#### Reflectivity

The reflectivity (Z) is a measure of the radar cross-section of targets that can be detected by weather radar, comparable to the effective backscatter area of a reconnaissance radar. It is the power reflected by hydrometeors (water drops, snow crystals, hail, and sleet grains). Reflectivity is defined as the total reflecting area of small particles per cubic meter with a dielectric constant greater than zero. This value is proportional to the sixth power of the diameter of an object with a spherical surface. Since each raindrop or snowflake has a different diameter, it is not possible to multiply the value by a number of objects, so the reflectivity is the sum of all individual objects in a space of one cubic meter, taking into account a model of the distribution of the different drop sizes:

mit

N0 = shape parameter (mm-7-µ·m3)
D = diameter of the drop (mm)
Λ = is the slope of the exponential (mm-1)(1)

The reflectivity Z depends on the size and number of raindrops per volume and has the unit of measurement mm⁶·m⁻³ and is proportional to the energy that is scattered back to the antenna by all scattering particles in the resolution cell. If the droplets are not spherical, D is the volume equivalent spherical diameter.

##### Reflectivity-Rain Rate Relationship

The reflectivity measured by the radar must now be put into relation with the amount of precipitation arriving on the ground. The rain rate R depends on the number of raindrops in the measured volume and is also a function of the fall velocity v(D), which in turn depends on the drop size. The size of the raindrops is proportional to D3:

However, since the energy received by the antenna depends on many factors, reflectivity was specially defined for meteorological targets by combining all other influences into only one factor and one exponent. The reflectivity now only depends on the properties of the targets. When it rains, the more and the larger the raindrops in the air, the greater the reflectivity. It is usually given in the logarithmic unit dBZ, where dB is the usual abbreviation for decibel and Z stands for reflectivity.

Reflectivities (Z) or their logarithmic values (dBZ) can be converted into precipitation rates (R, in [mm/h]) using the following relationship:

By long-term observations a large number of different values for a and b were determined meanwhile. These values are matched for each radar station and (for mobile devices: for each location) and are recorded in a table.

• a is 300 for rain in summer and 200 in winter and 1800 for snow
• b is for rain in summer 1.5 and in winter 1.6 and for snow 2.2

Depending on the radar configuration and the particular weather situation, several ambiguities are possible. For the quantitative analysis of the precipitation intensity, however, further comparative measurements must be used.

##### Comparative Reflectivity

Radar in recent years has become an important tool for the measurement of precipitation and the detection of hazardous weather conditions. Storms, hurricanes etc., develop by the transfer of heat energy from the ground or warm seas into the atmosphere. As warm moist air rises, the water vapor condenses to form cloud and releases the latent heat energy.

A storm can be regarded as a living entity; it grows, reaches a peak, then decays and fades away. It is not a stable object which moves with the wind. The weather radar therefore needs to scan the sky frequently enough to match the rate of change of the weather patterns.

For rainfall measurements an update rate of 15 minutes is sufficient and does not generate too vast a volume of data over 24 hour period, while for tracking hazardous conditions every 5 minutes is preferred.

Weather radar are required to detect and measure the rain intensity. They must be accurately calibrated and have a wide dynamic range (60 to 100 dBs or more) to cope with light rain at long-range and heavy rain near to the radar site. Radar echoes from weather phenomena are unlike those from aircraft, birds or surface clutter, which tend to be individual or group of echoes. Echoes from precipitation take the form of a very large number of scatters per unit volume and these particles can take on a variety of forms, including water droplets, ice crystals, hail, snow and mixtures of the above.

For this reason, and the variation in drop size distribution, there is no fixed relationship between precipitation rate and the radar echo.

 Case A This shows some light (non-precipitating cloud) from whitch the density of the returns will be relatively shallow. Case B This case depicts a cloud formation with some precipitation (perhaps light rain or drizzle for example). Considerably more echoes can be expected from precipitating weather than from non-precipitating weather. Case C This case shows heavy cloud with large quantities of rain held in it. This might be for example a heavy thunderstorm. The density of this formation will be very high and hence the returns will be quite intense (as shown).

Table 1: comparison of the strength of the returns against the possible weather

Based upon experience and study, under specific transmission frequencies, a comparison chart may be developed to allow the comparison of the strength and reflectivity of the returns against the possible weather (or object) it is from.

One principle however that is important to note is that the “levels” of the return expected from different objects is more a rough guide (or best guess) than a precise definitive table.

##### High Level Weather Reflectivity Table

Notice: The level of reflectivity of the echo received from each type of weather is not shown in specific units as this will vary between transmission frequency and will most likely not be the same for any two radar sites!

Each weather radar station will hold a “look-up” table of reflections intensities which it can use to help to interpret and distinguish between different types of weather and objects based on the back-scattered echoes received at the antenna.

Reflectivity Weather /
Object Type

Most Reflective
▼▼▼▼▼▼
▼▼▼▼▼
▼▼▼▼
▼▼▼
▼▼

Least Reflective

Ground clutter
Airborne Object
Wet Hail
Rain
Wet Snow
Dry Hail
Dry Snow
Drizzle

Table 2: comparison of the reflectivity against the possible weather

All objects carry some degree of reflectivity; for weather, this varies by its intensity. Therefore, the level and power of echoes received back at the antenna can be interpreted to make an intelligent guess at the type and severity of a weather formation.

Tuning: It is stressed that the levels of reflectivity are rough estimates. Tuning of systems would often be carried out using other sensors (such as rain gauges or any other independent accurate source of weather data and parameters) to ensure optimum performance (this is done on a site by site basis!).

All types of weather and object provide some level of echoed returns. Clearly solid formations such as terrain in the line of sight or flying mechanical objects will provide the highest degree of returns.

This table breaks down comparative return types for precipitation only (clearly, there are other types of weather but these are not considered in this table).

Rainfall is most often measured using a relationship between the reflectivity factor (Z in mm⁶/m⁻³) and its precipitation intensity (R in mm / hr-1). Pre-defined reflectivity tables are held at a station and used as the basis for the initial interpretation and calculation.

The rainfall rate R can be empirically related to the reflectivity factor Z by the expression: Z = aRb
where a and b are constants and R is the rainfall rate in mm/hr. The reflectivity factor Z is dependent on the size and number of rain drops per unit volume of space and has the units of mm⁶/m⁻³. Many researchers have produced a large variety of values a and b. The value of a and b will be specific to each radar station configuration (i.e. stored in a table). A Number of ambiguities are known and possible, depending on the radar configuration and the particular meteorological situation.

 stratiform rain Z = 200·R1.6 orographic rain Z = 31·R1.71 thunder storms Z = 286·R1.37 snow Z = 2000·R²

Table 3: Typical expressions for types of precipitation

There are other forms of identifiable weather which could be interpolated by weather radar systems (although, depending on the frequency spectrum of the system, the type of equipment used, its operational goals and the software of the station, not all of these might be available.
The types of information might cover;

• Rainfall (or storm intensity), further classified in terms of its precipiation intensity against echo intensity. Rainfall is commonly classified into 6 bands (light, moderate, heavy, very heavy, intense and extreme). Rainfall rates will be quite different between stratiform cloud and convective cloud formations. The FAA, for example, have issued a classification scale as an information circular.
• Non-precipitating clouds (liquid or ice)
• Fog and freezing fog - sometimes also providing a figure for the estimated visibility.
• Clear-air-turbulence (only with certain spectrum - most effective systems which can identify clear-air-turbulence operate in the L-band!)

In the absence of further information it is generally acceptance, in mid-latitude temperature climates, to use a default value of Z = 200R1.6. Usually Z is specified in a logarithmic scale where ZdB = 10 log Z.