This study aims at introducing two conservative thermodynamic variables (moist-air entropy potential temperature and total water content) into a one-dimensional variational data assimilation system (1D-Var) to demonstrate their benefits for use in future operational assimilation schemes. This system is assessed using microwave brightness temperatures (TBs) from a ground-based radiometer installed during the SOFOG3D field campaign, dedicated to fog forecast improvement.
An underlying objective is to ease the specification of background error covariance matrices that are highly dependent on weather conditions when using classical variables, making difficult the optimal retrievals of cloud and thermodynamic properties during fog conditions. Background error covariance matrices for these new conservative variables have thus been computed by an ensemble approach based on the French convective scale model AROME, for both all-weather and fog conditions. A first result shows that the use of these matrices for the new variables reduces some dependencies on the meteorological conditions (diurnal cycle, presence or not of clouds) compared to typical variables (temperature, specific humidity).
Then, two 1D-Var experiments (classical vs. conservative variables) are evaluated over a full diurnal cycle characterized by a stratus-evolving radiative fog situation, using hourly TB.
Results show, as expected, that TBs analysed by the 1D-Var are much closer to the observed ones than the background values for both variable choices. This is especially the case for channels sensitive to water vapour and liquid water. On the other hand, analysis increments in model space (water vapour, liquid water) show significant differences between the two sets of variables.
Numerical weather prediction (NWP) models at convective scale need accurate initial conditions for skilful forecasts of high impact meteorological events taking place at a small scale such as convective storms, wind gusts or fog. Observing systems sampling atmospheric phenomena at a small scale and high temporal frequency are thus necessary for that purpose
The accuracy of the analysed state in variational
schemes highly depends on the specification of the so-called background error covariance matrix.
Background error variances and cross-correlations between variables are known to be dependent on weather conditions
It is well known that most data assimilation systems were
based on the assumptions of homogeneity and isotropy of background error correlations.
To test these hypotheses,
The aim of the paper is to test a one-dimensional data assimilation method that would be less sensitive to the average vertical gradients of the (
The focus of the study will be on a fog situation from the SOFOG3D field campaign using a one-dimensional variational data assimilation system (1D-Var) for the assimilation of observed microwave brightness temperatures (TBs) sensitive to
Section
This section presents the methodology chosen for this study.
The definition of the moist-air entropy potential temperature
The motivation for using the absolute moist-air entropy
in atmospheric science was first described by
However, the version of
The conservative aspects of this potential temperature
Only the first-order approximation of
The first term
The first exponential on the right-hand side of Eq. (
While the variable
We consider here “open-system” thermodynamic processes, for which the second exponential takes into account the impact on moist-air entropy when the changes in specific content of water vapour are balanced, numerically, by opposite changes of dry air, namely with
This explains the new term
Although it should be possible to use
The new potential temperature
The general framework describing the retrieval of atmospheric profiles from remote-sensing instruments by statistical methods can be found in
The 1D-Var data assimilation system searches for an optimal state (the analysis) as an approximate solution of the problem minimizing a cost function
The first (background) term measures the distance in model space between a control vector
The 1D-Var assimilation defined previously with the variables
For the unsaturated case
For the saturated case (
In this situation, it is necessary to implicitly calculate the temperature
Taking into account this change of variables, the cost function can be written as
Then, its gradient given by Eq. (
The second term on the right-hand side of Eqs. (
The numerical experiments to be presented afterwards will use measurements made during the SOFOG3D field experiment (
Many instruments were located at the Saint-Symphorien super-site (Les Landes region), such as a HATPRO
This section presents the experimental context of 9 February 2020 at the Saint-Symphorien site characterized by (i) a radiative fog event observed in the morning and (ii) the development of low-level clouds in the afternoon and evening.
Reflectivity profiles at 95 GHz (dBZ) measured by the BASTA cloud radar in the first 500 m (top) and up to 12 000 m altitude (bottom), with UTC times given on the
Figure
Vertical profiles derived from 1 h forecasts of AROME background for all hours of the day 9 February 2020 at Saint-Symphorien (Les Landes region in France) for
Figure
Figure
Figure
Note that the dissipation of the fog is associated with a homogenization of
Channel numbers, band frequencies (GHz) and observation uncertainties (K) prescribed in the observation error covariance matrix
The observations to be assimilated are presented in the following.
The HATPRO MicroWave Radiometer (MWR) measures TBs at 14 frequencies
The
In 1D-Var systems, the integrated liquid water content, liquid water path (LWP), can be included in the control vector
Then, a set of reference matrices
The observation errors are those proposed by
The RTTOV model is used to calculate TBs in different frequency bands from atmospheric temperature, water vapour and hydrometeor profiles together with
surface properties (provided by outputs from the AROME model).
This radiative transfer model has been adapted to simulate ground-based microwave radiometer observations (RTTOV-gb) by
The 1D-Var algorithm was tested on the day of 9 February 2020 with observations from the HATPRO microwave radiometer installed at Saint-Symphorien. This section presents and discusses three aspects of the results obtained: (1) the study of background error cross-correlations; (2) the performance of the 1D-Var assimilation system in observation space by examining the fit of the simulated TB with respect to the observed ones; and (3) the performance of the 1D-Var assimilation system in model space in terms of analysis increments for temperature, specific humidity and liquid water content.
Figure
Background error cross-correlation matrices at 06:00 UTC 9 February 2020 without
When considering conservative variables, the correlations along the diagonal show a consistently positive signal in the troposphere (below level
We also note that these background error statistics are less dependent on the diurnal cycle and on the meteorological situation (e.g. in the presence of fog at 06:00 UTC and low clouds at 21:00 UTC), contrary to the
Same as Fig.
The 1D-Var results are now assessed in observation space by examining innovations (differences between observed and simulated TBs) from AROME background profiles and residuals. In the following, we have only used background error covariance matrices estimated at 06:00 UTC with a fog mask, for a simplified comparison framework of the two 1D-Var systems.
Figure
Differences in observed (channels
In terms of residuals, as expected from 1D-Var systems, both experiments significantly reduce the deviations of the observed TB from those calculated using the background profiles, especially for the first eight channels sensitive to water vapour and liquid water.
We can note that the residuals are not as reduced for channel
The temperature channels used in the zenith mode are only slightly modified as the deviations from the background values are much smaller than for the other channels.
During the second half of the day, characterized by the presence of clouds around
Bias/RMSE (K) of the background and analyses produced by EXP and REF against MWR TB observations. Statistics are computed either using all data or restricted to channels 1 to 5 between 02:00 and 08:00 UTC or channels 7 to 9 between 10:00 and 24:00 UTC (these two sub-samplings are represented by the dashed rectangular boxes in Fig.
In order to quantify these results for the 9 February 2020 dataset (all hours and all channels), the bias and root mean square error (RMSE) values are computed for the background and the analyses produced by REF and EXP. The innovations are characterized by a RMSE of
After examining the fit of the two experiments to the observed TBs, we assess the corrections made in model space. Figure
Profiles of analysis increments resulting from two 1D-Var experiments: REF (left) and EXP (right) for
The temperature increments are mostly located in the lower troposphere (below 650 hPa) with a dominance of negative values of small amplitude (around 0.5 K). This is consistent with the negative innovations observed in the temperature channels, highlighting a warm bias in the background profiles. The areas of maximum cooling take place in cloud layers (inside the thick fog layer below 900 hPa until 09:00 UTC and around 700 hPa after 12:00 UTC). The increments are rather similar between REF and EXP, but the positive increments appear to be larger with EXP (e.g. at 08:00 and 20:00 UTC around 800 hPa).
Concerning the profiles associated with moist variables, the structures show similarities between the two experiments but with differences in intensity. During the night and in the morning, the
Liquid water is added in both experiments between 03:00 and 07:00 UTC, close to the surface, where the Jacobians of the most sensitive channels to
The profiles of increments for
Some radiosoundings (RSs) have been launched during the SOFOG3D IOPs.
As only one RS profile was launched at 05:21 UTC in the case study presented in the article, no statistical evaluation of the profile increments can be carried out.
However, we have conducted an evaluation of the analysis increments obtained at 05:00 and 06:00 UTC (the 1D-Var retrievals were performed at a 1 h temporal resolution in line with the operational AROME assimilation cycles) around the RS launch time. As the AROME temperature background profile extracted at 06:00 UTC was found to have a vertical structure closer to the RS launched at 05:21 UTC, Fig.
Vertical profiles of absolute temperature
The temperature increments are a step in the right direction
by cooling the AROME background profile in line with the observed RS profile.
The two 1D-Var analyses are close to each other, but the EXP analysis produces a temperature profile slightly cooler compared to the REF analysis.
In terms of absolute humidity (
The aim of this study was to examine the value of using moist-air entropy potential temperature
To that end, a 1D-Var system has been used to assimilate TB observations from the ground-based HATPRO microwave radiometer installed at Saint-Symphorien (Les Landes region in south-western France) during the SOFOG3D measurement campaign (winter 2019–2020).
The 1D-Var system has been adapted to consider these new quantities as control variables. Since the radiative transfer model needs profiles of temperature, water vapour and cloud liquid water for the simulation of TB, an adjustment process has been defined to obtain these quantities from
The new 1D-Var has produced rather similar results in terms of the fit of the analysis to observed TB values when compared to the classical one using temperature, water vapour and LWP. Nevertheless, quantitative results reveal smaller biases and RMSE values with the new system in low cloud and fog areas. We also note that atmospheric increments are somewhat different in cloudy conditions between the two systems. For example, in the stratocumulus layer that formed during the afternoon, the new 1D-Var induces larger temperature increments and reduced liquid water corrections. Moreover, its capacity to generate cloud condensates in clear-sky regions of the background has been demonstrated. As a preliminary validation, the retrieved profiles from the 1D-Var have been compared favourably against an independent observation data set (one radiosounding launched during the SOFOG3D field campaign). The new 1D-Var leads to profiles of temperature and absolute humidity slightly closer to observations in the PBL.
The encouraging results obtained from this feasibility study need to be consolidated by complementary studies. Observed TBs at lower elevation angles should be included in the 1D-Var for a better constraint on temperature profiles within the atmospheric boundary layer. Indeed, larger differences in the temperature increments might be obtained between the classical 1D-Var system and the 1D-Var system using the new conservative variables when additional elevation angles are included in the observation vector. Other case studies from the field campaign could also be examined to confirm our first conclusions.
Finally, the conversion operator could be improved by accounting not only for liquid water content
The numerical code of the RTTOV-gb model together with the associated resources (coefficient files) can be downloaded from
PMarq supervised the work of ALB, contributed to the implementation of the new conservative variables in the computation of new background error covariance matrices and participated in the scientific analysis and manuscript revision. JFM developed the conversion operator and adjoint version and participated in the scientific analysis and manuscript revision. PMart supervised the modification of the 1D-Var algorithm, supported the use of the EDA to compute the background error covariance matrices, provided the instrumental data used in the 1D-Var and participated in the manuscript revision. ALB adapted the 1D-Var algorithm and processed all the data, prepared the figures and participated in the manuscript revision. BM developed and adapted the BUMP library to compute the background error covariance matrices for the 1D-Var and participated in the manuscript revision.
The contact author has declared that neither they nor their co-authors have any competing interests.
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The authors are very grateful to the two anonymous reviewers who suggested substantial improvements to the article.
The instrumental data used in this study are part of the SOFOG3D experiment.
The SOFOG3D field campaign was supported by METEO-FRANCE and the French ANR through the grant AAPG 2018-CE01-0004.
Data are managed by AERIS, the French national centre for atmospheric data and services.
The MWR network deployment was carried out thanks to support by IfU GmbH, the University of Cologne, the Met Office, the Laboratoire d'Aérologie, Meteoswiss, ONERA and Radiometer Physics GmbH.
MWR data have been made available, quality controlled and processed in the framework of CPEX-LAB (Cloud and Precipitation Exploration LABoratory,
This research has been supported by the Agence Nationale de la Recherche (grant no. AAPG 2018-CE01-0004), the European COST actions (ES1303 TOPROF and CA18235 PROBE) and JCSDA UCAR (SUBAWD2285).
This paper was edited by Maximilian Maahn and reviewed by two anonymous referees.