milk and egg production,

→ Fire danger in parched timber and grassland.

Why is weather forecasting imperfect?

We’ve all had careful plans upset by a bad weather forecast and are understandably

quick to find fault when actual conditions depart from the forecast.

So why are forecasts often so far from correct?

After all, with powerful computers, satellites, weather radar, and global

communication networks, it seems as if making a good forecast ought to be easy.

But, however, as much as the public might think so, this is definitely not the case - in

fact, accurate weather forecasting is extremely difficult. Why?

Imagine that you want to forecast tomorrow’s temperatures (T), and think about

just a few of factors that you must consider.

1- First, the temperature structure of the atmosphere depends in part on:

- Absorption and emission of radiation (shortwave and longwave), which itself

depends on the vertical and horizontal distribution of atmospheric gases, clouds,

and so on.

So, to compute the temperature at a point in the air, you need to begin with detailed

information about the composition of the atmosphere in three dimensions.

2- The constantly changing atmospheric water phases (ice, liquid, and vapor) also

affect the temperature by removing or adding latent heat to the air.

This means, we need to keep track of that, as well as radiation transfer. But, these

phase changes are influenced by vertical and horizontal motions in the atmosphere

close to the ground and aloft.

3- Another consideration is the continual interaction among the weather elements.

So, even though you’re only interested in temperature, you can’t pretend the winds

are unchangeable, but instead you are forced into the business of forecasting

atmospheric motion. Unfortunately, this is very difficult because the atmosphere is

dynamically unstable.

By this, we mean that small disturbances often grow into large features and

eventually dominate the field of motion. So, small and large scales should be

considered too.

Obviously, weather forecasting involves a set of interlocking problems, each difficult

to solve in isolation, let alone in combination.

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CLIM2000 (The Atmosphere and Weather) Lecture Notes Instructor: Dr. Esmaiel Malek (Associate Professor) Chapter Thirteen: Weather Forecasting and Analysis Knowing the weather in the future is vital to many human activities. A summer forecast of extended heavy rain and cool weather: → Construction under protective cover, → Advertising of umbrellas rather than bathing suits, → Alert farmer to harvest their crops before their fields become too soggy, → To support the heavy machinery for the job, → Flooding. A forecast calling for extended high temperature with low humidity: → Ice cream makers prepare for record sales, → Dairy farmers anticipate a decrease in milk and egg production, → Fire danger in parched timber and grassland. Why is weather forecasting imperfect? We’ve all had careful plans upset by a bad weather forecast and are understandably quick to find fault when actual conditions depart from the forecast. So why are forecasts often so far from correct? After all, with powerful computers, satellites, weather radar, and global communication networks, it seems as if making a good forecast ought to be easy. But, however, as much as the public might think so, this is definitely not the case - in fact, accurate weather forecasting is extremely difficult. Why? Imagine that you want to forecast tomorrow’s temperatures (T), and think about just a few of factors that you must consider. 1- First, the temperature structure of the atmosphere depends in part on:

Absorption and emission of radiation (shortwave and longwave), which itself depends on the vertical and horizontal distribution of atmospheric gases, clouds, and so on. So, to compute the temperature at a point in the air, you need to begin with detailed information about the composition of the atmosphere in three dimensions. 2- The constantly changing atmospheric water phases (ice, liquid, and vapor) also affect the temperature by removing or adding latent heat to the air. This means, we need to keep track of that, as well as radiation transfer. But, these phase changes are influenced by vertical and horizontal motions in the atmosphere close to the ground and aloft. 3- Another consideration is the continual interaction among the weather elements. So, even though you’re only interested in temperature, you can’t pretend the winds are unchangeable, but instead you are forced into the business of forecasting atmospheric motion. Unfortunately, this is very difficult because the atmosphere is dynamically unstable. By this, we mean that small disturbances often grow into large features and eventually dominate the field of motion. So, small and large scales should be considered too. Obviously, weather forecasting involves a set of interlocking problems, each difficult to solve in isolation, let alone in combination.

Weather forecasting in the U.S. began in the 1870s, by the National Weather Service (NWS). NWS was renamed into the National Weather Bureau. The National Oceanic and Atmospheric Administration (NOAA) was established in 1970 to include the reverted NWS and other environmental agencies. Forecasting Methods There is no single “correct” way to forecast the weather, depending on the length of forecast, the type information desired, and how much is known about the current state of the atmosphere. One can even attempt a forecast in the absence of any data about the current weather, provided that long-term information is available. Forecasting approaches:

Climatological forecasts,
Persistence forecasts,
Analog approach,
Numerical weather forecasting.
Climatological forecasts: They depend on the long-term averages (year-to-year) variability in weather conditions for the forecast day. For instance, a forecast of hot, muggy conditions with a chance of afternoon thunderstorms in Orlando, Florida, in mid-August has a reasonably good chance of proving to be correct. Such prognoses based on long-term averages are known as climatological forecasts.
Persistence forecasts: They rely completely on current conditions with no reference to climatology. A special case of persistence forecasting is used by all of us in everyday life. When we see clear skies and leave the umbrella behind, we’re betting that the prevailing conditions will continue and are making a short-term forecast on that basis (it might work for a little while, but will eventually fail). In other words, one could assume persistence in a trend to make a guess regarding changes in weather.
Analog approach: In this method, one tries to recognize similarities between current conditions and similar well-established patterns from before. Some subjective (depending on the forecaster’s expertise) and objective (depending on statistical relations) matters should be considered in this approach.
Numerical weather forecasting: This dominant method forecasts the weather based on computer programs that attempt to mimic the actual behavior of the atmosphere. That is, numerical weather models explicitly compute the evolution of wind, pressure, temperature, and other elements over time. By examining the output for a given point in time, one obtains a depiction of a three- dimensional state of the atmosphere for that moment. The numerical models typically used in weather forecasting are very large and can only be run on the most powerful computers, so-called supercomputers.

A short discussion about numerical forecast models is presented below:

If such “sub-scale” phenomena are to be considered, an error-prone process called “parameterization” is required.
Obviously, one wants high resolution so that small-scale processes and phenomena can be modeled and appear in the forecast, but this can come only at the cost of more computation. Roughly speaking, doubling the resolution leads to eight times the computation.
The resolution issue applies to the vertical coordinates, as well as the horizontal coordinates.
- The horizontal resolution of the Global Spectral Model is about 1o^ in latitude and longitude (about 60 miles). It has 28 levels in the vertical, ranging from the surface to the 2.7 mb level.
It has 8 levels below 800 mb, with increasing spacing to lower pressure (higher altitudes).
Operational versions of the Eta [the Greek letter Η ( η )] model have been run with increasing resolution since its inception, ranging from 80 km initially to 29 km, with 50 levels in the vertical, at the present time.
- The Nested Grid Model (NGM) has 16 layers and two grids. The smaller inner grid, centered over the U.S. and Canada, has a resolution of about 80 km. It lies completely within a larger, coarser outer grid that extends through the domain of much of the Northern Hemisphere (it has the advantage of confining most of the computation to the region of interest). B- Horizontal representation: Another major difference among the models is the horizontal representation. Many models adopt a grid representation , in which the domain is subdivided into a lattice of grid points. C- Physical processes:
Numerical models’ physics package includes: i- Atmospheric processes (such as condensation), ii- Atmosphere-surface interaction (such as friction between the atmosphere and ground), iii- Purely surface processes (such as soil moisture or depth of snow). Parameterization (radiation; convection, clouds, and precipitation; and surface properties and processes) is heavily used in the physics package. Different models not only include different processes, but also employ different parameterizations for the same processes. The governing equations are solved only at the grid points. The finer the grid, the higher is the model’s resolution. Implicit in this is the idea that the grid captures horizontal variation in the atmosphere and that intermediate values can be inferred knowing values at nearby grid nodes. In spectral representation , variables are represented as a series of “waves” in space, each having a characteristic wavelength (Global Spectral Model uses 126 waves). Advantages of the Spectral models are: I- Horizontal resolution is determined by the smallest of the “harmonics” or wavelengths present, so there is no escaping the problem of how to represent sub- scale processes.

II- Not all of the variables can be represented in spectral terms (the advective quantities such as heat and moisture, are treated this way). Other variables, such as radiation, must be computed on a point-by-point basis. III- The spectral representation applies only to the horizontal

Spectral models is layered in the vertical. Types of forecasts
Quantitative forecasts: Amount of the forecasted variable is specified - for instance: “3 inches of rain is expected.”
Qualitative forecasts: Provide only a categorical value for the predicted variable
- examples include: “rain / no rain”, “hurricane / no hurricane”, “above / below normal”, “cloudy / partly cloudy / mostly cloudy.”
Probability forecasts: Chance of some event is stated - for instance: Examples include: probability-of- precipitation (PoP) as “the rain chance today is 70 percent”, “there is a 60 percent chance of afternoon showers.” How is the weather data acquired? The start point for almost all weather forecasting is information about the current state of the atmosphere. To know the future, we begin with information about the present. The World Meteorological Organization (WMO), under the auspices of the United Nations, oversees the collection of the weather data across the globe from 179 nations. The WMO collects data from about:
10,000 land stations,
7,000 ship stations,
300 moored and drifting buoys, Land, ship, and buoy stations have automated weather sensors. Several weather satellites, a continuous basis from instruments aboard wide-bodied commercial aircrafts.
Weather radar, and
rockets. How is the weather data disseminated?
The data from all these sources are sent to the three World Meteorological Centers (WMC) at Washington, D.C .; Moscow, Russia ; and Melbourne, Australia , which in turn disseminate the data to all members of the WMO.
The member nations of the WMO maintain their own meteorological agencies that obtain and process the data and issue regional and nation forecasts.
In the U.S., the National Center for Environmental Prediction (NCEP) of the Weather Service performs these tasks, while in Canada they are handled by the Canadian Meteorological Center of the Atmospheric Environment Service (AES).
Of the approximately 10,000 relatively dense networks of surface observations in the U.S.,
About 120 are National Weather Service Offices,
The rest are Federal Aviation Administration (FAA) airport sites,
The Canadian AES operates about 270 surface stations.

2- Prediction phase 3- Post-processing phase 1- Analysis phase: In this step, three-dimensional observations are used to supply values corresponding to the starting (“current”) state of the atmosphere for all variables carried in the model. Unfortunately, the network of weather stations and radiosonde launches is highly irregular and doesn’t come close to providing even coverage. This step converts those irregular observations into “uniform” initial values. Though only a preparatory step, this is a difficult task. There are millions of data values from a variety of sources (satellites, ships, and so on) representing various moments in time. None of the measurements is completely free of error, and many are subject to large error. It is necessary to remove as much error as possible, while at the same time producing fields that are self-consistent (for instance, assigned wind velocities must satisfy the conservation of mass in the resulting wind field). 2- Prediction phase: Fundamentally, the job of a numerical model is to solve the governing equations as:

the equation of motion,
the equation of continuity,
the equation of energy, etc. Beginning with values delivered by the analysis phase, the model uses the governing equations to obtain new values a few minutes into the future. The process is then repeated, using the output from the first step as input for the next set of calculations. This process is then performed over and over as many times as necessary to reach the end of the forecast period (24, 48, or whatever hours). This is called the prediction phase of the model run. This results in many billions of calculations for each time step, despite the fact that there are just a handful of fundamental atmospheric variables (temperature, pressure, wind velocity vector, density and moisture). 3- Post-processing phase: The weather conditions forecasted by the model at regular intervals (for example every 12 hours) are presented in the form of mapping. The following series of maps are depicted for the forecast distributions: a. Sea level pressure and 1000 to 500 mb thicknesses, b. 850 mb heights and temperature, c. 700 mb heights and vertical velocities (ascent and descent), d. 500 mb heights and absolute vorticity values, e. Precipitation amounts. A 24-h precipitation forecast from three numerical models, along with the final (manual) and observed rainfall for June 2, 1992, is shown below. Regardless of that forecast’s lack of success, the model output is coupled with other information in producing official forecasts. The old rules must be constantly reevaluated in light of new model behavior.

Forecasts for a number of secondary variables, such as: maximum and minimum temperature, dew point, wind conditions, and probability of precipitation, are produced (using the statistical relationships between model output and observed surface conditions from the past). The output products are called model output statistics (MOS) and are designed to capture the effect of topography and other factors that influence local weather conditions. Numerical models have only limited ability to represent processes occurring near the surface, and they provide a rather generalized picture of the atmosphere. How good are today’s forecasts? There’s no single answer to this question. It depends very highly on:

the variable in question,
the forecast lead time,
the model used,
the place and season. For example, there’s no doubt that temperature, wind, and pressure distributions are forecasted far better than precipitation. Some statistical terms: Bias: The average error or bias is mostly defined as the difference between the average forecast value and the average observed value. Example: Given: The following errors occurred in daily temperature (in o^ F) forecast over three days: -5, 4, and 0.0. Find: The bias. Solution: (-5+4+0.0) / 3 = -0.33 o^ F. Mean absolute error (MAE): A mathematical equivalent definition of bias is simply the mean absolute error. In the other words, for each forecast, we find the absolute (i.e., disregard the sign of individual error) departure from observed and compute the average of those errors. Compute the MAE in the previous example. MAE = (5 + 4 + 0.00) / 3 = 3 o^ F. Root-mean-square error (RMSE): RMSE is just the square root of average squared error (which is calculated by first summing the square of each individual error in the series, then dividing by the total number of observations, then taking the square root). Compute the RMSE in the previous example. RMSE = {[(-5) 2 + (4) 2 + (0.0) 2 ] / 3}0.5^ = (13.67) 0.5^ = 3.7 o^ F. Measures of forecast accuracy and skill: Accuracy = Number of correct forecasts / total number of forecasts. Example: In Vancouver, Canada, the skies are cloudy 327 days each year, the average; then the accuracy is 327 / 365 = 90%. What is forecast skill (equitable threat score)? Skill measures forecast improvement above the climate average. Hypothetical distributions of observed and forecasted precipitation are illustrated below:

Weather maps and images: Although computers play a critical role in the analysis of weather, ultimately, the meteorologist applies her or his knowledge to produce the forecast that is issued to the general public. A typical surface weather map is illustrated below: The 850 mb weather map is depicted below (typically found about 1.5 km (1 mi) above equivalent sea level.) The 700 mb weather map is shown below. The 500 mb weather maps are depicted below (with an omega H.) The 300-mb map along the lines of equal wind velocity (isotachs) contoured at 20- knot (1 knot = 1.84 km / h) intervals. Shaded areas have winds in excess of 70 knots. Open areas within the shaded regions have winds greater than 110 knots. A radar composite map is revealed below. Thermodynamic diagrams The maps and images previously described provide two-dimensional views of atmospheric conditions, but they fail to provide detailed vertical information. Vertical profiles of temperature and dew point observed by radiosondes are plotted on thermodynamic diagrams (also called pseudo-adiabatic charts or Stuve thermodynamic diagrams). An example of sounding on a Stuve diagram is depicted below. What are lifted and K indices? Lifted index: The lifted index combines the average humidity in the lowest kilometer of the atmosphere, the predicted maximum temperature for the day, and the temperature at the 500 mb level, into a single number. The magnitude and sign of the values together indicate the potential for thunderstorms. For instance, negative values indicate sufficient water vapor and instability to trigger thunderstorms. More specifically, lifted index values between -2 and -6 indicate a high potential for thunderstorms, whereas, less than -6 suggests a threat of severe thunderstorms. K-index: The K-index uses values of temperature and dew point at the surface and the 850, 700, and 500 mb levels to translate the probability of heavy rains and thunderstorms. In general, K-values less than 15 indicate no potential for thunderstorms; values above 40 suggest that they are highly likely.

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