F. Mercier*1, L. Barthes1, A. Chazottes1, C. Mallet1

1 LATMOS/IPSL/UVSQ/CNRS

* francois.mercier@latmos.ipsl.fr

Results

4D-VAR data assimilation algorithm

Context and objectives

Data

Conclusions / Perspectives

Fig. 2 : Spectropluviometre

Fig. 3 : Micro-rain radar (MRR)

Optical disdrometer

Micro Rain Radar (MRR)

• Owner : LATMOS

• Type of measurements :

Water fluxes

• Location :

- Palaiseau (2010 – 2013)

- Ardèche (2013)

• Owner : Météo France

• Type of measurements :

Water volumes

• Location :

- Ardèche (2013)

Abstract

The goal of this work is to have a better understanding of the structure of rain and of the spatiotemporal variations of

the drop size distribution (DSD). For this purpose, we use two different kinds of data at different scales : firstly, a

Doppler vertically pointing radar which gives volumetric information on the DSDs at different heights ; secondly, a

disdrometer which gives flux information on the ground DSDs. In order to link these observations, we use the physics

of the DSDs evolution, which is mathematically represented by partial differential equations able to model different

phenomena, including advection of droplets by wind and gravity, collisions, or evaporation. As a first step, the model

takes only into account the advection (fall of droplets). The linking of observations thanks to the model is made by a

4D-VAR data assimilation algorithm. This algorithm appears able to retrieve the characteristics of the DSD fields on

simulated data and to produce realistic DSDs and vertical wind fields for quiet stratiform real rain events.

The droplet size greatly affects the interactions between

the rain drop and radio waves (Rayleigh / Mie scattering

theories).

Hence the study of the drop size distribution (DSD) is of

great importance for both radar (and microwave in

general) meteorology and telecommunications.

Moreover, a better understanding of the phenomena

acting during the fall of droplets could help to model the

rain in numerical weather forecasts.

A large number of models have been proposed

for the parameterization of DSD and its vertical

evolution, including a number of physical

phenomena (see beyond). But these models are

sometimes incompatible and hard to validate.

In this work, we want to control these models

with observations by assimilating different kinds

of data providing information at different scales.

Fig. 1 : Example of

auto break-up of a

large drop.

Extracted from

Villermaux and

Bossa 2009.

We use a numerical model of evolution of the DSDs to link these

heterogeneous observations.

Partial differential equations (PDE) more general model taking

account of different phenomena is of the form :

With � �, , , , � the number of drops by unit of volume and

diameter (�−3��−1).

As a first step, we limit the model to advection in a time/height

plane : We look for the DSDs just under

the freezing level.

We use the numerical model to

propagate these top DSDs at the

different heights and times.

We compare these DSDs and the

observations (Doppler spectra +

disdrometer data).

Evolution model

Fig. 5 : Diagram

describing the

assimilation

algorithm used

in this work.

- A new method for studying evolution and variability of DSDs from heterogeneous radar and disdrometer data.

- Appears quite robust on simulated data.

- Appears to satisfactorily retrieve both measurements and give realistic results on a case study of a quiet rain event.

- Needs to be validated with other independant measurements.

- Possibly underconstrained, especially in case of strong vertical wind field.

Prospects :

- Addition of microphysics phenomena parameterization.

- Use of Doppler cloud radar and/or wind profilers to get a good first

guest for the vertical wind field (to add constraints in the problem) and

to valid the results.

Here we focus on an

event which occurred

on the 12/10/2013 in

Ardèche.

This is a quiet event

(mean rainfall rate

around 2��/ℎ, see

figure 6).

Fig. 6 : Rainfall rates on the ground, as measured by the optical

disdrometer (red) and retrieved from data of both the

disdrometer and the radar by the assimilation algorithm (blue).

Fig. 7 : Doppler spectra at 900m height measured by the MRR

(top) on the 12/10/2013. Doppler spectra estimated from the

DSD retrieved by the assimilation algorithm (bottom).

Fig. 9 : 3 integrated

parameters of the

DSDs retrieved by the

algorithm : mean

diameter Dm (top),

normalised number

of drops No* (middle)

and slope of the DSD

calculated by linear

regression on the

logarithm of the DSD

(bottom). Fig. 8 : Vertical wind field retrieved by the algorithm for the 12/10/2013

event. Also are presented the mean and variance of this wind field for

each vertical layer (100m/layer).

Some conclusions for this event :

- the algorithm is able to very satisfactorily explain the observations (both radar doppler spectra

and ground disdrometer observations).

- The corresponding DSD and vertical wind fields are quite realistic, with patterns in accord with

what we could expect for such a stratiform event.

- It is hard to valid the results, all the available observations being used to produce them.

Fig. 4 : Location of the two

experimental sites. In Ardèche,

the instruments are deployed as

part of the HyMeX campaign.

This is a simplified model implying to limit the study to stratiform

rain events.

With � the drop falling velocity (gravity + vertical wind)

• We work both on simulated data (simulation of cloud base DSDs and wind fields

time series) and on real data.

���� �, , � = � �, ��� �, , �

���� = ���� ��� � + ���� � � � + ���� �� � �

Fig. 5 : Diagram summarizing the 4D-VAR

theoretical algorithm.

Retrievals of observations Vertical wind and DSD retrievals