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## Abstract

A new method to retrieve vertical profiles of liquid water content *M _{w}
*(

*z*), ice water content

*M*(

_{i}*z*), and ice particle size distribution

*N*(

_{i}*D*,

*z*), (where

*D*is the ice particle size and

*z*the vertical coordinate) in mixed nonprecipitating clouds using the observations of a zenith-viewing Doppler radar and of a microwave radiometer is proposed. In this method, the profile of the vertical air velocity deduced from Doppler radar measurements is used to describe the rate of production by the updrafts of water. vapor in excess of saturation with respect to ice. Using a

*Z*−

_{i}*M*power-law relation with an unknown linear parameter (let α

_{i}*, be this parameter) and initially assuming that*

_{i}*Z*is negligible with respect to

_{w}*Z*, (where

_{i}*Z*and

_{w}*Z*are the radar reflectivity factors of liquid water and ice particles respectively), the measured radar reflectivity factor profile

_{i}*Z*(≈

_{m}*Z*) is inverted to estimate

_{i}*N*(

_{i}*D*,

*z*). From

*N*(

_{i}*D*,

*z*), the profile of the rate of water vapor that can be consumed by pure deposition on ice particles is calculated. The difference between the rate of production of the exam water vapor and the rate of deposited water vapor is an expression of the rate of liquid water generation at each level. By writing that the integral of the liquid water along the profile has to be equal to the total liquid water deduced from the microwave radiometer measurement, an estimation of the α

_{i}parameter is obtained. From α

_{i}, an estimation of the profiles

*M*(

_{w}*z*),

*M*(

_{i}*z*),

*Z*(

_{w}*z*),

*Z*(

_{i}*z*) (=

*Z*−

_{m}*Z*), and

_{w}*N*(

_{i}*D*,

*z*) is calculated. If

*Z*is effectively negligible with respect to

_{w}*Z*, the computation of the retrieved profiles is ended. If not,

_{i}*Z*(

_{i}*z*) is corrected and a new estimation of the profiles is computed. The results of the numerical simulation of the algorithm are presented.

## Abstract

A new method to retrieve vertical profiles of liquid water content *M _{w}
*(

*z*), ice water content

*M*(

_{i}*z*), and ice particle size distribution

*N*(

_{i}*D*,

*z*), (where

*D*is the ice particle size and

*z*the vertical coordinate) in mixed nonprecipitating clouds using the observations of a zenith-viewing Doppler radar and of a microwave radiometer is proposed. In this method, the profile of the vertical air velocity deduced from Doppler radar measurements is used to describe the rate of production by the updrafts of water. vapor in excess of saturation with respect to ice. Using a

*Z*−

_{i}*M*power-law relation with an unknown linear parameter (let α

_{i}*, be this parameter) and initially assuming that*

_{i}*Z*is negligible with respect to

_{w}*Z*, (where

_{i}*Z*and

_{w}*Z*are the radar reflectivity factors of liquid water and ice particles respectively), the measured radar reflectivity factor profile

_{i}*Z*(≈

_{m}*Z*) is inverted to estimate

_{i}*N*(

_{i}*D*,

*z*). From

*N*(

_{i}*D*,

*z*), the profile of the rate of water vapor that can be consumed by pure deposition on ice particles is calculated. The difference between the rate of production of the exam water vapor and the rate of deposited water vapor is an expression of the rate of liquid water generation at each level. By writing that the integral of the liquid water along the profile has to be equal to the total liquid water deduced from the microwave radiometer measurement, an estimation of the α

_{i}parameter is obtained. From α

_{i}, an estimation of the profiles

*M*(

_{w}*z*),

*M*(

_{i}*z*),

*Z*(

_{w}*z*),

*Z*(

_{i}*z*) (=

*Z*−

_{m}*Z*), and

_{w}*N*(

_{i}*D*,

*z*) is calculated. If

*Z*is effectively negligible with respect to

_{w}*Z*, the computation of the retrieved profiles is ended. If not,

_{i}*Z*(

_{i}*z*) is corrected and a new estimation of the profiles is computed. The results of the numerical simulation of the algorithm are presented.

## Abstract

A method of radar measurement of drift, generated by the wet cooling towers of power plants, is proposed. The water given off by the evaporative towers consists of two kinds of droplets: the recondensation droplets—generally less than 20 μm in diameter and with a negligible rate of fall—and the drift droplets, arising from spraying of cooling water, entrained out of the tower in the exhaust air flow. Both components partake in the radar reflectivity of the plumes. A very close relation is found between the water content and the reflectivity factor of the recondensation cloud. For a same liquid water content, the reflectivity of the recondensation cloud is 20 dB lower than that of warm cumulus clouds. The knowledge of the cooling tower working point and of the surrounding air conditions enables the evaluation of the recondensation cloud contribution to the reflectivity. In the next step, assuming that the drift droplet population is represented by a gamma distribution, functional relations are developed enabling the computation of the number density, the water content and the precipitation rate of cooling tower drift from the radar reflectivity factor of the drift component. Some observations are presented to illustrate the proposed method and to show that, owing to the presence of the cooling droplets, the radar outlines of the plume noticeably differ from its visual outlines. The radar thus enables a quantitative monitoring of the microstructure of the plumes emitted by the atmospheric cooling tower parks, i.e., a measurement of the efficiency of the drift droplet eliminators.

## Abstract

A method of radar measurement of drift, generated by the wet cooling towers of power plants, is proposed. The water given off by the evaporative towers consists of two kinds of droplets: the recondensation droplets—generally less than 20 μm in diameter and with a negligible rate of fall—and the drift droplets, arising from spraying of cooling water, entrained out of the tower in the exhaust air flow. Both components partake in the radar reflectivity of the plumes. A very close relation is found between the water content and the reflectivity factor of the recondensation cloud. For a same liquid water content, the reflectivity of the recondensation cloud is 20 dB lower than that of warm cumulus clouds. The knowledge of the cooling tower working point and of the surrounding air conditions enables the evaluation of the recondensation cloud contribution to the reflectivity. In the next step, assuming that the drift droplet population is represented by a gamma distribution, functional relations are developed enabling the computation of the number density, the water content and the precipitation rate of cooling tower drift from the radar reflectivity factor of the drift component. Some observations are presented to illustrate the proposed method and to show that, owing to the presence of the cooling droplets, the radar outlines of the plume noticeably differ from its visual outlines. The radar thus enables a quantitative monitoring of the microstructure of the plumes emitted by the atmospheric cooling tower parks, i.e., a measurement of the efficiency of the drift droplet eliminators.

## Abstract

One of the potential atmospheric effects of energy dissipation at large power parks is the mesoscale modification of the precipitation field. Meteorological conditions favorable for such an influence mainly correspond to naturally precipitating atmospheres and make the identification of the anthropogenic components difficult. In this paper, millimetric Doppler radar data are used in order to analyze the three-dimensional structure of snowfalls associated, in a perturbed environment, with a natural-draft cooling tower park. The plumes observed spread out in the atmospheric boundary layer with spread angles of 15°–30° over a distance of more than 20 km. Their main characteristics compare favorably with Koenig's numerical simulation results.

## Abstract

One of the potential atmospheric effects of energy dissipation at large power parks is the mesoscale modification of the precipitation field. Meteorological conditions favorable for such an influence mainly correspond to naturally precipitating atmospheres and make the identification of the anthropogenic components difficult. In this paper, millimetric Doppler radar data are used in order to analyze the three-dimensional structure of snowfalls associated, in a perturbed environment, with a natural-draft cooling tower park. The plumes observed spread out in the atmospheric boundary layer with spread angles of 15°–30° over a distance of more than 20 km. Their main characteristics compare favorably with Koenig's numerical simulation results.

## Abstract

A new method for the estimation of the rain rate using a polarimetric radar at attenuated wavelengths is proposed. At attenuated wavelengths, the differential reflectivity for horizontal and vertical polarization, *Z*
_{DR}, is the addition of a term depending on the drop shape, *Z*
_{DRs}, and a term depending on the differential attenuation for the two polarizations. *A*
_{DP}. The differential attenuation can be interpreted as an estimation of the integral of the rain rate along the radar beam. The principle of the method is the following. along the radar beam a first estimation of the rain rate *R*, in each range gate, is calculated from the single-wavelength radar reflectivity factor *Z* using the usual iterative attenuation correction scheme and a combination of a *Z−R* and an *A−R* relation, where *A* is the single polarization attenuation coefficient. This result permits one to obtain an estimation of *Z*
_{DRs}. The difference between the measured value of *Z*
_{DR} and *Z*
_{DRs}, is a measure of *A _{DP}
*. Then the integral of

*R*along the radar beam, deduced from the single polarization reflectivities, is constrained to be equal to the integral of

*R*deduced from

*A*

_{DP}. This constraint is used to adjust iteratively one of the two parameters of the

*Z−R*relation (let a be this parameter), the other being maintained constant at a mean value. The, adjusted α enables the calculation of

*R*in each gate. The radial observed with the radar can he partitioned, and the algorithm applied independently to the individual segments with one value of α

_{ A }computed for each segment. The method is independent from the radar calibration and from the attenuation by undetected clouds since it is based on a differential measurement. This algorithm is also usable as a qualitative hail detector, as well as a detector of anomalous propagation. Simulations of these various functions are presented.

## Abstract

A new method for the estimation of the rain rate using a polarimetric radar at attenuated wavelengths is proposed. At attenuated wavelengths, the differential reflectivity for horizontal and vertical polarization, *Z*
_{DR}, is the addition of a term depending on the drop shape, *Z*
_{DRs}, and a term depending on the differential attenuation for the two polarizations. *A*
_{DP}. The differential attenuation can be interpreted as an estimation of the integral of the rain rate along the radar beam. The principle of the method is the following. along the radar beam a first estimation of the rain rate *R*, in each range gate, is calculated from the single-wavelength radar reflectivity factor *Z* using the usual iterative attenuation correction scheme and a combination of a *Z−R* and an *A−R* relation, where *A* is the single polarization attenuation coefficient. This result permits one to obtain an estimation of *Z*
_{DRs}. The difference between the measured value of *Z*
_{DR} and *Z*
_{DRs}, is a measure of *A _{DP}
*. Then the integral of

*R*along the radar beam, deduced from the single polarization reflectivities, is constrained to be equal to the integral of

*R*deduced from

*A*

_{DP}. This constraint is used to adjust iteratively one of the two parameters of the

*Z−R*relation (let a be this parameter), the other being maintained constant at a mean value. The, adjusted α enables the calculation of

*R*in each gate. The radial observed with the radar can he partitioned, and the algorithm applied independently to the individual segments with one value of α

_{ A }computed for each segment. The method is independent from the radar calibration and from the attenuation by undetected clouds since it is based on a differential measurement. This algorithm is also usable as a qualitative hail detector, as well as a detector of anomalous propagation. Simulations of these various functions are presented.

## Abstract

A database on the rain rate collected with disdrometers at various sites located from the middle to tropical latitudes is used to analyze the variations of the parameters of the probability density function of rain rate *P*(*R*). Experimental evidence shows that 〈*R*〉, the area-average rain rate, and *F*(τ), the fractional area occupied by rain rate exceeding a fixed threshold τ, are highly linearly related; that is, 〈*R*〉 = *S*(τ)*F*(τ), with *R* > τ. From the values of *P*(*R*), the variations of the proportionality factor *S*(τ) are computed. The *P*(*R*) can be represented by a lognormal distribution; the parameters of that distribution, the average *m _{R}
* and the variance σ

^{2}

_{ R }, are shown to be very tightly linked by the relation σ

^{2}

_{ R }= 5m

^{2}

_{ R }. This is one of the reasons for the stability of

*S*(τ). Using this relation, analytical expressions of

*P*(

*R*) and

*S*(τ) as functions of

*m*only are proposed. Varying the integration time used for

_{R}*R*measurements between 1 and 5 min does not significantly modify the parameters of

*P*(

*R*) or the computed

*S*(τ) values.

## Abstract

A database on the rain rate collected with disdrometers at various sites located from the middle to tropical latitudes is used to analyze the variations of the parameters of the probability density function of rain rate *P*(*R*). Experimental evidence shows that 〈*R*〉, the area-average rain rate, and *F*(τ), the fractional area occupied by rain rate exceeding a fixed threshold τ, are highly linearly related; that is, 〈*R*〉 = *S*(τ)*F*(τ), with *R* > τ. From the values of *P*(*R*), the variations of the proportionality factor *S*(τ) are computed. The *P*(*R*) can be represented by a lognormal distribution; the parameters of that distribution, the average *m _{R}
* and the variance σ

^{2}

_{ R }, are shown to be very tightly linked by the relation σ

^{2}

_{ R }= 5m

^{2}

_{ R }. This is one of the reasons for the stability of

*S*(τ). Using this relation, analytical expressions of

*P*(

*R*) and

*S*(τ) as functions of

*m*only are proposed. Varying the integration time used for

_{R}*R*measurements between 1 and 5 min does not significantly modify the parameters of

*P*(

*R*) or the computed

*S*(τ) values.

## Abstract

The relationships between the radar reflectivity factor *Z* and significant physical cloud parameters are studied from a dataset collected with an instrumented aircraft in non- or very weakly precipitating warm clouds. The cloud droplet populations for each flight are statistically described from histograms showing the relative importance and the extent of the precipitating and nonprecipitating component in the cloud field. The limit between precipitating and nonprecipitating warm clouds is found to be about *Z* = 0.032 mm^{6} m^{−3} (− 15 dBZ). No clear correlation appears between *Z* and liquid water content or median volume diameter in cloud samples that contain droplets larger than about 200 μm in diameter. Some relationships are proposed for smaller droplets in natural clouds. No significant difference is found between dynamically induced artificial clouds and natural ones.

## Abstract

The relationships between the radar reflectivity factor *Z* and significant physical cloud parameters are studied from a dataset collected with an instrumented aircraft in non- or very weakly precipitating warm clouds. The cloud droplet populations for each flight are statistically described from histograms showing the relative importance and the extent of the precipitating and nonprecipitating component in the cloud field. The limit between precipitating and nonprecipitating warm clouds is found to be about *Z* = 0.032 mm^{6} m^{−3} (− 15 dBZ). No clear correlation appears between *Z* and liquid water content or median volume diameter in cloud samples that contain droplets larger than about 200 μm in diameter. Some relationships are proposed for smaller droplets in natural clouds. No significant difference is found between dynamically induced artificial clouds and natural ones.

## Abstract

Because of a lack of data, the structural characteristics of rain fields over the sea are poorly documented. Coastal radars offer an opportunity to observe the distribution of rain parameters at the land–sea transition. In this study, two datasets on rain fields collected over the Atlantic coast: one at midlatitude, in a westerly general atmospheric circulation, that is, onshore, in the southwest of France, the other at tropical latitude, in an easterly general atmospheric circulation, that is, offshore, in the west of Senegal (Africa), are analyzed. In the two areas, the rain volume, or cumulative rainfall, is found to be markedly larger over land than over sea. However this difference is due mainly to a higher rain occurrence and duration over land than over sea. The mean rain rate, when raining, is almost the same over land and over sea at midlatitude and at tropical latitude. In addition, the mean rain rate is found to be constant through rain fields in which strong gradients of cumulative rainfall are observed [when no other kind of forcing (not considered in this work), notably orographic, is present]. Thus, for example, in Senegal a meridional change of the annual cumulative rainfall from 300 to 1200 mm over 400 km is not associated with any mean rain-rate variation. In a similar way, the parameters of the probability density function of the rain rate and the distribution of the statistical variation coefficient are not influenced by the gradient of the cumulative rainfall. The studied rain fields are thus approximately ergodic. These results strengthen the validity of the probability density function of rain rate as a climatic characteristic of rain fields and the reliability of the statistical method of estimating the average rainfall by area integrals over large space scales and timescales. The variation coefficient of the rain rate is found to be constant and close to 2.24 over sea and over land for mid- and tropical latitudes.

## Abstract

Because of a lack of data, the structural characteristics of rain fields over the sea are poorly documented. Coastal radars offer an opportunity to observe the distribution of rain parameters at the land–sea transition. In this study, two datasets on rain fields collected over the Atlantic coast: one at midlatitude, in a westerly general atmospheric circulation, that is, onshore, in the southwest of France, the other at tropical latitude, in an easterly general atmospheric circulation, that is, offshore, in the west of Senegal (Africa), are analyzed. In the two areas, the rain volume, or cumulative rainfall, is found to be markedly larger over land than over sea. However this difference is due mainly to a higher rain occurrence and duration over land than over sea. The mean rain rate, when raining, is almost the same over land and over sea at midlatitude and at tropical latitude. In addition, the mean rain rate is found to be constant through rain fields in which strong gradients of cumulative rainfall are observed [when no other kind of forcing (not considered in this work), notably orographic, is present]. Thus, for example, in Senegal a meridional change of the annual cumulative rainfall from 300 to 1200 mm over 400 km is not associated with any mean rain-rate variation. In a similar way, the parameters of the probability density function of the rain rate and the distribution of the statistical variation coefficient are not influenced by the gradient of the cumulative rainfall. The studied rain fields are thus approximately ergodic. These results strengthen the validity of the probability density function of rain rate as a climatic characteristic of rain fields and the reliability of the statistical method of estimating the average rainfall by area integrals over large space scales and timescales. The variation coefficient of the rain rate is found to be constant and close to 2.24 over sea and over land for mid- and tropical latitudes.

## Abstract

A dual-wavelength method to differentiate supercooled water from ice and to measure mass content in each phase in cold stratiform clouds is proposed and discussed. The differential attenuation *A*
_{
d
}, whose direct measurement is available with dual-wavelength radar, is a linear function of the liquid water content *M*
_{
w
} (the contribution from ice hydrometeors is negligible in comparison). Measuring both *A*
_{
d
} and the radar reflectivity factor *Z*
_{
e
} leads to a system of two equations expressed as functions of *M*
_{
w
} and *M*
_{
I
} (ice water content); its solution provides the values of both *M*
_{
w
} and *M*
_{
I
} between any two ranges along the radar beam, and as a consequence the distribution pattern of those two parameters within the cloud. Simulations of the method on two idealized cloud structures with various spatial distributions of *M*
_{
w
} and *M*
_{
I
} are shown. From a comparative study, the wavelength couple of 3.2 cm and 0.86 cm has been selected as the most suitable one, either for ground-based midrange cloud observations or for an airborne radar.

## Abstract

A dual-wavelength method to differentiate supercooled water from ice and to measure mass content in each phase in cold stratiform clouds is proposed and discussed. The differential attenuation *A*
_{
d
}, whose direct measurement is available with dual-wavelength radar, is a linear function of the liquid water content *M*
_{
w
} (the contribution from ice hydrometeors is negligible in comparison). Measuring both *A*
_{
d
} and the radar reflectivity factor *Z*
_{
e
} leads to a system of two equations expressed as functions of *M*
_{
w
} and *M*
_{
I
} (ice water content); its solution provides the values of both *M*
_{
w
} and *M*
_{
I
} between any two ranges along the radar beam, and as a consequence the distribution pattern of those two parameters within the cloud. Simulations of the method on two idealized cloud structures with various spatial distributions of *M*
_{
w
} and *M*
_{
I
} are shown. From a comparative study, the wavelength couple of 3.2 cm and 0.86 cm has been selected as the most suitable one, either for ground-based midrange cloud observations or for an airborne radar.

## Abstract

Anomalous propagation (AP) of ground-based radar beam results in the detection of ground echoes beyond the horizon. One year of data gathered with an S-band meteorological radar located on the coast in southwest France is used to analyze the spatial distribution of AP ground echoes (APE). The APE distributions of duration and reflectivity in the radar-observed area are found to be strongly related to the main feature of the regional orography and topography up to the farthest distance (250 km) observed by the radar, notably the nature of the surface, the topographic orientation with respect to the radar beam direction, and the altitude. The distribution of APE in the studied area is found to be strongly anisotropic around the radar, with wide differences between land and sea. Rain accumulation equivalent to the APE is, in certain places, of the same order or higher than the real rain depth. The distribution of the ground surfaces, as calculated from a ground numerical model, compares qualitatively well with the APE radar reflectivity distribution.

## Abstract

Anomalous propagation (AP) of ground-based radar beam results in the detection of ground echoes beyond the horizon. One year of data gathered with an S-band meteorological radar located on the coast in southwest France is used to analyze the spatial distribution of AP ground echoes (APE). The APE distributions of duration and reflectivity in the radar-observed area are found to be strongly related to the main feature of the regional orography and topography up to the farthest distance (250 km) observed by the radar, notably the nature of the surface, the topographic orientation with respect to the radar beam direction, and the altitude. The distribution of APE in the studied area is found to be strongly anisotropic around the radar, with wide differences between land and sea. Rain accumulation equivalent to the APE is, in certain places, of the same order or higher than the real rain depth. The distribution of the ground surfaces, as calculated from a ground numerical model, compares qualitatively well with the APE radar reflectivity distribution.

## Abstract

The raindrop size distributions (DSDs) observed over a short span usually have an erratic shape, with several relative maxima. This multimodal structure is studied from disdrometer data acquired in tropical and midlatitude areas. It is shown that some modes of DSDs have a persistence larger than several minutes and can be spotted from one DSD to the next one as they migrate through the size classes. It is demonstrated that *N*
_{
m
}, the number of modes of DSDs, for diameter larger than 2 mm, is not related to the mean rain rate but depends on the rain-rate fluctuations. Statistical evidence of such a relation is given. The spread of DSDs is found to be dependent on its multimodal structure, that is, on *N*
_{
m
}. The large values of *N*
_{
m
} are associated with low values of slope *λ* and intercept *N*
_{0} of the fitted exponential distribution.

In order to explain the dependence of the DSD shape on *N*
_{
m
}, a conceptual model is proposed in which the modes are interpreted as resulting from an overlapping of rain shafts. The associated DSD is termed a synthetic drop size distribution (SDSD). It is shown that the overlapping of rain shafts generated from a sequence of rain cells of increasing intensity, such as observed at the leading edge of a convective system, results in undersloping SDSDs. In the reverse configuration, that is, with a sequence of rain cells with decreasing intensity, such as observed at the ending edge of a convective system, it results in oversloping SDSDs. Observations in agreement with these conclusions are presented. The readability of the modal structure of the DSDs depends on several factors in such a way that an apparent multimodal structure is not necessary for a DSD to be an SDSD. It is suggested that most of the DSDs observed at the ground are synthetic DSDs.

## Abstract

The raindrop size distributions (DSDs) observed over a short span usually have an erratic shape, with several relative maxima. This multimodal structure is studied from disdrometer data acquired in tropical and midlatitude areas. It is shown that some modes of DSDs have a persistence larger than several minutes and can be spotted from one DSD to the next one as they migrate through the size classes. It is demonstrated that *N*
_{
m
}, the number of modes of DSDs, for diameter larger than 2 mm, is not related to the mean rain rate but depends on the rain-rate fluctuations. Statistical evidence of such a relation is given. The spread of DSDs is found to be dependent on its multimodal structure, that is, on *N*
_{
m
}. The large values of *N*
_{
m
} are associated with low values of slope *λ* and intercept *N*
_{0} of the fitted exponential distribution.

In order to explain the dependence of the DSD shape on *N*
_{
m
}, a conceptual model is proposed in which the modes are interpreted as resulting from an overlapping of rain shafts. The associated DSD is termed a synthetic drop size distribution (SDSD). It is shown that the overlapping of rain shafts generated from a sequence of rain cells of increasing intensity, such as observed at the leading edge of a convective system, results in undersloping SDSDs. In the reverse configuration, that is, with a sequence of rain cells with decreasing intensity, such as observed at the ending edge of a convective system, it results in oversloping SDSDs. Observations in agreement with these conclusions are presented. The readability of the modal structure of the DSDs depends on several factors in such a way that an apparent multimodal structure is not necessary for a DSD to be an SDSD. It is suggested that most of the DSDs observed at the ground are synthetic DSDs.