Geosci. Model Dev., 9, 27212739, 2016 www.geosci-model-dev.net/9/2721/2016/ doi:10.5194/gmd-9-2721-2016 Author(s) 2016. CC Attribution 3.0 License.
Francesco De Angelis1, Domenico Cimini2,1, James Hocking3, Pauline Martinet4, and Stefan Kneifel5
1CETEMPS, University of LAquila, LAquila, Italy
2IMAA-CNR, Potenza, Italy
3Met Ofce, Exeter, UK
4Mto France CNRM/GAME, Toulouse, France
5Institute for Geophysics and Meteorology, University of Cologne, Cologne, Germany
Correspondence to: Francesco De Angelis ([email protected])
Received: 23 March 2016 Published in Geosci. Model Dev. Discuss.: 9 May 2016 Revised: 14 July 2016 Accepted: 27 July 2016 Published: 19 August 2016
Abstract. Ground-based microwave radiometers (MWRs) offer a new capability to provide continuous observations of the atmospheric thermodynamic state in the planetary boundary layer. Thus, they are potential candidates to supplement radiosonde network and satellite data to improve numerical weather prediction (NWP) models through a variational assimilation of their data. However in order to assimilate MWR observations, a fast radiative transfer model is required and such a model is not currently available. This is necessary for going from the model state vector space to the observation space at every observation point. The fast radiative transfer model RTTOV is well accepted in the NWP community, though it was developed to simulate satellite observations only. In this work, the RTTOV code has been modied to allow for simulations of ground-based upward-looking microwave sensors. In addition, the tangent linear, adjoint, and K-modules of RTTOV have been adapted to provide Jacobians (i.e., the sensitivity of observations to the atmospheric thermodynamical state) for ground-based geometry. These modules are necessary for the fast minimization of the cost function in a variational assimilation scheme. The proposed ground-based version of RTTOV, called RTTOV-gb, has been validated against accurate and less time-efcient line-by-line radiative transfer models. In the frequency range commonly used for temperature and humidity proling (2260 GHz), root-mean-square brightness temperature differences are smaller than typical MWR uncertainties ( 0.5 K)
at all channels used in this analysis. Brightness temperatures
RTTOV-gb adapting the fast radiative transfer model RTTOV for the assimilation of ground-based microwave radiometer observations
(TBs) computed with RTTOV-gb from radiosonde proles have been compared with nearly simultaneous and co-located ground-based MWR observations. Differences between simulated and measured TBs are below 0.5 K for all channels except for the water vapor band, where most of the uncertainty comes from instrumental errors. The Jacobians calculated with the K-module of RTTOV-gb have been compared with those calculated with the brute force technique and those from the line-by-line model ARTS. Jacobians are found to be almost identical, except for liquid water content Jacobians for which a 10 % difference between ARTS and RTTOV-gb at transparent channels around 450 hPa is attributed to differences in liquid water absorption models. Finally, RTTOV-gb has been applied as the forward model operator within a one-dimensional variational (1D-Var) software tool in an Observing System Simulation Experiment (OSSE). For both temperature and humidity proles, the 1D-Var with RTTOV-gb improves the retrievals with respect to the NWP model in the rst few kilometers from the ground.
1 Introduction
The planetary boundary layer (PBL) is the single most important undersampled part of the atmosphere (National Research Council, 2008). While the thermodynamical state of the atmosphere is well measured at the surface by ground
Published by Copernicus Publications on behalf of the European Geosciences Union.
2722 F. De Angelis et al.: RTTOV-gb
in situ sensors and in the upper troposphere by satellite sounders, there is currently an observational gap in the PBL.According to the WMO Statement Of Guidance For Global Numerical Weather Prediction (WMO, 2014), there are four priorities for atmospheric variables not adequately measured in the PBL: wind proles, temperature and humidity proles in cloudy areas, precipitation, and snow mass. Ground-based microwave radiometers (MWRs) provide temperature and humidity proles in both clear- and cloudy-sky conditions with high temporal resolution and low-to-moderate vertical resolution, with information mostly residing in the PBL (Ci-mini et al., 2006). Ground-based MWRs offer to bridge the current observational gap by providing continuous temperature and humidity proles in the PBL. When combined with satellite observations, the total information content of the derived atmospheric proles can be signicantly enhanced (Ebell et al., 2013). The data assimilation (DA) of MWR observations into numerical weather prediction (NWP) models may be particularly important in nowcasting and severe weather (fog, convection, turbulence, etc.) initiation. The assimilation of MWR data has been recently investigated (Ci-mini et al., 2014; Caumont et al., 2016), assimilating temperature and humidity prole retrievals from a network of13 MWR members from the international MWRnet network (Cimini et al., 2012). Results showed neutral-to-positive impact. However, these experiments used retrieved variables (temperature and humidity proles), whereas the assimilation of raw measurement (TBs) is found to have more impact on the NWP forecasts in the case of satellite data (Geer et al., 2008).
Accordingly, a potential way to increase the impact of MWR DA is to assimilate measured radiance (or brightness temperatures, TBs) directly instead of retrieved proles.With this type of assimilation, all the degrees of freedom for signal of MWRs (Lhnert et al., 2009) can be used to improve the NWP model forecast in the PBL. In order to assimilate TB, a radiative transfer (RT) forward model is needed.The RT model allows the TB to be computed for selected radiometer channels based on the NWP model state vector.TB differences between the modeled and measured observations can be used within a variational scheme (Courtier et al., 1998) that takes the corresponding uncertainties into account to retrieve temperature and humidity proles in the rst few kilometers from the ground, where MWRs provide the maximum information content. In addition, the Jacobians (i.e., partial derivatives with respect to the state vector) of the radiative transfer model are required to minimize the distances of the atmospheric state from both the rst guess and the observations in a variational data assimilation process. These Jacobians represent the sensitivities of observations to the atmospheric thermodynamical state.
The fast RT model RTTOV (Radiative Transfer for the TIROS Operational Vertical Sounder (TOVS)) is widely used to simulate radiance from space-borne passive sensors. RTTOV has already been used for many years by many na-
tional meteorological services for assimilating downward-looking observations from visible, infrared, and microwave radiometers, spectrometers, and interferometers (Hocking et al., 2015, and references therein) aboard satellite platforms.The FORTRAN-90 code originally developed at ECMWF in the early 90s (Eyre, 1991) was intended for TOVS direct radiance assimilation within three- and four-dimensional variational analysis schemes (3DVAR, 4DVAR). Subsequently the original code has gone through several developments (e.g., Saunders et al., 1999; Matricardi et al., 2001), more recently within the EUMETSAT NWPSAF, of which RTTOV v11.3 is the latest version available. Since its rst implementation and throughout its current version, RTTOV has been developed and exploited for satellite observation perspective only. The model allows rapid simulations of radiance for a suite of passive sensors given the atmospheric state vector, i.e., proles of temperature, gas concentration, cloud liquid water content, and surface properties. The only one variable gas needed for RTTOV v11 in the microwave band is water vapor. An important feature of RTTOV is that, in addition to the forward (or direct) radiative transfer, it also computes the Jacobians,i.e., the gradient of the radiance with respect to the state vector at the location in state space specied by the input state vector values. The Jacobians are calculated in tangent linear (TL), adjoint (AD), and K-modules of RTTOV.
There are other fast RT models used by the NWP community for satellite data assimilation, like the Community Radiative Transfer Model (CRTM Ding et al., 2011). However, to our knowledge no fast RT model is currently available to simulate ground-based radiometric observations. In this work, version 11.2 of RTTOV has been modied to handle ground-based microwave radiometer observations.The efforts for adapting RTTOV to ground-based observations started within the COST action ES1202 (EG-CLIMET) and have been continued within the COST action ES1303 (TOPROF). The ground-based version of RTTOV developed here, called RTTOV-gb, is able to simulate brightness temperatures from ground-based upward-looking microwave radiometers. In addition, the TL, AD, and K-modules of RTTOV have been adapted to provide Jacobians for ground-based geometry. We believe that the availability of RTTOV-gb with its K-module will enable more widespread and better use of MWR observations in NWP models.
This paper introduces RTTOV-gb, the ground-based version of the fast radiative transfer model RTTOV. In Sect. 2 we describe the modications made to the original RTTOV code for the ground-based radiative transfer calculation. Section 3 discusses the performance of RTTOV-gb by evaluating its simulations against those from accurate line-by-line RT models (3.1), against ground-based real MWR observations(3.2), against analytic Jacobian calculations (3.3), and nally within a one-dimensional variational (1D-Var) assimilation scheme (3.4). Section 4 summarizes the ndings and draws the nal conclusions.
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2 The formulation of the radiative transfer model
2.1 Radiative transfer model
Given a state vector x (the atmospheric thermodynamical state prole in radiative transfer problem), the radiance vector (or brightness temperature) y is computed as
y = H(x), (1) where H is the radiative transfer model (also referred to as the observation operator).
The core of RTTOV-gb simulates ground-based radiometer radiance using an approximated form of the radiative transfer equation (RTE) for ground-based (upward-looking) observation geometry:
LATM,i = i,toa Bi (TBKG) +
1
[integraldisplay]
i,toa
level j = N, PN = 1050 hPa, surface air temperature
TN = TS, iN = 1 for all channels.
For the ground-based perspective and each channel (omitting the i index for convenience), we dene
8 <
:
[Delta1]j = j+1 j
[Delta1]Bj = Bj Bj+1
[Delta1]dj = dj dj+1
, (3)
where [Delta1]dj is the optical depth of the single layer j, and dj is the level-to-surface optical depth.
The contribution of the cosmic background radiation is
LCOSMIC = 1 B (TBKG) with 1 = toa. (4)
The atmospheric contribution is
LA =
M
[integraldisplay]
[integraldisplay]
j
Bd) + ST, (5)
j+1
X1 j=M
(
Bi (T )d, (2)
where LATM,i is the radiance at the ground for channel i, neglecting scattering effects, Bi is the Planck radiance at channel i for a scene temperature T , i,toa is the transmittance from the surface to the top of the atmosphere, and TBKG is the microwave cosmic background temperature (2.728 K). Note that in the spectral range under consideration (2060 GHz), scattering is negligible for particles of the size of atmospheric molecules and cloud droplets, and even for larger ice and snow particles (Kneifel et al., 2010). From a ground-based perspective, the transmittances and optical depths are accumulated from the surface to the space instead of from the space to the surface as in the original RTTOV satellite perspective. Consequently, several subroutines have been modied to reverse the accumulation of transmittances and optical depths through the atmospheric path (see Sect. 6).
The RTE (2) is valid for both clear- and cloudy-sky conditions because in the microwave band, RTTOV takes the liquid water as an absorbing species into account, and its effects are included through a contribution to the transmittance prole. The rst term of the right-hand side of the RTE (2) is the cosmic background radiation; the second term is the atmospheric contribution.
The RTE (2) has been numerically solved over N atmospheric levels which are numbered from the top of the atmosphere as follows:
level j = 1, pressure Pj = 0.005 hPa, temperature Tj =
T1, transmittance ij = i,toa for channel i; levels from j = 2 to j = N 1, Pj are pressures of the
xed-pressure levels, ij is the surface-to-level transmittance for channel i;
level j = M, the rst level which lies strictly above
the input 2 m pressure (i.e., M <= N and PM < P2m),
ij = i,M for channel i;
B (T )d + ST =
LEV=1
where
[integraldisplay]
j
j+1
Bd = j+1Bj+1 j Bj +
1[Delta1]dj [Delta1]Bj [Delta1]j
= [Delta1]j [Bj+1 + [Delta1]Bj
1[Delta1]dj ] j [Delta1]Bj , (6)
and ST is the contribution of the rst layer above the surface:
ST = BS(1 M) (BM BS) + (BM BS)
(1 M)
1dM , (7)
with BS the Planck function evaluated at the input 2 m temperature.
In Eq. (4) we have used a parameterization of the Planck function (i.e., the so-called linear-in-tau assumption, where tau means the optical depth of the single layer, corresponding to [Delta1]d in the notation used in this study). In the linear-in-tau assumption, the source function throughout the layer is linear with the optical depth of the layer (Saunders, 2010):
B [T ([Delta1]d)] = Bj+1 + (Bj Bj+1)
[Delta1]d
[Delta1]dj , (8)
where Bj is the Planck function for the top of the layer, Bj+1
is the Planck function at the bottom of the layer, and [Delta1]dj is
the optical depth of the layer. In the ground-based perspective, [Delta1]d goes from 0 to [Delta1]dj from the bottom to the top of the layer.
The radiance for each channel i is then converted to an equivalent black-body temperature, which is usually called brightness temperature (TB), using the inverse Planck function.
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2724 F. De Angelis et al.: RTTOV-gb
Figure 1. Vertical spacing of proles levels used for RTTOV in this analysis. Level altitudes and altitude differences between levels are reported respectively with blue and green lines. Note that the y axis is in logarithmic scale.
2.2 The input atmospheric proles and near-surface variables
The input prole data may be supplied on an arbitrary set of pressure levels. These consist of vertical proles of temperature (K) and humidity (ppmv) for clear-sky conditions, and additional cloud liquid water content (CLW in kg kg1)
proles for simulating cloudy conditions. In addition, pressure, temperature, and humidity values at 2 m altitude are required. The transmittance calculations described below are performed using atmospheric layers bounded by a number of xed pressure levels. RTTOV-gb interpolates the input proles to the xed pressure levels for the transmittance calculation, but note that the RTE is integrated in the pressure levels supplied by the user (Hocking, 2014).
Currently RTTOV-gb uses xed 101 pressure levels from0.005 to 1050 hPa for the transmittance calculation. These levels have been specically selected for the ground-based perspective to be denser close to ground (34 levels below 2 km) than those usually used for the satellite perspective. Moreover they were chosen to improve the accuracy of the optical depth prediction scheme used by RTTOV-gb compared to that obtained with the levels used for satellite simulations. The vertical spacing of levels is shown in Fig. 1 in terms of level altitude differences.
2.3 Transmittance model
The main variable computed in the radiative transfer model is the atmospheric optical depth for each channel i and for each atmospheric layer j. The optical depths depend on the viewing angle of the instrument, pressure, temperature, and concentrations of the absorbing species. The optical depth differ-
ences between adjacent pressure levels are obtained through a linear combination in Xkj , the so-called predictors (j being the level and k the number of predictors, from 1 to NP ).
The predictors are derived from the input state vector prole and depend on the elevation angle and pressure P , temperature T , and specic humidity q at the considered level and the level above that. The optical depth from the surface to the level j in channel i along a path at an angle from the vertical, dij , is obtained as follows:
dij = di,j+1 +
P
Xk=1aijkXkj (P,T ,q, ), (9)
with aijk the regression coefcients between optical depths and predictors.
The contribution of the water vapor to the optical depth is treated separately from that of uniformly mixed gases although they are calculated with two algorithms of the same form. There are three types of predictors for satellite perspective, predictors 7 (Matricardi et al., 2001), 8 (Matricardi, 2005), and 9 (Saunders, 2010), each of which is better suited for a specic application. The predictors used in RTTOV to parameterize the optical depths refer to the reference temperature and specic humidity proles (i.e., the average of the training prole set, respectively T refj and qrefj). Additionally, the number of predictors depends on the selected gas.
We found the predictors 7 to give the best results for the ground-based geometry, and thus they are used herewith to train RTTOV-gb. The predictors 7 and the prole variables involved in the predictors calculation are listed in Appendix A. Note that predictors 7 were originally developed for satellite simulations up to 60 zenith angles and as such, the errors in the optical depth prediction increase for zenith angles above 75 (i.e., for elevation angles below 15 ).
For MWR observations of the PBL thermodynamics, these scanning angles turn out to be crucial because of the information carried by opaque channels on the PBL temperature prole. Thus, it is foreseen that an alternative set of predictors, specic for low-elevation angles in the ground-based geometry, may be worth investigating and developing in the future, though it is beyond the scope of this study.
The coefcients aikj are calculated by linear regression of
di,j di,j+1
[bracerightbig]
against Xkj . For the regression, dij are calculated using a line-by-line (LBL) model for a set of atmospheric proles. LBL RT models provide accurate calculation of the atmospheric transmittances and radiance, given the atmospheric prole of gas concentrations, and predened spectral frequency grid. The LBL optical depths must cover the full spectral range of all the radiometer channels of interest and provide a sufcient resolution to represent the transmittances in the channel spectral bands accurately. The LBL model described by Rosenkranz (1998; R98 herewith) has been used for gas absorption to calculate the clear-sky transmittances needed in the RTTOV-gb regression coefcients computation. Here we use 83 proles from an NW-
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y @x1@y , y@x2@y , y@x3@y ... y@xN@y[bracketrightbigg](15)
For very large systems, it may be not feasible to calculate the full Jacobian matrix K, and the tangent linear and adjoint operations are computed instead.
The TL code is derived directly from the forward model because it represents the analytic derivative of the radiance (forward model outputs) with respect to the atmospheric state vector x. The AD code is derived from the TL code. Finally, the K code is obtained from the AD code distributing the AD level derivatives through the number of channels. Before running TL, AD, and K models, the direct model needs to be run because many of the intermediate variables calculated by the direct model are needed by the TL, AD, and K-modules.
3 Performance of RTTOV-gb
The performance of RTTOV-gb has been tested in four different ways, reported in the following subsections: validation against the LBL RT model used as reference for the training and against another independent reference LBL RT model(3.1); a comparison of TB simulated with RTTOV-gb from a radiosonde prole dataset with nearly co-located MWR measurements (3.2); a comparison of Jacobians calculated with the RTTOV-gb K-module and the brute force method, and also with Jacobians computed with an analytical model (3.3); the exploitation of RTTOV-gb as a forward model operator within a one-dimensional variational scheme (3.4).
3.1 Comparison with line-by-line model computed radiance
To compare RTTOV-gb against the LBL model adopted for the regression training, we computed clear-sky TB with both RTTOV-gb and R98 at selected channels from the set of 83 atmospheric proles used in the training phase. Resulting TB differences are a measure of the regression error.Here we focus on the systematic (bias) and root-mean-square (rms) TB differences. We consider 14 channels commonly used by commercial MWRs, in particular the Humidity And Temperature PROler (HATPRO, Rose et al., 2005): 22.24,23.04, 23.84, 25.44, 26.24, 27.84, 31.40, 51.26, 52.28, 53.86,54.94, 56.66, 57.30, and 58.00 GHz. Channels from 22 to31 GHz are in the so-called K-band, while channels from 51 to 58 GHz are in the so-called V-band.
Table 1 shows bias and rms at four elevation angles (90, 30, 19, and 10 ) and four elevation angle combinations used
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PSAF prole dataset interpolated on 101 pressure levels, already used for training RTTOV. It is important to emphasize that this prole set was carefully chosen from a set of more than 100 million proles to represent a wide range of physically realistic atmospheric states (Matricardi, 2008).Transmittances are computed for six selected scanning angles which are discussed in Sect. 3.1. We limit the lowest elevation angle used in the training phase to 10 because of the limitation of the predictors 7 that has already been mentioned.
If the optical depths for uniformly mixed gases and water vapor are dMij and dWij respectively, the total optical depth is
dij = dMij + dWij . (10)
Then, optical depths are converted to transmittances:
ij = exp(dij ). (11)
Finally, RTTOV-gb computes the output radiance and TB from the derived transmittances and the input vertical temperature prole using the radiative transfer Eq. (2).
2.4 Jacobians: tangent linear, adjoint, and gradient matrix models
The Jacobian matrix K gives the change in radiance y for a change in any element of the state vector x, assuming a linear relationship about a given atmospheric state x0:
y = K(x0) x. (12)
The elements of K contain the partial derivatives yi/ xj , where the subscript i refers to the channel and j to the layer number. The Jacobian provides the radiance sensitivity for each channel given unit perturbations at each level of the state vector and in each of the surface parameters. It shows clearly, for a given prole, which layers in the atmosphere are most sensitive to changes in temperature and variable gas concentrations for each channel. The K-module of RTTOV computes the K(x0) matrix for each input prole. Alternatively, the Jacobians can be computed with the so-called brute force (BF) method, where K is estimated by perturbing each element of the atmospheric state vector, repeating the RTTOV direct module iteratively. However, the calculations of the Jacobians with the BF method are slower and less rigorous than with the K-module of RTTOV.
It is not always necessary to store and access the full matrix K; thus, the RTTOV package has routines to compute the tangent linear only, i.e., the change in radiance yi for a given change in atmospheric prole x around an initial atmospheric state x0.
y (x0) =
x @y1@x , x@y2@x , x@y3@x ... x @ynchan @x
Similarly, the adjoint routines compute the change in any quantity of the state vector (e.g., T , q, surface variables etc.) x around an assumed atmospheric state x0, given a change in the radiance y.
rx
= rxy ry = K(x0)T ry (14)
x (x0) =
[bracketrightbigg]
[bracketleftbigg]
@ @x1 ,
(13)
with @
@x = rx =
@
@x2 ,...,
@ @xN
[bracketrightbigg]
2726 F. De Angelis et al.: RTTOV-gb
Table 1. Statistics for the comparison between RTTOV-gb and the line-by-line model R98 (Rosenkranz, 1998) at elevation angles 90, 30, 19, and 10 (R98 minus RTTOV-gb). The HATPRO channel number (Chan no.), the channel central frequency, bias, and rms for each RTTOV training conguration are reported. The values which are larger than 0.5 K are highlighted in bold.
Bias (K) rms (K)
Elevation angle 90
Chan no. Frequency (GHz) 9026 9016 9010 905 9026 9016 9010 905
1 22.24 0.007 0.016 0.004 0.170 0.033 0.059 0.047 0.373
2 23.04 0.002 0.009 0.011 0.159 0.029 0.052 0.050 0.352
3 23.84 0.005 0.002 0.023 0.132 0.028 0.043 0.053 0.308
4 25.44 0.009 0.011 0.029 0.087 0.029 0.036 0.056 0.224
5 26.24 0.009 0.011 0.028 0.074 0.029 0.035 0.054 0.195
6 27.84 0.008 0.012 0.025 0.059 0.029 0.034 0.050 0.158
7 31.40 0.009 0.011 0.023 0.049 0.033 0.038 0.049 0.128
8 51.26 0.017 0.024 0.043 0.101 0.175 0.176 0.159 0.244
9 52.28 0.021 0.025 0.039 0.070 0.202 0.201 0.186 0.246
10 53.86 0.010 0.012 0.015 0.001 0.116 0.118 0.115 0.122 11 54.94 0.002 0.003 0.004 0.008 0.023 0.023 0.023 0.023
12 56.66 0.001 0.001 0.001 0.001 0.007 0.007 0.007 0.007 13 57.30 0.001 0.001 0.001 0.001 0.005 0.005 0.005 0.005 14 58.00 0.000 0.001 0.001 0.001 0.004 0.004 0.004 0.004
Elevation angle 30
Chan no. Frequency (GHz) 9026 9016 9010 905 9026 9016 9010 905
1 22.24 0.002 0.027 0.020 0.036 0.033 0.047 0.046 0.180
2 23.04 0.000 0.025 0.019 0.029 0.030 0.047 0.043 0.173
3 23.84 0.002 0.020 0.016 0.014 0.026 0.040 0.040 0.162
4 25.44 0.004 0.013 0.013 0.007 0.024 0.037 0.037 0.150
5 26.24 0.004 0.010 0.012 0.012 0.023 0.036 0.035 0.145
6 27.84 0.003 0.008 0.011 0.016 0.024 0.037 0.033 0.137
7 31.40 0.004 0.006 0.010 0.019 0.155 0.043 0.036 0.131
8 51.26 0.010 0.018 0.027 0.079 0.029 0.171 0.162 0.211
9 52.28 0.016 0.019 0.026 0.073 0.138 0.149 0.143 0.174
10 53.86 0.003 0.007 0.008 0.005 0.026 0.028 0.028 0.027
11 54.94 0.001 0.001 0.001 0.001 0.007 0.007 0.007 0.007
12 56.66 0.000 0.000 0.000 0.000 0.002 0.002 0.002 0.002
13 57.30 0.000 0.000 0.000 0.000 0.001 0.001 0.001 0.001
14 58.00 0.000 0.000 0.000 0.000 0.001 0.001 0.001 0.001Elevation angle 19
Chan no. Frequency (GHz) 9026 9016 9010 905 9026 9016 9010 905
1 22.24 0.050 0.004 0.065 0.203 0.078 0.044 0.086 0.317
2 23.04 0.053 0.005 0.070 0.189 0.079 0.042 0.089 0.298
3 23.84 0.056 0.007 0.074 0.158 0.083 0.038 0.090 0.259
4 25.44 0.046 0.007 0.070 0.099 0.089 0.036 0.087 0.192
5 26.24 0.039 0.006 0.066 0.080 0.089 0.036 0.084 0.171
6 27.84 0.028 0.005 0.059 0.055 0.091 0.036 0.078 0.149
7 31.40 0.018 0.004 0.052 0.035 0.103 0.043 0.077 0.139
8 51.26 0.020 0.013 0.018 0.003 0.139 0.128 0.132 0.152
9 52.28 0.031 0.012 0.004 0.021 0.085 0.085 0.085 0.097
10 53.86 0.004 0.001 0.000 0.003 0.013 0.010 0.010 0.011
11 54.94 0.002 0.000 0.000 0.001 0.005 0.003 0.003 0.004 12 56.66 0.000 0.000 0.000 0.000 0.001 0.001 0.001 0.001 13 57.30 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 14 58.00 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
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Table 1. Continued.
Bias (K) rms (K)
Elevation angle 10
Chan no. Frequency (GHz) 9026 9016 9010 905 9026 9016 9010 905
1 22.24 0.299 0.324 0.626 0.930 0.428 0.381 0.681 1.035
2 23.04 0.297 0.317 0.632 0.955 0.461 0.369 0.685 1.027
3 23.84 0.391 0.312 0.648 0.998 0.662 0.356 0.698 1.067
4 25.44 0.544 0.294 0.664 1.055 1.214 0.343 0.716 1.128
5 26.24 0.573 0.284 0.663 1.065 1.414 0.342 0.718 1.143
6 27.84 0.592 0.270 0.659 1.075 1.685 0.349 0.716 1.159
7 31.40 0.594 0.260 0.680 1.129 2.023 0.377 0.731 1.205
8 51.26 0.000 0.088 0.337 0.609 0.272 0.103 0.350 0.633
9 52.28 0.021 0.029 0.106 0.202 0.083 0.034 0.112 0.214
10 53.86 0.022 0.000 0.007 0.014 0.037 0.003 0.011 0.021
11 54.94 0.005 0.000 0.002 0.004 0.009 0.001 0.003 0.006
12 56.66 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.001
13 57.30 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001
14 58.00 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Figure 2. (a1) TB at K-band channels (2035 GHz) computed by RTTOV-gb (red stars) and LBL R98 (black stars) from prole no. 8 of the dependent set. (a2) Same as (a1), but for V-band channels (5060 GHz). (b1) TB differences (R98 minus RTTOV-gb) at K-band channels. (b2) Same as (b1), but for V-band channels.
for regression training (predictors 7 are used). This comparison allow us to investigate the best performing combination. The four sets of elevation angles are 905342353026 ;
904230241916 ; 904230241910 ; and 9042 3019105 .
Bias and rms are lower than the manufacturer error specication for HATPRO channels ( 0.5 K Rose et al., 2005)
for all the considered training sets and elevation angles, with the exception of 2231 GHz channels at 10 elevation angle with the training sets 9026, 9010, and 905 . This result seems to conrm that predictors 7 are not ideal for elevation angles lower than 15 . However, it is encouraging to note that even at 10 , bias and rms are within the instrumental error for all the channels when the training set 9016 is adopted. Note that the agreement at low-elevation angles is better for the V-band opaque channels, which are most important for
PBL temperature retrieval. Table 1 shows that the best among the considered training congurations is the set of elevation angles from 90 to 16 . Somewhat surprising, this conguration gives acceptable results even at 10 , despite this elevation angle being outside the training angle range.
Figure 2 shows two spectra computed at HATPRO channels by RTTOV-gb and LBL R98 for the same atmospheric prole belonging to the dependent set. For this particular case, TB differences between the two models are within0.1 K for all channels.
For the whole 83-prole dataset, Fig. 3 shows statistics
(bias, rms, and maximum value) of the LBL R98 minus
RTTOV-gb TB difference at four elevation angles (90, 30, 19, and 10 ). The best training conguration determined above (elevation angles from 90 to 16 ) is used. At 90 elevation, bias and rms are respectively less than 0.030 and 0.060 K for
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2728 F. De Angelis et al.: RTTOV-gb
Figure 3. Bias (black solid line), rms (blue dashed line), and maximum (cyan dashed line) of TB difference between RTTOV-gb and LBL R98 (Rosenkranz, 1998) for the dependent 83-prole set and the best training conguration (R98 minus RTTOV-gb). Top panels: K-band channels; bottom panels: V-band channels. Panels (a),(b),(c), and (d) report results at 90, 30, 19, and 10 elevation angle, respectively. Note that the top panel (d) has a different y axis scale with respect to the other top panels.
K-band (2231 GHz), while they are 0.003 and 0.025 K for the V-band opaque channels (5458 GHz). For these channels the maximum difference does not exceed 0.15 K. The agreement is slightly worse at transparent V-band channels (5154 GHz), with bias, rms, and maximum difference respectively within 0.03, 0.2, and 0.6 K. The larger discrepancies at transparent V-band channels are probably due to the combined inuence of temperature and water vapor, which likely decreases the correlation of layer opacity with the two thermodynamical variables. Similar results are found for other elevation angles, such as 30 and 19 . Note that the error statistics at 90 elevation (i.e., zenith) are about 1 order of magnitude larger than the analogous statistics of the original nadir-looking RTTOV (Saunders, 2002, 2010). We believe the reason is the behavior of the two terms contributing to the total radiance (Eq. 2), i.e., the background and the atmospheric contributions. Uncertainty in atmospheric optical depth, as those induced by regression, will inuence the total radiance through the effects on these two terms. For the satellite (downward-looking) case, these effects tend to compensate due to a warmer background (e.g., overestimated optical depths cause more emission from the atmosphere but
less contribution from the relative warmer background). Conversely, for the ground-based perspective there is no compensation of the two terms because of the cold cosmic background (e.g., overestimated optical depths causes more emission from the atmosphere and less contribution from the relative colder background).
Figure 3 shows bias, rms, and maximum difference respectively up to 0.3, 0.4, and 1.5 K for K-band channels at 10
elevation. These are signicantly larger compared to higher elevation angles. This is attributed to the use of predictors 7, which are not designed for elevation angles lower than 15 .
This may also be due to the fact that 10 is outside the elevation angle range used in the training conguration (9016 ).
However, Table 1 shows that extending the range of training elevation angles to 10 or less generally degrades statistics.
In any case, we highlight that the rms errors in Fig. 3 are smaller than the uncertainty associated with TB observations ( 0.5 K) for all channels and all elevation angles.
Similarly, RTTOV-gb has been compared with the reference LBL model using an independent set of 52 proles(i.e., not used for training). The same 101 pressure levels described earlier are used. Bias, rms, and maximum of LBL
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son et al., 2011; Eriksson and Buehler, 2015), and a completely different prole dataset. In this test, HATPRO observations are simulated using RTTOV-gb and ARTS from a set of 1327 thermodynamic proles from the AROME analysis over Bordeaux from April to October 2014. AROME is the French convective-scale NWP model with a 2.5 km horizontal grid mesh developed by Mto France (Seity et al., 2010). Both clear- and cloudy-sky conditions are considered. This dataset, which is limited in space, time, and thus in atmospheric conditions, was chosen to demonstrate the performance of RTTOV-gb in typical deployment environment.Since the goal of this analysis is to test the fast RT modeling (RTTOV-gb) with respect to accurate LBL calculation, all other settings being equal, ARTS settings for absorption model have been selected to adopt the same absorption model as RTTOV-gb as much as possible: R98 for oxygen and water vapor absorption, and the model described in Liebe et al. (1993) for cloud liquid water (referred as MPM93 within ARTS). Note that MPM93 is the only option for liquid water absorption available in ARTS. Conversely RTTOV-gb is consistent with the original RTTOV, which adopts a combination of Liebe et al. (1991) and Lamkaouchy et al. (1997) models (English et al., 1999).
This comparison is presented in Fig. 5 in terms of bias, standard deviation (SD), and rms of ARTS minus RTTOV-gb TB differences at 90 elevation angle. Here we have discarded TB differences that are larger than 3 SD from the mean (21 proles out of 1327). Biases less than 0.18 K for K-band and less than 0.08 K for opaque V-band channels are found. The rms and standard deviation are close, ranging from 0.1 to 0.25 K for K-band channels, and within 0.1 K
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Table 2. Statistics for the comparison between RTTOV-gb and the line-by-line model R98 (Rosenkranz, 1998) with the best RTTOV training conguration and the independent prole set (R98 minus RTTOV-gb). HATPRO channel number (Chan no.), the channel central frequency, bias, and rms at elevation angles 90, 30, 19, and 10 are reported.
Training conguration: elevation angles from 90 to 16
Bias (K) rms (K)
Chan no. Frequency (GHz) 90 30 19 10 90 30 19 10
1 22.24 0.008 0.021 0.004 0.282 0.049 0.045 0.042 0.326
2 23.04 0.002 0.020 0.006 0.276 0.042 0.045 0.042 0.319
3 23.84 0.007 0.017 0.008 0.273 0.035 0.044 0.045 0.320
4 25.44 0.018 0.001 0.009 0.257 0.032 0.042 0.051 0.339
5 26.24 0.011 0.007 0.009 0.247 0.031 0.041 0.052 0.342
6 27.84 0.009 0.004 0.008 0.232 0.031 0.040 0.053 0.346
7 31.40 0.008 0.001 0.010 0.230 0.036 0.046 0.061 0.365
8 51.26 0.004 0.017 0.015 0.094 0.156 0.159 0.127 0.115
9 52.28 0.004 0.009 0.004 0.033 0.169 0.131 0.076 0.039
10 53.86 0.001 0.002 0.001 0.002 0.095 0.025 0.015 0.012
11 54.94 0.002 0.000 0.000 0.000 0.023 0.011 0.008 0.003
12 56.66 0.002 0.000 0.000 0.000 0.010 0.004 0.002 0.000 13 57.30 0.001 0.000 0.000 0.000 0.009 0.003 0.001 0.000 14 58.00 0.001 0.000 0.000 0.000 0.008 0.002 0.001 0.000
R98 minus RTTOV-gb TB differences are shown in Fig. 4.
Results are for the best training conguration and for elevation angles 90, 30, 19, and 10 . Statistics are similar to those obtained with the dependent prole set. In this case, however, the error statistics are of the same order of magnitude as the analogous performance of the original nadir-looking RTTOV with an independent prole set (Saunders, 2002, 2010).For elevation angles down to 19 , biases range from less than 0.002 K for the opaque channels to 0.020 K for K-band, while rms is less than 0.060 K for K-band and 0.025 K for the opaque channels. The maximum TB differences do not exceed 0.5 K. Similarly to the test with the dependent prole set, larger discrepancies are found in the transparent V-band channels (5154 GHz) and for K-band channels at 10 elevation. All the statistics obtained with the independent prole set and the best training conguration are summarized in Table 2. Consistently with the dependent test, the independent test in Fig. 4 and Table 2 conrms that the rms errors are smaller than the uncertainty associated with TB observations for all channels and all elevation angles.
The previous tests against the reference LBL R98 model have also been performed at the 22 frequency channels (2260 GHz) used by another commercial microwave radiometer, the MP-3000A (Cimini et al., 2011, 2015). Statistics, reported in Table 3 in terms of bias and rms, are similar to those obtained for HATPRO channels, at both K- and V-band.
Note that LBL R98 is the model used to train the regression scheme. In order to perform a completely independent test, we compare RTTOV-gb with an independent reference radiative transfer model, the Atmospheric Radiative Transfer Simulator (ARTS, Buehler et al., 2005; Eriks-
2730 F. De Angelis et al.: RTTOV-gb
TB observations. From the three tests above, we can conclude that in the elevation angle range from 90 to 10 , the forward model error due to the use of the fast RT with respect to the reference LBL model is within the instrument uncertainty. This conrms that RTTOV-gb can be safely deployed in place of an LBL model into variational assimilation schemes.
3.2 Comparison with real observations
Another way to evaluate RTTOV-gb is to compare TB simulated from radiosonde proles with TB measured by a nearly co-located microwave radiometer. This comparison provides an end-to-end evaluation of the model, though radiosonde drift, MWR calibration, nite beamwidth, discretization, and instrumental noise all contribute to the total uncertainty. Nevertheless, observations minus background model (O B)
differences are the primary input for direct radiance assimilation into an NWP model, and thus need to be investigated and understood. For this analysis, we exploit a dataset of 365 radiosonde proles collected over Bordeaux from April to October 2014, together with the nearly simultaneous TB observed by a ground-based microwave radiometer (HAT-
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Figure 4. Same as Fig. 3 but for the independent 52-prole set (R98 minus RTTOV-gb). Top panels: K-band channels; bottom panels: V-band channels. Panels (a),(b),(c), and (d) report results at 90, 30, 19, and 10 elevation angle, respectively. Note that top panel (d) has a different y axis scale to the other top panels.
for V-band opaque channels (5558 GHz). Similar to previous tests, larger discrepancies are found in the more transparent V-band channels (5154 GHz) with an rms error up to 0.5 K at 51 GHz in cloudy-sky; but here the rms is dominated by a bias contribution induced by systematic differences found between LBL and ARTS at these three channels ( 0.30.5 K, not shown). This may be caused by small
differences in the implementation of the R98 gas absorption and/or the radiative transfer code. This issue is currently under investigation, though its understanding goes beyond the scope of this paper. Comparing Figs. 4 and 5, we notice slightly larger differences (by 0.10.2 K) in the RTTOV-gb vs. ARTS than in the RTTOV-gb vs. R98 tests. We attribute this to the fact that RTTOV-gb is totally independent of ARTS and moreover to the specic prole dataset, which likely introduces biases with respect to the RTTOV-gb training climatology. Note that TB differences for all the channels are of the same order of magnitude as those found between ARTS and the original nadir-looking RTTOV (Buehler et al., 2006). This demonstrates comparable capabilities between RTTOV-gb and the original version of RTTOV. The rms TB differences between RTTOV-gb and ARTS at 90 elevation are within 0.5 K, thus below the uncertainty associated with
F. De Angelis et al.: RTTOV-gb 2731
Table 3. Statistics for the comparison between RTTOV-gb and the line-by-line model R98 at MP-3000A channels with the best RTTOV training conguration, for both the dependent (top) and independent (bottom) prole set (R98 minus RTTOV-gb). MP3000A channel number (Chan no.), the channel central frequency, bias, and rms at elevation angles 90, 30, 19, and 10 are reported.
Dependent prole set
Bias (K) rms (K)
Chan no. Frequency (GHz) 90 30 19 10 90 30 19 10
1 22.23 0.016 0.027 0.004 0.319 0.059 0.047 0.044 0.376
2 22.50 0.015 0.026 0.004 0.321 0.058 0.047 0.044 0.378
3 23.03 0.009 0.025 0.005 0.318 0.053 0.045 0.042 0.370
4 23.83 0.002 0.020 0.007 0.313 0.043 0.040 0.038 0.357
5 25.00 0.010 0.014 0.007 0.300 0.039 0.037 0.037 0.346
6 26.23 0.011 0.010 0.006 0.284 0.037 0.036 0.036 0.343
7 28.00 0.011 0.008 0.005 0.270 0.036 0.037 0.037 0.3500
8 30.00 0.011 0.006 0.004 0.266 0.038 0.040 0.040 0.366
9 51.25 0.024 0.018 0.013 0.088 0.177 0.171 0.128 0.104
10 51.76 0.024 0.019 0.013 0.056 0.189 0.164 0.111 0.066
11 52.28 0.025 0.019 0.012 0.029 0.203 0.149 0.085 0.034
12 52.80 0.029 0.020 0.008 0.011 0.207 0.116 0.052 0.014
13 53.37 0.019 0.017 0.002 0.002 0.181 0.068 0.022 0.005
14 53.85 0.012 0.007 0.001 0.000 0.120 0.029 0.010 0.003 15 54.40 0.006 0.000 0.001 0.000 0.055 0.012 0.006 0.002
16 54.94 0.004 0.001 0.000 0.000 0.023 0.007 0.003 0.001 17 55.50 0.002 0.001 0.000 0.000 0.013 0.004 0.002 0.000
18 56.02 0.001 0.000 0.000 0.000 0.009 0.003 0.001 0.000
19 56.66 0.001 0.000 0.000 0.000 0.007 0.002 0.000 0.000
20 57.29 0.001 0.000 0.000 0.000 0.005 0.001 0.000 0.000
21 57.96 0.001 0.000 0.000 0.000 0.004 0.001 0.000 0.000
22 58.80 0.000 0.000 0.000 0.000 0.004 0.001 0.000 0.000Independent prole set
Bias (K) rms (K)
Chan no. Frequency (GHz) 90 30 19 10 90 30 19 10
1 22.23 0.008 0.022 0.003 0.284 0.049 0.046 0.042 0.157
2 22.50 0.008 0.021 0.005 0.279 0.048 0.046 0.043 0.158
3 23.03 0.002 0.020 0.006 0.277 0.042 0.045 0.042 0.154
4 23.83 0.007 0.017 0.008 0.274 0.035 0.044 0.045 0.164
5 25.00 0.012 0.011 0.009 0.263 0.033 0.043 0.051 0.206
6 26.23 0.011 0.007 0.009 0.247 0.031 0.041 0.052 0.236
7 28.00 0.010 0.004 0.008 0.232 0.031 0.040 0.053 0.257
8 30.00 0.008 0.002 0.009 0.228 0.033 0.043 0.057 0.273
9 51.25 0.005 0.018 0.016 0.094 0.156 0.160 0.128 0.067
10 51.76 0.005 0.014 0.010 0.061 0.162 0.149 0.105 0.039
11 52.28 0.005 0.009 0.004 0.037 0.170 0.131 0.077 0.020
12 52.80 0.004 0.000 0.001 0.015 0.169 0.098 0.044 0.015
13 53.37 0.003 0.007 0.003 0.005 0.145 0.056 0.021 0.015
14 53.85 0.002 0.002 0.002 0.002 0.097 0.026 0.015 0.012
15 54.40 0.000 0.002 0.001 0.001 0.047 0.015 0.011 0.007
16 54.94 0.002 0.000 0.000 0.000 0.023 0.011 0.008 0.003
17 55.50 0.002 0.000 0.000 0.000 0.016 0.007 0.005 0.001
18 56.02 0.002 0.000 0.000 0.000 0.013 0.005 0.003 0.001
19 56.66 0.001 0.000 0.000 0.000 0.010 0.004 0.002 0.000 20 57.29 0.000 0.000 0.000 0.000 0.009 0.003 0.001 0.000 21 57.96 0.000 0.000 0.000 0.000 0.008 0.002 0.000 0.000 22 58.80 0.000 0.000 0.000 0.000 0.007 0.002 0.000 0.000
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2732 F. De Angelis et al.: RTTOV-gb
Figure 5. Bias (black solid line), standard deviation (red dashed line), and rms (blue dashed line) of TB differences between RTTOV-gb and the reference radiative transfer model ARTS (Eriksson and Buehler, 2015), for both clear (a12) and cloudy (b12) sky conditions (ARTS minus RTTOV-gb). Panels (a1, b1a2, b2) are for K- and V-band channels, respectively. All panels report results at 90 elevation angle.
PRO) operated at the radiosonde launching site. The dataset was rst reduced to clear-sky conditions. To be conservative, clear-sky conditions have been selected using three-fold screening, based on (i) ceilomenter cloud base height (CBH),(ii) sky infrared temperature (TIR), and (iii) 20 min standard deviation of liquid water path (LWP) from HATPRO.
Thus, periods with CBH below maximum range (8000 m), TIR > 30 C, or LWP > 102 kg m3 were rejected. More
over, cases with integrated water vapor differences between microwave radiometer and radiosonde proles larger than 1 mm have been discarded in order to reduce instrumental uncertainties involved in the comparison. After this screening, only 23 proles remained for the analysis. Bias, standard deviation, and rms differences between TB observed by the microwave radiometer and simulated with both RTTOV-gb and ARTS are shown in Fig. 6. With respect to the MWR observations, RTTOV-gb shows bias from 0.02 K at 22.24 GHz to0.5 K at 23.84 GHz in the K-band and from 0.16 to 0.31 K in the V-band opaque channels. The rms errors range from 0.90 to 0.47 K in the K-band and from 0.41 to 0.64 K in the V-band opaque channels. Larger bias is found at V-band transparent channels: 12 K at 51.26 GHz and 45 K at 52.28 GHz with either RTTOV-gb or ARTS simulations. Note that RTTOV-gb and ARTS show similar statistics with respect to MWR observations. This result is very important as it suggests that forward model errors due to the fast model approximation are not dominant. Note that bias values of the same order of magnitude for the 5154 GHz range were previously reported (Hewison et al., 2006; Lhnert and Maier, 2012; Martinet et al., 2015; Blumberg et al., 2015), employing MWRs of different types and manufacturers. This may be attributed to a combination of uncertainties from instrument calibration and gas absorption models. In fact, semi-transparent channels (as in the 5154 GHz range) suffer from larger calibration uncertainties due to the lack of a close reference-temperature calibration point. In addition, their response is inuenced by the water vapor continuum and oxygen line
Figure 6. Bias (black line), standard deviation (red line), and rms (blue line) of differences between TB measured with the microwave radiometer and TB simulated from radiosonde proles respectively with RTTOV-gb (solid lines) and the reference radiative transfer model ARTS (dashed lines), both for clear-sky conditions at 90
elevation angle (measurements minus simulations).
coupling, which contribute signicantly to the uncertainties because their parametrization is extrapolated from laboratory measurements to typical atmospheric conditions. It is beyond the scope of this paper to investigate spectroscopy issues, but our results support previous evidence and point to the need for further lab measurements (Boukabara et al., 2005; Cadeddu et al., 2007). Considering that O B systematic dif
ferences are usually evaluated and removed before assimilating data into NWP, we believe that statistics in Fig. 6 support the safe use of RTTOV-gb for direct radiance assimilation of MWR TB into NWP models.
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Figure 7. Jacobians calculated with the RTTOV-gb BF method and K-module. (a1) Temperature Jacobians for V-band channels; (b1) absolute humidity for K-band channels. Note that the BF method (solid line) and K-module (dashed line) are not distinguishable as they nearly completely overlap. Panels (a2, b2) show Jacobian differences between BF and K, for temperature and absolute humidity respectively.
3.3 Comparison of Jacobians
After testing the RTTOV-gb direct module, the RTTOV-gb
Jacobians calculation needs to be tested in order to provide a complete tool for a fast and safe MWR data assimilation. First, a consistency test of the Jacobians calculated with TL-, AD-, and K-modules of RTTOV-gb has been performed to ensure the correctness of the TL/AD/K coding modied for a ground-based perspective. The test resulted in nearly the same Jacobians for TL, AD-, and K-modules. Subsequently, the temperature and humidity Jacobians calculated with the RTTOV-gb K-module have been compared with those computed with the brute force (BF) method for a specic cloudy-sky prole. The BF method calculates the Jacobian by nite differences by calling the direct module multiple times after perturbing each individual input prole variable. The consistency of K-module with BF was conrmed using the RTTOV test suite (Brunel and Hocking, 2014), bearing in mind that some small differences between the Jacobians are expected. Figure 7 shows the temperature and absolute humidity Jacobians for the V- and K-bands channels. The Jacobians computed with RTTOV-gb BF and K-module are almost identical with differences smaller than 1 %. As expected, the TB sensitivity to atmospheric temperature is higher in the low tropo-sphere, especially in the PBL, and it increases with frequency in the spectral range between 51 and 58 GHz. Between 22 and 31 GHz, the sensitivity of the TBs to water vapor is almost independent of altitude and decreases with increasing frequency.
The Jacobians for cloud liquid water (CLW) are needed when cloudy-sky conditions are considered. Figure 8 shows a comparison of CLW Jacobians calculated with the RTTOV-gb K-module and the BF method. Similar to temperature and humidity, they are found to be almost identical (differences smaller than 0.1 %, likely due to truncation errors). As expected, the TB sensitivity to CLW increases with frequency in the K-band, while it decreases with frequency in the V-
Figure 8. Cloud liquid water Jacobians calculated with the RTTOV-gb BF method and K-module (left) and Jacobian differences between BF and K (right), for K-band (top) and V-band (bottom) channels, respectively. Note that the BF method (solid) and K-module (dashed) are not distinguishable as they nearly completely overlap.
band due to the increasingly dominant oxygen absorption.
TBs are sensitive to CLW at all levels up to 322 hPa (about 10 km), where RTTOV, and thus also RTTOV-gb, have set their upper limit for non-zero CLW.
For a completely independent test, Jacobians calculated with the RTTOV K-module have been compared with those computed with the reference radiative transfer model ARTS. ARTS Jacobians are derived from a semi-analytical expression described in Eriksson and Buehler (2015). As shown in Fig. 9, temperature and humidity Jacobians from ARTS and RTTOV-gb are found to be almost identical, either for K-band and V-band channels, with differences smaller than 3 % for temperature and 5 % for humidity. Figure 10 shows the comparison of CLW Jacobians from ARTS and RTTOV-
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2734 F. De Angelis et al.: RTTOV-gb
Figure 9. As in Fig. 7, but for Jacobians calculated with ARTS (solid line) and the RTTOV-gb K-module (dashed line). Panels (a2, b2) show Jacobian differences between ARTS and RTTOV-gb K-module, for temperature and absolute humidity respectively.
y H(x)
TR1
y H(x)
[bracketrightbig]
+
Figure 10. As in Fig. 8, but for Jacobians calculated with ARTS (solid line) and the RTTOV-gb K-module (dashed line).
gb. These are similar to each other, both in shape and order of magnitude, from the surface up to 322 hPa (RTTOV cloud limit). However, differences of about 10 % occur around 450 hPa, particularly at transparent channels (31, 51, and52 GHz). These are likely due to small differences in the liquid water absorption models in ARTS and in RTTOV-gb, as mentioned above in Sect. 3.1. However, for a typical CLW prole, these model differences lead to small TB differences (order of 0.1 K) and are thus deemed as negligible.
3.4 1D-Var application
Finally, RTTOV-gb has been tested as a forward model within a one-dimensional variational (1D-Var) scheme. For this purpose, the 1D-Var software package provided by the NWPSAF (Weston, 2014) has been adapted in the framework of the COST Action TOPROF to exploit RTTOV-gb. Among other modications, the 1D-Var tool has been modied to al-
low the assimilation of observations at different elevation angles for the same instrument. The 1D-Var approach searches the atmospheric state x that minimizes both the distance to the background xb and the observation y. The cost function
J needs to be minimized, modifying the different variables dened in the control vector x (Cimini et al., 2010):
J =
1
2
1
2[x xb]TB1 [x xb]. (16)
Here B represents the background-error covariance matrix and R the observation error covariance matrix. H represents the observation operator, in our case RTTOV-gb. The background prole comes from a short-range forecast of an NWP model or from a co-located radiosonde. Here, xb is a 3 h forecast from the French convective-scale model AROME. The Jacobians needed to minimize the cost function J are calculated with the RTTOV-gb K-module.
The aim is to retrieve temperature and humidity proles and column-integrated liquid water path from MWR observations through a 1D-Var retrieval approach exploiting RTTOV-gb. According to this aim, an Observing System Simulation Experiment (OSSE) was set up with 224 AROME analyses proles in February 2015 over the Alps with the new horizontal grid mesh of 1.3 km. These analyses are made of 90-level pressure, temperature, specic humidity, and liquid water content proles, typical of an alpine valley and mountainous region in winter. Both clear-and cloudy-sky conditions are considered. Starting from the AROME unperturbed proles (the truth), background proles are created by perturbing the initial AROME proles according to the background error covariance matrix B. In this study, the B matrix was computed from an AROME ensemble assimilation system, following the approach used to derive this matrix operationally at Mto France (Brousseau et al., 2011). By applying RTTOV-gb to the unperturbed AROME, observations are created by adding synthetic ob-
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F. De Angelis et al.: RTTOV-gb 2735
servation errors to the RTTOV-gb simulations. The synthetic random errors are assumed to follow a diagonal R matrix with reasonable standard deviations, i.e., 0.21.0 K de
pending on channels (Hewison, 2007).
In clear-sky conditions, temperature and specic humidity are used as control variables in the 1D-Var. A comparison between temperature and humidity retrievals obtained with 1D-Var and the corresponding unperturbed and background proles for two retrieval examples are shown in Fig. 11. As expected, the 1D-Var retrievals are closer to the truth than the background proles. In this case 1-D-Var provides an improvement with respect to the background in the rst 2 km for temperature and in the rst 4 km for humidity, which is encouraging for future data assimilation experiments. A comprehensive evaluation of RTTOV-gb plus 1D-Var for data assimilation using real MWR observations will be the subject of future work.
Here, we just underline that the main advantage of RTTOV-gb with respect to LBL models is the considerably lower computation time. Of course the priority of LBL models is more accuracy than speed, though settings may be tuned to improve the computation performances. Although a detailed analysis on computation speed goes beyond the scope of this paper, we found that RTTOV-gb is faster than our implementation of ARTS (Martinet et al., 2015) for both the direct and Jacobian calculations. Moreover, our tests demonstrate that the computation time for Jacobians is shorter by a factor of 8 for the RTTOV-gb K-module than for the direct module with the brute force method.
4 Summary
Version 11.2 of the fast radiative transfer model RTTOV, developed for space-borne sensors, has been successfully modied to simulate ground-based microwave radiometer observations. In addition to the direct module, which allows ground-based MWR observations to be simulated, the TL-, AD-, and K-modules of RTTOV have been modied in order to provide temperature, humidity, and cloud liquid water Jacobians for the ground-based perspective. We introduced the ground-based version of RTTOV, called RTTOV-gb, and demonstrated its potential for fast MWR TB simulations from thermodynamic proles. RTTOV-gb has been validated against accurate, but less time-efcient, reference line-by-line models and real MWR observations. Results demonstrate its applicability as a forward model within a variational scheme for fast and safe MWR data assimilation into NWP models. It is believed that the direct assimilation of TB, instead of retrieved proles, may improve the impact of MWR observations for temperature and humidity proles analysis in the rst few kilometers from the ground, where MWRs provide the maximum information content.
The performance of RTTOV-gb has been validated by comparison with TB simulated with the line-by-line model
R98 (Rosenkranz, 1998), the same model as used for the RTTOV training phase. For both dependent and independent prole sets, rms errors are below the typical TB uncertainty of ground-based MWRs ( 0.5 K), ranging from a maximum
of 0.06 K for the water vapor band to 0.025 K for the V-band opaque channels. Larger discrepancies are observed at the transparent V-band channels (51 and 52 GHz), with an rms within 0.20 K, and at elevation angle 10 . TBs simulated with
RTTOV-gb from AROME analyses have also been compared with those simulated with the reference line-by-line model ARTS. At 90 elevation, for both clear- and cloudy-sky conditions TB differences do not exceed 0.25 K in terms of biases and rms at all HATPRO channels except for the transparent V-band channels 5152 GHz (up to 0.5 K in cloudy-sky conditions). Finally, RTTOV-gb has been validated by radiosonde-derived TB with real nearly collocated MWR observations. In this case, the rms error increases with respect to the RTTOV-gb/LBL comparisons, ranging from 0.90 to0.47 K in the K-band and from 0.41 to 0.64 K in the V-band opaque channels. Larger discrepancies were found at V-band transparent channels, which may be explained by calibration and gas absorption uncertainties. However, the statistics of RTTOV-gb and ARTS simulations with respect to MWR observations are similar for each channel, suggesting that forward model errors due to the fast model approximation are not dominant. Temperature, humidity, and cloud liquid water Jacobians computed with RTTOV-gb K-modules were found to be similar in shape and magnitude with those calculated with the brute force method or with the ARTS model.
Finally, RTTOV-gb has been tested as a forward model within a 1D-Var software package in an OSSE to improve AROME thermodynamic proles estimated by directly assimilating synthetic MWR TB. For both temperature and humidity proles, the 1D-Var considerably improves the retrievals with respect to the background, in the rst few kilometers from the ground. Concerning the computation speed, RTTOV-gb with K-module is found to be 8 times faster in computing Jacobians than the brute force method. As expected, RTTOV-gb is demonstrated to be faster than the line-by-line models such as ARTS for both the direct and the Jacobians calculation.
Ultimately, this analysis conrms that RTTOV-gb is able to correctly simulate ground-based MWR radiance and to reproduce reasonable temperature, humidity, and cloud liquid water Jacobians. In conclusion, RTTOV-gb is well suited for serving as a forward model in a variational data assimilation scheme for a direct, safe, and fast NWP data assimilation of real MWR radiance observations. As from the user perspective, RTTOV-gb works exactly the same as RTTOV; its implementation and maintenance shall require minimal technical overheads at those NWP centers already using RTTOV.This shall facilitate the road towards the data assimilation of ground-based MWRs worldwide.
www.geosci-model-dev.net/9/2721/2016/ Geosci. Model Dev., 9, 27212739, 2016
2736 F. De Angelis et al.: RTTOV-gb
Figure 11. Temperature (a) and humidity (b) proles of background (blue line), truth (red line), and 1D-Var retrievals (cyan line) for two clear-sky proles.
5 Code and data availability
The original RTTOV v11.2 can be obtained via the request form on the NWPSAF website (NWPSAF, 2013; http://nwpsaf.eu/site/software/rttov/rttov-v11/
Web End =http: http://nwpsaf.eu/site/software/rttov/rttov-v11/
Web End =//nwpsaf.eu/site/software/rttov/rttov-v11/ http://nwpsaf.eu/site/software/rttov/rttov-v11/
Web End = ).
The efforts for adapting RTTOV to ground-based observations started within the COST (http://www.cost.eu/
Web End =http://www.cost.eu/ ) action ES1202 (EG-CLIMET) and have been continued within the COST action ES1303 (TOPROF, http://www.toprof.eu/
Web End =http://www.toprof.eu/ ). The modications needed to adapt the radiative transfer equation from the satellite-to the ground-based perspective have been made in the subroutine src/main/rttov_integrate.F90. The RTTOV subroutines that have been modied in RTTOV-gb to reverse the way that transmittances and optical depths are initialized and accumulated are src/main/rttov_transmit.F90 and src/main/rttov_opdep.F90 respectively. The calculation of the predictors 7 for the ground-based perspective has been adapted in the subroutine src/main/rttov_profaux.F90.Modications made in the direct module of RTTOV v11.2 code have been imported in the corresponding TL-, AD-, and K-modules subroutines
(i.e., rttov_integrate_tl.F90, rttov_integrate_ad.F90, rttov_integrate_k.F90; rttov_transmit_tl.F90, rttov_transmit_ad.F90, rttov_transmit_k.F90; rttov_opdep_l.F90, rttov_opdep_ad.F90, rttov_opdep_k.F90). The conditions of release of RTTOV-gb are currently under discussion among NWPSAF and COST action TOPROF. This may happen through an integration of RTTOV-gb into future RTTOV releases or as a stand-alone package disseminated through the TOPROF website.
All the information needed to download the ARTS code can be found on the website: http://www.radiativetransfer.org/
Web End =http://www.radiativetransfer. http://www.radiativetransfer.org/
Web End =org/ .
The NWPSAF proles, from which we interpolated the prole sets used for the RTTOV-gb training and independent test, are available at https://nwpsaf.eu/deliverables/rtm/profile_datasets.html
Web End =https://nwpsaf.eu/deliverables/rtm/ https://nwpsaf.eu/deliverables/rtm/profile_datasets.html
Web End =prole_datasets.html .
The AROME analyses used for ARTS/RTTOV-gb comparison and 1D-Var application, and the MWR/radiosondes dataset used for the validation against real MWR measurement, can be obtained by emailing [email protected].
Geosci. Model Dev., 9, 27212739, 2016 www.geosci-model-dev.net/9/2721/2016/
F. De Angelis et al.: RTTOV-gb 2737
Appendix A
The predictors Xkj introduced in Sect. 2 are functions of the absorbing gas, the zenith angle , the pressure, temperature, and water vapor mixing ratio proles, and nally the reference temperature and water vapor mixing ratio proles(i.e., the average of the training prole set). These are dened in Matricardi et al. (2001) and briey summarized below. Introducing at each xed level j the pressure P prof(j),
the temperature, and the water vapor mixing ratio T prof(j)
and Wprof (j), and the corresponding reference T ref(j) and Wref(j), the following variables are dened:
T (j) =
hT prof (j) + T prof (j + 1)[bracketrightBig] /2
T (j) = [bracketleftBig]
T ref (j) + T ref (j + 1)[bracketrightBig]
/2
Table A1. Predictors 7 used for mixed gases and water vapor (after Matricardi et al., 2001).
Predictor 7 Mixed gases Water vapor X1,j sin( ) sin2( )W2
r (j)
X2,j sin2( ) (sin( )Ww(j))2
X3,j sin( )Tr(j) (sin( )Ww(j))4
X4,j sin( )T 2
r (j) sin( )Wr(j) T (j)
X5,j Tr(j) psin( )Wr (j)
X6,j T 2
r (j)
4
psin( )Wr (j)
X7,j sin( )Tw(j) sin( )Wr(j)
X8,j sin( )Tw(j)
Tr(j) (sin( )Wr(j))
3
X9,j psin( ) (sin( )Wr(j))4
X10,j psin( )
4
pTw(j) sin( )Wr (j) T (j)| T (j)|
X11,j 0 psin( )Wr (j)
[parenrightbig] T
(j)
X12,j 0 (sin( )Wr(j))2
Ww
X13,j 0 psin( )W
r (j)Wr(j) Ww(j)
hWprof (j) + Wprof (j + 1)[bracketrightBig] /2
W (j) = [bracketleftBig]
Wref (j) + Wref (j + 1)[bracketrightBig]
W (j) =
X14,j 0 sin( )
W2r(j) Tr(j)
/2
hP prof (j) + P prof (j + 1)[bracketrightBig] /2
Tr (j) = T (j)/T (j)
T (j) = T (j) T (j)
Wr (j) = W(j)/W (j)
Tw (j) =
j
X15,j 0 sin( )
W2r(j)
T 4
r (j)
P (j) =
Xl=N1P (l + 1)[P (l + 1) P (l)]Tr(l + 1),
with Tw (j = N) = 0 at the surface.
Ww (j) =
[braceleftBigg]
j
Xl=N1P (l + 1)[P (l + 1) P (l)]W(l)
[bracerightBigg][slashBig]
Xl=N1P (l + 1)[P (l + 1) P (l)]W (l)[bracerightBigg]
The RTTOV predictors 7 are derived from the variables above as listed in Table A1.
[braceleftBigg]
j
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2738 F. De Angelis et al.: RTTOV-gb
Acknowledgements. This work has been stimulated through the COST Action ES1303 (TOPROF), supported by COST (European Cooperation in Science and Technology). Part of the work was supported by the EU H2020 project GAIA-CLIM (Ares(2014)3708963/Project 640276). The authors would like to acknowledge the NWPSAF and Met Ofce, in particular Peter Rayer, for providing support with RTTOV coding, and Mto France, for providing AROME analyses and measurements performed in the Bordeaux campaigns.
Edited by: K. GierensReviewed by: two anonymous referees
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Copyright Copernicus GmbH 2016
Abstract
Ground-based microwave radiometers (MWRs) offer a new capability to provide continuous observations of the atmospheric thermodynamic state in the planetary boundary layer. Thus, they are potential candidates to supplement radiosonde network and satellite data to improve numerical weather prediction (NWP) models through a variational assimilation of their data. However in order to assimilate MWR observations, a fast radiative transfer model is required and such a model is not currently available. This is necessary for going from the model state vector space to the observation space at every observation point. The fast radiative transfer model RTTOV is well accepted in the NWP community, though it was developed to simulate satellite observations only. In this work, the RTTOV code has been modified to allow for simulations of ground-based upward-looking microwave sensors. In addition, the tangent linear, adjoint, and K-modules of RTTOV have been adapted to provide Jacobians (i.e., the sensitivity of observations to the atmospheric thermodynamical state) for ground-based geometry. These modules are necessary for the fast minimization of the cost function in a variational assimilation scheme. The proposed ground-based version of RTTOV, called RTTOV-gb, has been validated against accurate and less time-efficient line-by-line radiative transfer models. In the frequency range commonly used for temperature and humidity profiling (22-60 GHz), root-mean-square brightness temperature differences are smaller than typical MWR uncertainties (∼ 0.5 K) at all channels used in this analysis. Brightness temperatures (TBs) computed with RTTOV-gb from radiosonde profiles have been compared with nearly simultaneous and co-located ground-based MWR observations. Differences between simulated and measured TBs are below 0.5 K for all channels except for the water vapor band, where most of the uncertainty comes from instrumental errors. The Jacobians calculated with the K-module of RTTOV-gb have been compared with those calculated with the brute force technique and those from the line-by-line model ARTS. Jacobians are found to be almost identical, except for liquid water content Jacobians for which a 10 % difference between ARTS and RTTOV-gb at transparent channels around 450 hPa is attributed to differences in liquid water absorption models. Finally, RTTOV-gb has been applied as the forward model operator within a one-dimensional variational (1D-Var) software tool in an Observing System Simulation Experiment (OSSE). For both temperature and humidity profiles, the 1D-Var with RTTOV-gb improves the retrievals with respect to the NWP model in the first few kilometers from the ground.
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Neither ProQuest nor its licensors make any representations or warranties with respect to the translations. The translations are automatically generated "AS IS" and "AS AVAILABLE" and are not retained in our systems. PROQUEST AND ITS LICENSORS SPECIFICALLY DISCLAIM ANY AND ALL EXPRESS OR IMPLIED WARRANTIES, INCLUDING WITHOUT LIMITATION, ANY WARRANTIES FOR AVAILABILITY, ACCURACY, TIMELINESS, COMPLETENESS, NON-INFRINGMENT, MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. Your use of the translations is subject to all use restrictions contained in your Electronic Products License Agreement and by using the translation functionality you agree to forgo any and all claims against ProQuest or its licensors for your use of the translation functionality and any output derived there from. Hide full disclaimer