• Between 1950 and 1980, the various meteorology services throughout the world build weather radars to follow precipitation by its reflectivity. Initially these radars were for local use in the great centers with a limited number of angles. They were operated in real-time by the meteorologists who were to follow the echoes on cathode screens.

In the Years 1970, the various radars start to be organized in networks with a beginning of standardization. The first systems of capture of the images were developed. The number of probed angles increases what makes it possible to obtain volumes of data in three dimensions. The horizontal cuts (CAPPI) and verticals are developed. One thus studies the structure of the storms and other clouds (amongst other things by Isztar Zawadski). The groups of research multiplied throughout the world, in particular NSSL in the United States in 1964, which starts to test on the variation of the polarization of the signal radar like on the use of the effect Doppler.

• Between 1980 and 2000, the weather networks of radars spread in North America, in Europe, with the Japan and in some other countries. The conventional radars are replaced by radars being able to detect not only the intensity of precipitations but also their rate of travel (Doppler effect). In the United States, these radar installation of wavelength of 10 cm called NEXRAD or WSR-88D starts in 1988 and finishes with beginning of the year 90. With the Canada, the first Doppler radar is that of 10 centimetres to the McGill University in 1993 and the second with King City (a radar of 5 centimetres), in the north of Toronto. The Canadian Réseau of weather radars is modernized in this direction starting from 1998. The France (network ARAMIS) and the other European countries convert at the end of the years 1990 and 2000.

the fulgurating development of the Informatique makes it possible to treat the data radars in real-time to make a multitude of direct products (CAPPI, PPI, office plurality of precipitations, etc) but also of the algorithms which make it possible to locate dangerous precipitations (storms, pouring rain, gusts under the clouds, etc) and to envisage their displacement in the short run.

• After 2000, research which was carried out on the double polarization of the signal radar start to find applications practical in the detection of the type of precipitations. The France, the Canada, the United States, the Australia and others transformed some of their radars to use this concept in pre-operational mode.

Of research is in hand since 2003 to use antennas network with ordering of phase assembled in three-dimensional Radar with electronic sweeping to replace the mechanical survey in electronic sweeping, therefore faster.

Principles of the weather radar

Emission

Thus, an impulse probes a Volume atmosphere which increases with the distance to the radar like $\backslash ,\; hr^2\; \backslash \; theta^2$ (H: width of the impulse, R the distance to the radar and $\backslash \; theta$ the aperture of the beam). One sees on the image of right-hand side the volume which occupies two impulses left at times different from a radar. With typical dimensions of a beam radar, probed volume thus varies from 0,001 km ³ close to the radar, up to 1 km ³ to 200 km of this one. However, it is considered that one can solve only half of this volume, that is to say h/2 (see Compression of impulse).

Reflection

Position

$Distance\; =\; C\; \backslash \; \backslash \; frac\; \{\backslash \; Delta\; T\}\; \{2\}$ (C = Speed of light = 299 792,458 Km/s).

The maximum distance that one can probe without ambiguity depends on the $\backslash ,\; \backslash \; Delta\; t$ used between two subsequent impulses. Indeed, the position of any return which arrives of a first impulse, After left one second impulse, will be badly interpreted like ghost of the latter. In general, one uses a listening time of about 1 Milliseconde, that is to say thousand times the duration of the impulse. That allows a useful maximum range of approximately 250 km.

In addition to the distance, one can calculate the height above the ground where the targets are. That is calculated by knowing the angle of elevation in the radar and the curve of the Ground. It is also necessary to take account of the variation of the Densité of the layers of the atmosphere. Indeed, the beam radar is not propagated in straight line as in the vacuum but follows a curved trajectory because of the change of the Index of refraction with altitude.

Strategy of survey

Because of the curve of the Earth and change of index of refraction of the air from which we come to speak, the survey will not be able “to see” under a certain height which depends on the distance to the radar and the minimal angle used. It will not be able “to also see” more close to the radar that the trajectory of the maximum angle used. The figure on the left watch the height versus the distance of a series of angles typically used by a Canadian weather radar. They go from 0,3 to 25 degrees.

Types of data

Reflectivity (in Decibel or dBZ)

The echo of return reflected by the targets is also analyzed for its intensity in order to establish the rate of precipitation in probed volume. One uses a wavelength radar between 1 and 10 cm so that the return acts according to the law of Rayleigh, i.e. the intensity of return is proportional to a power of the diameter of the targets in as much as those (rain, flakes, etc) are much smaller than the wavelength of the beam radar. It is what one names the Réflectivité (Z). This intensity varies in fact as the 6^e power of the diameter of the targets of diameter D (the sixth moment) multiplied by the Distribution of the drops of rain (NR of Marshall-Micrometer caliper ) what gives a function Gamma truncated:

$Z\; =\; \backslash \; int\_\; \{0\}\; ^\; \{Dmax\}\; N\_0\; e^\; \{-\; \backslash \; Lambda\; D\}\; D^6dD$

This Z is in $mm^6\; m^\; \{-\; 3\}$, which gives rather unusual units. Moreover, this formula does not take account of the nature of the target. To obtain the equivalent REFLECTIVITY (Z_e) which sees the radar, one must standardize and multiply by the square of the permittivity (K) of the target to take account of its effectiveness to reflect.

$Z\_e\; =\; |K|^2\; \backslash \; left\; (\backslash \; frac\; \{Z\}\; \{Z\_0\}\; \backslash \; right)\; =\; \backslash \; left\; (\backslash \; frac$

Speed Doppler

Pulsated radar

$O\; \backslash \; serious\; \{U\}:\; \backslash \; quad\; \backslash \; begin\; \{boxes\}\; X\; =\; distance\; \backslash \; radar-target\; \backslash \; \backslash \; \backslash \; lambda\; =\; length\; \backslash \; of\; wave\; \backslash \; \backslash \; \backslash \; Delta\; T\; =\; time\; \backslash \; between\; \backslash \; two\; \backslash \; impulses\; \backslash \; end\; \{boxes\}.$

The intensity of a subsequent impulse ghost of the same probed volume but where the targets slightly moved is given by:

$I\; =\; I\_0\; sin\; \backslash \; left\; (\backslash \; frac\; \{4\; \backslash \; pi\; (x\_0\; +\; v\; \backslash \; Delta\; T)\}\{\backslash \; lambda\}\; \backslash \; right)\; =\; I\_0\; sin\; \backslash \; left\; (\backslash \; phi\_0\; +\; \backslash \; Delta\; \backslash \; phi\; \backslash \; right)$

Thus $\backslash \; Delta\; \backslash \; phi\; =\; \backslash \; left\; (\backslash \; frac\; \{4\; \backslash \; pi\; v\; \backslash \; Delta\; T\}\; \{\backslash \; lambda\}\; \backslash \; right)$

$v\; =\; speed\; \backslash \; of\; the\; \backslash \; target\; \backslash \; =\; \backslash \; frac\; \{\backslash \; lambda\; \backslash \; Delta\; \backslash \; phi\}\; \{4\; \backslash \; pi\; \backslash \; Delta\; T\}$

Doppler dilemma

Let us look at maximum speed now that one can measure without ambiguity. Like the angle $\backslash ,\; \backslash \; phi$ can vary only between - $\backslash \; pi$ and +$\backslash \; pi$, one cannot note an high speed with:

$Vitesse\_\; \{max\}\; =\; \backslash \; pm\; \backslash \; frac\; \{\backslash \; lambda\}\; \{4\; \backslash \; Delta\; T\}$

It is what is called the speed of Nyquist. To obtain a better determination the speed of the targets, it is necessary to send very brought closer impulses, therefore with $\backslash ,\; \backslash \; very\; small\; Delta\; t$. But it is also known that the range in reflectivity is

$x\; =\; \backslash \; frac\; \{C\; \backslash \; Delta\; T\}\; \{2\}$

what requires large a $\backslash \; Delta\; t$ to be sure position of the echoes returning by far without ambiguity. This Doppler dilemma thus limits the useful range of the radars which uses this effect. It is thus necessary to make a compromise which in general made that the Doppler radars have a range useful from 100 to 150 km.

Improvement

The Canadian Network of weather radars, using a wavelength of 5 cm, is equipped with this kind of radar treatment since 1999. Without the technique, one would note there a nonambiguous speed between 11 and 15 m/s for a range of 150 km. By using the technique with two rates, one obtains 48 m/s without changing the maximum range. If one wanted to change this range, the beach of rates of repetitions usable would be lower and nonambiguous maximum speed would be lower also, even with this technique.

The radars of the operational network French ARAMIS are equipped with such a diagram recently (2006). This technique makes it possible to extend the maximum range to more than 200 km while having a nonambiguous speed of about 60 m/s (Tabary and Al 2006). In this case, one uses three rates of repetitions to extend even more the beach speeds. But still there, the dilemma exists, one does nothing but change the slope of the lines on the graph.

Interpretation

If one remembers that the radar turns on 360 degrees, he will thus see all the components of projection the speed of these drops on his axis of aiming. The whole speeds on a full rotation will take the values of a cosine. Extremely of that, one can thus deduce the direction and the speed of precipitations (+ that of the wind).

One however neglected the falling speed of the drops but it is weak for the angles of elevation under 3 degrees inside 150 km in the radar what are generally the required angles. A glance more in height must hold account of it.

Double polarization

See also: Polarization (optical),

In general, the majority of the hydrometeors have a larger axis according to the horizontal one (e.g. the drops of rain become oblates while falling because of resistance of the air). The dipolar axis of the water molecules thus tends to be aligned in this direction and the beam radar will be generally horizontally polarized to benefit from a maximum return.

If one sends at the same time an impulse with vertical polarization and another with horizontal polarization, one will be able to note a difference in several characteristics between these returns:

* If the targets have a form flattened as in the image opposite, while probing with two waves of which one is of vertical polarization (V) and the other horizontal one (H), one obtains to stronger intensities ghost of that having the horizontal axis. On the other hand if the orthogonal returns are equal that indicates a round target. That is called the difference of Réflectivité or the differential reflectivity ($Z\_\; \{Dr.\}$);

* the beam radar probes a more or less large volume according to the characteristics of the transmitting antenna. What cost is the addition of the waves reflected by the individual targets in volume. As the targets can change position in time the ones compared to the others, the intensity of the waves V and H remains constant only if the targets have all the same form. The report/ratio of intensity between the channels H and V returning of successive surveys is called the coefficient of correlation ($\backslash \; rho\_\; \{hv\}$) and thus gives an idea of the homogeneity or not targets in probed volume;

* the phase of the wave changes when it crosses a medium of different density. By comparing the rate of phase shift of the wave of return with the distance, the specific differential phase or $K\_\; \{dp\}$, one can evaluate the quantity of crossed matter;

* One can also compare dephasing between the returns H and V ( differential of phase or $\backslash \; phi\_\; \{dp\}$).

The radars, called to double polarization , which use this type of survey can thus obtain indications on the shape of the targets like on the mixture of forms. This can be used, in addition to the intensity of the return, for an identification direct of the type of precipitations (rain, snow, spindly, etc) thanks to a algorithm. NCAR in the United States, was one of the centers pioneers in this field with Dusan S. Zrnic and Alexandre V. Ryzhkov. NOAA puts at the test since the beginning of the years a 2000 operational radar of this type and thinks of equipping all its network from here the end with this decade. The university McGill (Montreal, Canada) also has a radar which is equipped with it and the data are used operationally by Environnement Canada. EC. has another polarized radar with King City in northern suburbs of Toronto in development mode. Finally, Weather-France could have its first polarized radars in 2008.

More details:

American radar of development

Canadian application

Principal types of produced images

All the data obtained by the survey radar are posted according to their format. Certain products are used to post several types of data whereas others are more specific.

PPI (Seen panoramic with constant angle of elevation)

See also: Plane Position Indicator

As the data probed by the radar form an angle of elevation at the same time, the first images were those of a panoramic posting of the data of each angle individually (PPI). This type of data must be interpreted by remembering that the beam radar rises above the ground as one moves away from the radar. Thus what one sees close to the radar is on much low level than than one sees to 200 km.

It results from it that a cloud with rates of rain raised to 30 km of the radar can seem to decrease or increase intensity as it moves away from the radar. In fact, as our beam is higher in the cloud at the second time, it looks at another section of this last.

A PPI is also afflicted with returns coming from the ground close to the radar. This gives very strong returns which can be badly interpreted as being strong precipitations.

USE: All types of data: reflectivity, radial speed and various fields of polarimetry.

CAPPI (Seen panoramic at constant altitude)

See also: Constant Altitude Plan Position Indicator

To mitigate the problems of the PPI, the CAPPI was developed by the Canadian researchers. They are in fact a horizontal cut through the unit the angles of elevation probed by the radar. According to the number of angles and rises in those, one can make a more or less precise cut. According to the level of our cut, it also happens that at a certain distance we do not have any more data with required altitude. What is then seen on the CAPPI, they are the data of the PPI more close to this level.

For example, on the image of the angles higher on page, the 24 angles spread out from 0,5 to 25 degrees and we can thus make a CAPPI through these data. The fatty lines in tooth-ornaments represent CAPPI with 1,5 and 4 km of altitude. Notice that beyond 120 km, the angle low passes above 1,5 km and that to 200 km it exceeds the 4 km. Thus the portion of the CAPPI which will be beyond these limits will be thus rather a PPI of the angle low.

USE: Especially for the reflectivity which is a field with weak vertical gradients. Used with the Doppler data of the radar of the University McGill (Montreal, Canada) although the field of the winds is more changing with altitude and gives a result more mitigated.

(Examples in real-time University McGill Canada Environment)

Chart of office plurality of precipitations

One of the principal utilities of the weather radars is to be able to remotely detect precipitations for hydrometric uses. For example, the monitoring services of the flow of the rivers, warning of floods, planning of work of stopping, etc have all need to know the quantities of rain and snow which fall on broad fields. The radar supplements a network of pluviometers ideally because it covers a large surface. First being able to be used to gauge the second.

To make an image of accumulations, it is thus necessary to multiply the rate of precipitation obtained on low level in survey radar by the desired duration. As precipitations move, one can take the rate only at one moment given and it is thus necessary to make several surveys with regular intervals and to distribute precipitation between each step of time.

For example, if one generates a PPI or CAPPI of low level at every 10 minutes. By comparing these images by means of computer, one can draw from it the speed and the direction of displacement of the owner of precipitations. The rate of precipitations X (by minute), which moves point has at the point B between two steps of time, will thus leave 10 X millimetres of rain. One distributed then this quantity also all along the way of has to B. to obtain accumulations over greater periods (hours, days, etc), it is thus enough to add the data of several steps with time of survey.

This product has various names: chart or image of accumulations (Canada), water blade (France or in Hydrology), chart heights of precipitations, etc

Chart of the tops of echoes

Another field of application of the radars is that of aviation. A very useful chart for this field is that of the tops of precipitations. Indeed, the aircraft wish knowledge the height of the tops of the clouds, inter alia those of the storms, to know at which altitude to fly in order to avoid the dangerous clouds. Like the weather radar a volume in three dimensions probes, one can thus find the height there to which precipitations finish. It is not the height strictly speaking clouds, since the top of those contains only droplets not enough large to be visible with the radar, but it approaches some.

The way of proceeding is simply to take the data since the highest angle towards low and to note the height and the places with each angle of sight where one will exceed a rate threshold of precipitations. The weaker this rate will be, the more one approaches the real top of the cloud.

Vertical cuts

In order to know the vertical structure of the clouds, which is important to recognize their type, a product of vertical cut of the data of the radars at developed summer.

Animations

All the derivative products of the data radar can be animated. The user can thus see the evolution of the owner of reflectivities, speeds, etc and draw some from information on the displacement and the dynamics of the weather phenomenon observed.

For example, one can extrapolate displacement to envisage in the short run the arrival of the rain on a town of interest. One can also notice the development or the reduction in the Précipitation S.

In the following sections, we will speak about the various types of returns to the radar which do not come from Hydrométéore S and which harm interpretation. An animation is very useful to locate the Artéfact S nonweather which have a random behavior (noise, abnormal propagation) or which does not move (echoes of ground). However, some other artefacts, like the returns coming from the birds, move in the same way that a precipitation would do it and the use of an animation will not make it possible it to only locate them.

Mosaics of radars

The data of only one weather radar are useful if one looks only with short range and over a rather short time. However, for seeing the displacement of precipitations well, the exits of several radars must be put in network on a mosaic chart. As the various radars can have different characteristics, of which their calibration, and to have zones of stepping, it is necessary to envisage a decision tree to choose some value to put in a point in order to have a continuum.

For the radars which can have a certain attenuation in strong precipitations, like those of 5 cm wavelength, one will in general put the data of the radar having the strongest return in a point if two radars cover this place. For the radars not having notable attenuation, like those of 10 cm, one will put the value of the radar rather nearest.

This can also vary between the winter and the summer. In the first case, there can be much difference of position due to transport by the winds and in variations of the rate of precipitations by sublimation (Virga). That can lead to a great difference between the level of the data of the radar and the ground.

Here some sites to see the data in networks:

Canada environment

American radar by NOAA

Data of the network of [[Weather-France] (ARAMIS)]

Czech Republic

Republic of South Africa

Automatic algorithms

For better locating the contained informations in the data of a radar, various algorithms Informatique S were developed. Indeed, a meteorologist with the informed eye and with much experiment will be able to interpret these exits but certain details requires too much attention. This is particularly true Doppler data which give only the radial component.

The principal algorithms of reflectivity are:

• quantity of total precipitation (CHEAP in English) in the column what makes it possible to locate the most important clouds like the storms.
• That of Rafale Potentielle which connects the CHEAP one and the height of the top of the echoes radar. The more the quantity of water concentrates in the cloud, the more the gust will be strong when the heart of precipitations goes down.
• Presence of hail.

Principal algorithms for Doppler speeds (see Algorithms Doppler):

• Location of rotations in the storms. With a weather radar one cannot see the Tornade S, because they are smaller than the usual resolution, but one can see creating in the stormy cells rotations which will be able to concentrate in tornado if the conditions are favorable.
• Repérage of the shearing of the winds in the low levels which gives an idea where produces important gusts.

Limitations and artefacts

The interpretation of the data radar depends on several assumptions which are not always filled:

• standard Atmosphere

• Obedience with the law of Rayleigh and direct relationship between the return and the rate of precipitation
• the volume probed by the beam is filled with targets (drops, flakes, etc) weather , all of the same type and with a uniform concentration
• No Atténuation
• No phenomenon of amplification
• the side lobes is negligible.
• the form of the beam with semi-power can be represented in an approximate way by a Gaussian curve.
• the incidental and retrodiffused waves are linearly polarized.
• the multiple diffusion is negligible (not return to multiple reflections on various targets).

The beam radar is propagated in the atmosphere and meets many things in addition to the rain or snow. It is thus necessary to know to recognize the signature of these artefacts to be able to interpret the data correctly.

Abnormal propagation (nonstandard atmosphere)

One takes as assumption that the beam radar will move in a standard atmosphere where the temperature decreases according to a normal curve with altitude. The calculation of the position of the echoes and their altitude depends on this assumption.

Suréfraction

This type of false echoes is easily locatable by looking at a sequence of images if there are no precipitations. One sees there in certain places of the very strong echoes which vary intensity in time without changing place. Moreover, there is a very great variation of intensity between close points. Like that occurs in night inversion, the whole starts after laying down it sun and disappears in the morning.

On the other hand, if the inversion is due to a pre-frontal inversion (hot Front), there can be precipitation mixed with the abnormal propagation what makes detection more problematic.

The extreme of this phenomenon occurs when the inversion is if marked and on a thin layer which the beam radar becomes trapped in the layer in Guide of wave and rebounds several times on the ground before returning to the radar. This creates echoes of abnormal propagation in multiple concentric bands.

Infraréfraction

Targets out of the law of Rayleigh

One of the assumptions of interpretation radar is that the return of the targets is proportional to the diameter of the targets. This occurs when the drops are about 10 times lower than the wavelength used. If the targets are too small, the dipole of the water molecules contained in the target (e.g. droplets of cloud a few microns in diameter) will be too small to be excited and the return will be invisible for the radar.

On the other hand if the target approaches the wavelength (spindly e.g. of 5 cm), the dipole of the target will be excited in a nonlinear way and the return will not be proportional any more. This zone is called the diffusion according to the Théorie of Mie.

Thus an operational weather radar (5 and 10 cm in general) cannot perceive drizzle or the clouds. On another side, if the reflectivity exceeds 50 dBZ, it is very probable that we deal with hail but one cannot specify the rate of precipitation of them.

Probed volume not filled and gradients with reflectivity

The beam radar has a certain width and one takes data with a definite number of impulses on each angle of sight like to discrete angles of elevation. It results from it that we have data which realize the values of reflectivity, speed and polarization on volumes of targets. More one is far, as one saw higher, more this volume is tall.

In the figure opposite, one sees in top a vertical cut carried out when a storm passed above a Profileur of winds. This last has a resolution of 150m according to the vertical and 30m according to the horizontal one with the result that one can see details enormously. One can amongst other things see that the reflectivity changes quickly at certain places (Gradient).

Let us compare this image with that of bottom, simulated starting from the characteristics of a beam weather radar of 1 degree of width, at a distance from 60  km. One very clearly sees the degradation which is particularly important in the zones where the gradient is strong. This shows how the data of the radars can easily derogate of the assumption that probed volume is filled with targets, uniformly laid out.

Nonweather targets

In addition to the rain, snow, glaze and other precipitations, the weather radar can receive echoes coming from other sources. The principal pollutants of the data are:

• birds, especially in times of migration

• insects at very low altitude
• electronic lures that from the military aircrafts
• the solid obstacles like the mountains can drop, the buildings, the planes
• the reflection coming from water levels to shaving angle.

Each one of these artefacts has particular characteristics which make it possible to recognize them true precipitation for an informed eye. We will see low than it is possible by combining the reflectivity, Doppler speeds and polarization to filter them.

Attenuation

Consequently, the weather radars generally use a wavelength of 5 cm or more. With 5 centimetres, at the time of intense rains, one notes a loss of signal downstream from those on the image radar (see image). The attenuation is however of null with acceptable in weak precipitations with moderated and snow. This is why the majority of the countries of the moderate areas (Canada and a good part of Europe) use this wavelength. It requires a less expensive technology (Magnétron and of smaller antenna). The nations having a prevalence of storms violent one use a wavelength of 10 centimetres which is attenuated in a negligible way under all the conditions but is more expensive (Klystron). It is the case of the United States, Taiwan and others.

The shorter wavelengths are strongly attenuated, even by moderated rain, but can have a certain utility with short range, where the resolution is finer. Certain American stations of Télévision use radars of 3 centimetres to cover their audience in addition to local NEXRAD.

Brilliant bands

As we saw before, the return of reflectivity is proportional to the diameter and the permittivity of the target. Between a snowflake and a drop of of the same mass rain, there is an important difference of these two variables but in the opposite direction. Thus the diameter of a flake is much larger than that of the drop but the permittivity is much smaller. When one calculates Z of each one of these two targets, one realizes that the difference is approximately 1,5 dBZ in favor of the drop.

When snow, in altitude, goes down towards the ground and meets air above the freezing point, it is transformed into rain. Thus one expects that the reflectivity increases approximately 1,5 dBZ between a data radar taken in snow and a catch in the rain. With the altitude where snow starts to melt, there is however a raising of the reflectivities up to 6,5 dBZ. What arrives?

On this level, we deal with wet flakes. They still have a large diameter, approaching that of the snowflakes, but their permittivity approaches that of the rain. We have then the two factors supporting a greater reflectivity and it results from it a zone which one calls the brilliant band. In the data radar, on PPI or CAPPI, which cross this level one will then see a raising of the intensities of precipitations which is not real.

Several techniques were developed to filter this artefact by several weather services.

Geometry of the beam

The emitted beam is not a brush as a laser beam but it rather has the shape of an owner of Diffraction by a slit since the emitted wave leaves by the slit a tube guides wave at the focal point of a parabolic antenna . The central peak (the beam radar) is more or less a curve Gaussienne but there are secondary peaks which also can illumer the targets out of the main axis. All is made to minimize the energy of the secondary peaks to a weak fraction of the central peak but they are never null.

When the beam radar passes on a particularly strong echo, the return of the energy of the central peak is in the axis of aiming. The returns of the secondary peaks (see secondary Lobe) arrive, as for them, at the same time when the central peak illuminates another angle of sight. Like the receiver the angle of sight of the central peak notes, the returns of the secondary peaks are thus noted with a bad Azimuth what creates a weak forgery return on each side of our true echo.

Multiple reflections

The beam radar is reflected by the target in all the directions. In general, the return coming from multiple reflections in the cloud is negligible. Under certain conditions where the heart of precipitation is intense (like the Grêle), part of the energy sent towards the ground will turn over to the cloud and will be considered towards the radar. There will be then a reflection with three bodies. As this echo arrives later that the initial echo of the cloud (longer way), it will be placed incorrectly at the rear of truths echoes of precipitations.

Current and future solutions