PPrroocceeeeddiinnggss 1st Workshop

Madrid, Spain23-27 September 2002

1st Workshop of the International Precipitation Working Group

STATUS OF RAINFALL DATA ASSIMILATION AT ECMWF

Peter Bauer1, Jean-François Mahfouf1, Virginie Marécal1, Frédéric Chevallier1, Philippe Lopez1, and Emmanuel Moreau1

Abstract With the increasing sophistication of data assimilation systems the operational assimilation of rainfall information in numerical weather prediction (NWP) models becomes feasible. Similar to other data major issues are the data quality control, the estimation of observation errors, and the sensitivity of the model physical parameterizations to the data to be included in the analysis. This paper reviews past and present activities at the ECMWF from the experimental tests evaluating model sensitivity towards the system configuration planned for operations in 2004. The aspect of rainfall rate vs. direct radiance assimilation is covered. 1. Introduction The assimilation of satellite derived rain rates in NWP models has made important progress during the last decade due to advances in data assimilation techniques and the availability of improved satellite instruments (Treadon, 1997, Krishnamurti et al., 2001, Hou et al., 2001, Marécal and Mahfouf, 2002a). Data assimilation systems based on variational techniques have been recently implemented at a number of operational meteorological centers. The design of variational assimilation systems allows an increasing use of non-conventional observations such as satellite radiances and/or geophysical products. Quantitative precipitation retrieval has become much more accurate using new satellite instruments such as the Precipitation Radar (PR) onboard the Tropical Rainfall Measuring Mission (TRMM) and the TRMM Microwave Imager (TMI). However, due to the instrument-dependent algorithm performance and the difficult assessment of retrieval errors the direct assimilation of radiances presents an attractive alternative. Direct radiance assimilation is well established at the European Centre for Medium-Range Weather Forecasts (ECMWF) for clear-sky satellite observations in atmospheric temperature and moisture analysis. This system provides a framework for evaluating radiance assimilation also for cloud and rain affected observations. To introduce this subject, the results from past rain rate assimilation experiments are summarized in Section 2. Issues such as the dependence of the analysis on rain rate retrieval algorithm performance and the definition of retrieval errors are discussed. Section 3 introduces direct radiance assimilation and compares against rain rate assimilation for a case study. The results are summarized in Section 4 and perspectives are developed. 1 European Centre for Medium-Range Weather Forecasts (ECMWF), Shinfield Park, Reading, Berkshire RG2 9AX, UK

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2. Rainrate assimilation 2.1 Rainfall retrieval The European Community (EC) and the European Space Agency (ESA) jointly funded a three-year project (EuroTRMM, between February 1998 and February 2001) based on the use of TRMM data. The objective of EuroTRMM was twofold: (1) to process TRMM rainfall products for providing assimilation and verification data for numerical weather prediction models; (2) to attempt the assimilation of precipitation data in the ECMWF model and to use the precipitation data for testing and tuning of convection schemes.

Figure 1. Bayesian retrieval errors as a function of rain rate at product resolution from PATER (a), BAMPR (b), and 2A12 (c). The solid lines are standard deviations between TMI and PR retrievals at the same spatial resolution (from Bauer et al., 2002).

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Figure 2. Retrieval errors after spatial averaging to 60 km with and without accounting for spatial error correlation from PATER (a), BAMPR (b), and 2A12 (c) over a 6h observation period on August 27, 1998 (from Bauer et al., 2002).

Objective (1) included the development of two alternative algorithms for rainfall rate estimation from TMI data: PATER (PR-Adjusted TMI Estimation of Rainfall; Bauer, 2001, Bauer et al., 2001) and BAMPR (Bayesian Algorithm for Microwave-based Precipitation Retrieval; Mugnai et al., 2001). These were compared against TRMM standard product 2A12 (Kummerow et al., 1996) to assess assimilation performance as a function of algorithm output.

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All algorithms employ the Bayesian retrieval principles and therefore provide both error and rainfall rate estimates. However, two issues affect the pre-processing of this data for assimilation: (1) the product resolution is different (13x15 km2 for 2A12/BAMPR vs. 27x44 km2 for PATER) while spatial sampling is identical and (2) the retrieval databases, which originate from combined cloud resolving model (CRM) - radiative transfer (RT) simulations, are based on different profile selections. Therefore different retrievals of rain rates and different error estimates can be expected even though the same radiometer observations are used. This will obviously affect the analysis. Fig. 1 shows examples of errors vs. rain rate estimates from the three algorithms. Despite the fact that the algorithms were applied to different TMI data sets their gross behavior is quite similar. Errors decrease from 200% at low rain rates (0.1 mm h-1) to 50-70% at high rain rates (10-20 mm h-1). However, individual errors vary quite substantially between algorithms for a given rain rate. Interestingly, these theoretical errors correspond well when compared to standard deviations between TMI and PR measurements (Bauer et al., 2002). In the variational assimilation, the observation errors determine how much the analysis is drawn to the data. The dependence of errors on rain rates shown in Fig. 1 indicates that the analysis is only weakly constrained at low rain rates Before assimilation, the data has to be averaged to represent an observation that is equivalent to the model grid scale. The effect of spatial correlation on error averaging is illustrated in Fig. 2 for all products; here, the same TMI data set was used. Error differences of 25-50% between algorithms are identified after averaging due to the reduction of scatter. At model resolution (~45 km), the errors reduce to 50-100% at low and 25-50% at high rain rates; however, neglecting spatial correlation underestimates the errors by a factor of 3 (Bauer et al., 2002). This examples highlights the importance of both accurate error estimates and the estimation of their spatial correlation. 2.2 1D-Var+4D-Var assimilation Within the EuroTRMM project, a method allowing the assimilation of surface rain rates in the operational ECMWF 4D-Var analysis system was developed (Marécal and Mahfouf, 2002a). The assimilation is carried out by first applying a 1D-Var retrieval of temperature and humidity profiles. The model’s first guess profiles and their error covariance matrices generate surface rain rates by applying the operational convection scheme. These are compared to the observed rain rates followed by a minimization of a cost function representing the Euclidian distance between model state and its first guess as well as model state in observation space and observation. The outputs are updated temperature and humidity profiles which are provided to the 4D-Var assimilation system as pseudo-observations of temperature and humidity. The method was tested using NASA operational surface rain rate products (2A12 product version 5). Results showed a positive impact on both analysis and forecast performances in the tropics, such as better trajectories of tropical cyclones in the analyses, a reduction of the root-mean-square wind vector forecast errors and a reduction of the model precipitation ‘spin-down’ (Marécal and Mahfouf, 2000, Marécal and Mahfouf, 2002a). Based on these results further studies were initiated to evaluate how sensitive the model analysis is to the employed rainfall product (Marécal et al., 2002). As mentioned, quantitative precipitation estimates vary largely between algorithms and this should affect both analysis and forecast. Fig. 3 shows a comparison of ECMWF model surface rain rates and those from the three retrieval algorithms over the tropics between August 18 and September 2, 1998. Fig. 3a represents the average model vs. retrieval difference when either all observations or only those greater zero are used. The comparison indicates that rain area is important and that the model tends to generate larger rain systems than those observed. The PATER estimates are closer to the model rain rates while both BAMPR and 2A12 retrieve more intense rain. This causes smaller root-mean-square differences and higher correlations between model and PATER (Fig. 3b, c).

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a) b) c)

Figure 3. Global mean background departure statistics of TCWV in kg m-2 from the 1D-Var analysis over 15 days comparing different TMI rain rate retrieval algorithms (from Marécal and Mahfouf, 2002a). Systematic difference between observations and model (a, in mm h-1), root mean square difference (b, in mm h-1), and correlation (c).

Fig. 4 shows the difference between first-guess and analyses from hurricane Bonnie on August 25, 1998. The three regions (A, B and C) are those in which the analysis fields were most strongly modified. In region A, the three experiments provide consistently drier atmospheres with respect to the control experiment (without rain rate assimilation) with maximum differences of 4 kg m-2, 3 kg m-2 and 2 kg m-2 for PATER, BAMPR, and 2A12, respectively. Here, the model is producing too much precipitation compared to any of the three TMI estimates. The magnitude of the increments of TCWV from the rain rate assimilation experiments is well correlated to the difference between the model and the three TMI rain rates (not shown here).

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Figure 4. TCWV fields in kg m-2 from 4D-Var analysis on May 25, 1998 at 18UTC. Control experiment (a) and after assimilating rain rates from PATER (b), BAMPR (c), and 2A12 (d), respectively (from Marécal and Mahfouf, 2002a).

In regions B and C, the three rain assimilation experiments produce total column water vapor (TCWV) fields that are different with respect to each other by up to 4 kg m-2. All three algorithms provide a moister atmosphere than the control experiment. In contrast to region A, there is no obvious correlation between the intensity of the TMI rain rate fields and the TCWV analysis: the largest (weakest) rain rates are not directly related to the moistest (driest) TCWV field. This is due to (1) the assimilation experiments are run in a cycling mode meaning that each analysis benefits from all the previous analyses and thus from the TMI data that were previously assimilated. This is the reason why the PATER experiment is producing an increase of TCWV in regions B and C (6 kg m-2 at maximum) with respect to the control although a reduction of first-guess precipitation was required to fit the PATER rain rate observations; (2) 4D-Var analyses depend on the availability of 1D-Var TCWV observations which again is subject to the success of the 1D-Var minimization that is related to the rain rate observation and its error. For instance, BAMPR produces large rain rates with large errors in the central part of the cyclone. This leads to a weak constraint in 1D-Var and thus to 1D-Var TCWV estimates close to the model background state. For 2A12 the large rain rates correspond to a smaller error meaning that in this case 1D-Var is less often successful. However, once it is successful, the impact is more pronounced because of the large TCWV estimates provided by 1D-Var.

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2.3 Implementation issues The experiments described above were carried out by performing the 1D-Var retrievals outside the operational system and by using the Jacobians of the convection scheme to obtain increments of temperature and humidity from rain rate departures. Since both elements are computationally not very efficient an alternative (linear) convection scheme was implemented and compared to the operational convection scheme for a single satellite observation. Secondly, the direct 4D-Var assimilation was tested which also includes variables of the model dynamics in the control vector (Marécal and Mahfouf, 2002b). Four experiments were set up with an artificial observation being twice and half the first-guess rain rate at a single location in the center of a tropical storm in the Eastern Arabian Sea on May 26, 2001. While the minimization succeeded in both directions using the linear convection scheme the operational mass-flux scheme was not able to produce rain rates as much as twice the first-guess rate. Secondly, in direct 4D-Var mode both schemes occasionally failed to minimize. While the first issue is directly related to linearity vs. non-linearity of the convection schemes, the second problem has more serious implications. Model humidity is represented in grid-point space in the outer (high-resolution) optimization loop and in spectral space in the inner (low-resolution) optimization loop. This produces a slightly different temporal development of humidity in both cases to which the convection scheme responds. This in turn may increase the cost function when switching from one loop to the other.

Figure 5. TCWV increments in kg m-2 from the 1D-Var+4D-Var analysis on May 26, 1998 (solid lines: positive, dashed lines: negative; from Marécal and Mahfouf, 2002b). Simplified convection scheme at 15h (a) and 18h (b) vs. operational scheme at 15h (c) and 18 (d).

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Fig. 5 illustrates the differences between two experiments that is the TCWV increments using the 1D-Var+4D-Var assimilation at a single location (doubling the rain rate) using the operational convection scheme and the simplified scheme, respectively. Also shown is the temporal development of the increments after three hours indicating the spatial/temporal dissipation of the increment. The smaller increment from the operational scheme originates from the lower first guess rain rates. The location of the maximum corresponds to the location of the observation after being transported back in time, i.e. to the beginning of the assimilation window. The shape of the increments is generated by the spread of the structure function describing the horizontal correlation length as a function of wavenumber. This already suggests that these structure functions have to be revised for rain data assimilation to avoid an excessive spread of information beyond the limits of the rain system. 3. Radiance assimilation 3.1 Radiative transfer A computationally efficient RT-model is required to allow the direct assimilation of radiances. In contrast to the assimilation of rain rates, the output from the convection scheme serves as an input to the RT-model that produces observation-equivalent quantities, i.e. radiances. For our purposes, the model of Bauer et al. (1998) was optimized for efficiency (Bauer, 2002) to be integrated into the RT-model that is operationally used for clear-sky RT-calculations at ECMWF (RTTOV, Matricardi et al., 2002). The code uses pre-calculated tables of hydrometeor optical properties at all microwave channels in use. The solution of the RT-equation is based on the Eddington approximation (e.g. Kummerow, 1993). Since the inverse sensitivity of hydrometeor profiles to radiance departures is needed within the 1D-Var minimization, both tangent-linear and adjoint versions of the code were developed. Preliminary tests show that the computations are only 5-6 times slower than RT-calculations in clear skies. Given the limited global occurrence of rain systems, no considerable computational burden will therefore be added to the system. The model has been tested (Moreau et al., 2002) against a multiple stream doubling-adding model for more than 55,000 profiles. Both models agree within radiometer noise limits (~1 K) except for extreme cases of scattering when snow water columns exceed ~2 kg m-2. However, a strong dependence on the treatment of sub-grid scale variability was found when modeled radiances were compared to SSM/I observations (Chevallier and Bauer, 2002). An independent column approach that separates between the clear-sky, cloudy, and rainy parts of the grid box was shown to considerably improve the agreement between the data. Furthermore, both models participated in an international model validation effort and performed equally well as the contesters (Smith et al., 2002). 3.2 1D-Var+4D-Var assimilation The 1D-Var assimilation procedure works as follows: The model first guess temperature and humidity profiles serve as input for the cloud and convection schemes which produce hydrometeor profiles. Of these, the rain and cloud liquid water are defined as control variables for the radiance 1D-Var algorithm. The forward RT-model calculates TMI or SSM/I radiances which are compared to the observations. Radiance departures are determined and converted to hydrometeor content increments by using the adjoint of the radiative transfer model. Finally, the Jacobians of the convection scheme provide increments to the temperature and humidity profiles. Fig. 6 shows a case study of super-typhoon Mitag on May 5, 2002. In this figure, both rain rate and radiance assimilation are represented. The comparison between the first-guess rain rates and those from the rain rate analysis indicates a rather strong constraint by the first-guess field (Fig. 6a, c). The system’s location and dimension did not change as much as needed. It is evident that the assimilation has difficulties to generate rainfall if there is none in the background. This is because

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the gradient with respect to rainfall is zero if rainfall itself is zero. In contrast, after radiance assimilation the analysis resembles rather closely the observed rainfall distribution with respect to system location, dimension and intensity (Fig. 6b, d). In radiance space the departures always show sensitivity to moisture changes so that rain generation in clear/cloudy skies is possible. Moreover, using cloud and rain-water content profiles in the control vector (vs. only surface rain rate) allows a more sensible adjustment of moisture profiles. 4. Perspectives The benefit of rainfall data assimilation in an operational and rather sophisticated numerical weather prediction modeling system has been demonstrated using surface rain rate retrievals from TRMM data. The assimilation experiments have highlighted problem areas which are crucial for future operational systems: (1) The different performance of satellite rainfall retrieval errors and their representation on model-equivalent spatial dimensions. (2) The response of the model physics to observational information. This aspect covers the choice of the control variable and the non-linearity of the cloud/convection scheme. This affects directly the success of the minimization that is the data used in the analysis.

a) c)

b) d)

Figure 6. Surface rain rates of the model background (a), from TMI observations (Bauer et al., 2001), after rain rate assimilation (c), and after radiance assimilation (d) for supertyphoon Mitag on May 5, 2002.

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In direct radiance assimilation, the observational part is treatable with much better accuracy because the observation plus modeling errors are far easier to quantify and independent of retrieval algorithms. When hydrometeor water contents are used as control variables both cloud and rain model physics can be modified at the same time. Therefore our preliminary comparisons have shown a superior performance of radiance assimilation with a small loss of computational efficiency. Crucial issues such as the definition of background errors and their spatial decorrelation as a function of system dynamics will be a major research subject at ECMWF following the studies presented in this paper. The success of the assimilation experiments has stimulated further activities for the revision of the model’s cloud and rain microphysics, in particular with respect to the linearized versions of the forward modeling codes which are used in the minimization. This will also impact future projects which focus on the assimilation of non-precipitating cloud information from satellite missions such as Cloudsat and EarthCARE. If the recent development of spatial resolution of the ECMWF model is extrapolated into the future, the spatial scales of observations and global models converge. This will allow a much more sophisticated assimilation of highly variable and small scale cloud and precipitation data with a presumably large impact on weather forecast skill. 5. References Bauer, P., 2001: Over-ocean rainfall retrieval from multi-sensor data of the Tropical Rainfall

Measuring Mission. Part I: Design and evaluation of inversion databases. J. Atmos. Oceanic Technol., 18, 1315-1330.

—————, 2002: Microwave radiative transfer modelling in clouds and precipitation. Part I: Model description. EUMETSAT NWP SAF Report No. 5, 27 pp.

—————, L. Schanz, and L. Roberti, 1998: Correction of three-dimensional effects for passive microwave retrievals of convective precipitation. J. Appl. Meteor., 37, 1619-1632.

—————, P. Amayenc, C. D. Kummerow, and E. A. Smith, 2001: Over-ocean rainfall retrieval from multi-sensor data of the Tropical Rainfall Measuring Mission. Part II: Algorithm implementation. J. Atmos. Oceanic Technol., 18, 1838-1855.

—————, J.-F. Mahfouf, W. S. Olson, F. S. Marzano, S. Di Michele, A. Tassa, and A. Mugnai, 2002: Error analysis of TMI rainfall estimates over ocean for variational data assimilation. Q. J. Roy. Meteor. Soc., 128, 2129-2144.

Chevallier, F., and P. Bauer, 2002: Model rain and clouds over oceans: Comparison with SSM/I observations. Mon. Wea. Rev., in press.

Hou, A. Y., S. Zhang, A. da Silva, W. S. Olson, C. D. Kummerow, and J. Simpson, 2001: Improving global analysis and short-range forecast using rainfall and moisture observations derived from TRMM and SSM/I passive microwave sensors. Bull. Amer. Meteor. Soc., 81, 659-679.

Krishnamurti, T. N., S. Surendran, D. W. Shin, R. J. Correa-Torres, T. S. V. Vijaya Kumar, E. Williford, C. D. Kummerow, R. F. Alder, and J. Simpson, 2001: Real-time multianalysis-multimodel superensemble forecasts of precipitation using TMI and SSM/I products. Mon. Wea. Rev., 129, 2861-2883.

Kummerow, C., 1993: On the accuracy of the Eddington-approximation for the radiative transfer in the microwave frequencies. J. Geophys. Res., 98, 2757-2765.

—————, W. S. Olson, and L. Giglio, 1996: A simplified scheme for obtaining precipitation and vertical hydrometeor profiles from passive microwave sensors. IEEE Trans. Geosci. Remote Sens., 34, 1213-1232.

Marécal, V., and J.-F. Mahfouf, 2000: Variational retrieval of temperature and humidity profiles from TRMM precipitation data. Mon. Wea. Rev., 128, 3853-3866.

—————, and —————, 2002a: Four dimensional variational assimilation of total column water vapour in rainy areas. Mon. Wea. Rev., in press.

—————, and —————, 2002b: Experiments on 4D-Var assimilation of rainfall data using an incremental formulation. Q. J. Roy. Meteor. Soc., in press.

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—————, —————, and P. Bauer, 2002: Comparison of TMI rainfall estimates and their impact on 4D-Var assimilation. Q. J. Roy. Meteor. Soc., 128, 2737-2758.

Matricardi, M., F. Chevallier, and S. Tjemkes, 2002: An improved general fast radiative transfer model for the assimilation of radiance observations. Q. J. Roy. Meteor. Soc., submitted.

Moreau, E., P. Bauer, and F. Chevallier, 2002: Microwave radiative transfer modelling in clouds and precipitation. Part II: Model evaluation. EUMETSAT NWP SAF Report No. 6, 21 pp.

Mugnai, A., S. di Michele, F. S. Marzano, and A. Tassa, A., 2001: Cloud-model based Bayesian techniques for precipitation profile retrieval from TRMM microwave sensors. Proc. EuroTRMM Workshop on Assimilation of Clouds and Precipitation in NWP Models, Reading, UK, November 2000, 323-346

Smith, E. A., P. Bauer, F. S. Marzano, C. D. Kummerow, D. McKague, A. Mugnai, and G. Panegrossi, G., 2002: Intercomparison of microwave radiative transfer models for precipitating clouds. IEEE Trans. Geosci. Remote Sens., 40, 541-549.

Treadon, R. E., 1997: Assimilation of satellite derived precipitation with the NCAP GDAS. Ph.D. dissertation, The Florida State University, 348 pp.