P r o c e. d i n g s. 1st Workshop. Madrid, Spain September 2002

Transcription

1 P r o c e e d i n g s 1st Workshop Madrid, Spain September 2002

2 SYNERGETIC USE OF TRMM S TMI AND PR DATA FOR AN IMPROVED ESTIMATE OF INSTANTANEOUS RAIN RATES OVER AFRICA Jörg Schulz 1, Peter Bauer 2, and Clemens Simmer 1 Abstract Rainfall estimation from satellite data over land surfaces still represents a challenge because neither at visible/infrared nor at microwave wavelengths do raindrops provide significant contributions to the total signal to allow a direct estimation of rain rate. Additionally, surface emissivity models for land surfaces in the microwave are still of quasi empirical character. Thus Bayesian approaches based on radiance libraries constructed from cloud resolving model results are still difficult to realise. Because of all this difficulties empirical algorithms over land surfaces are still popular. The combination of TRMM s TMI and PR sensors provide an excellent tool for the evaluation of available rainfall detection and estimation techniques as well as for new developments. The rain detection part of the presented new algorithm whose fundamentals are based on a methodology developed by Conner and Petty, consists of a two-stage approach to distinguish precipitation signatures from other effects: (1) Contributions from slowly varying parameters (surface type and state) are isolated by comparing observed brightness temperatures to those obtained from previous orbits only containing rain-free observations. (2) Effects of more dynamic parameters, i.e., surface temperature and moisture, are reduced by successive subtraction from the observations by means of principal component analysis. For this purpose, the general signatures of both temperature and moisture variations are deduced from radiative transfer simulations. The technique is first applied to TMI observations and compared to co-located measurements of PR over regions in Africa, North and South America, India as well as Australia. To quantitatively estimate the rain water content Heidke skill scores as a function of rain water content and brightness temperature range are used to efficiently calibrate the near surface rainfall intensities with a polynomial fit where the coefficients depend on location and time. Application to TMI data and comparison with the TRMM 2A12 V5 product indicates an improved performance of detecting rain water contents lower than 0.1 g m -3. A comparison with the 2A25 product over a ten month period (Mar Oct 2000) showed that the algorithm is able to explain ~65% of the variance of the PR estimated rainfall. However, remaining rms errors between the new algorithm and the PR for instantaneous estimates of the rain water content remain high at ~100% for rain water contents less than 0.1 g m -3, decreasing to 25% - 50% for rain water contents up to 1 g m Meteorological Institute, University of Bonn, Auf dem Hügel 20, D Bonn, Germany 2 ECMWF, Shinfield Park, Reading, UK 1

3 1. Introduction The estimation of rainfall over land surfaces is an ongoing challenge because neither at VIS/IR wavelengths nor at microwave wavelengths do raindrops provide significant contributions to the total signal to allow a direct estimation of rain rate. Principally, cloud top temperature and reflectivity is related to space-time averages of surface rainfall in those methods. The loose physical connection between these quantities prohibits an instantaneous estimate. At microwaves, surface emissivity is high and spatially variable which increases the uncertainty of the atmospheric contribution estimate compared to estimates over ocean surfaces. The main information over land surfaces comes from scattering by precipitating ice particles. However, since the beginning of remote sensing both wavelength regions were exploited (Petty, 1995) and recent accuracy assessments indicate average errors of at best % with strong dependence on season and region as well as dataset resolution (Smith et al., 1998). Thus, algorithm improvements may only be achieved if local surface conditions are accounted for and if the signal to rain rate relationship is based on data which is more representative of global rainfall system variability. With the launch of the Tropical Rainfall Measuring Mission in November 1997, the first spaceborne precipitation radar (PR) became available (Kummerow et al., 1998). It is a single frequency (13.8 GHz), electronically scanning radar with nominal resolutions of 4.3 km and 0.25 km in the horizontal and vertical dimensions, respectively. The cross-track scan pattern covers a 215 km swath consisting of 49 beams along a scan angle of ±17. Its sensitivity is specified with 0.17 mm h -1 with a calibration accuracy of ~0.8 db. A microwave radiometer is available on the same platform (TRMM Microwave Imager, TMI) providing measurements at 10.65, 19.35, 21.3, 37.0, and 85.5 GHz on a conical scan with a nearly constant surface incident angle of 52.8 and a swath width of 760 km. All channels measure vertically and horizontally polarised radiances (expressed as blackbody temperatures, TB) except the 21.3 GHz channel which only measures vertically polarised radiances. Since only one antenna is used for all channels the spatial resolution of the effective field of view (EFOV) depends on frequency and ranges from 37 km x 63 km at GHz to 5 km x 7 km at 85.5 GHz. The TRMM orbit is not sun-synchronous and covers latitudes between 38 N and 38 S. Thus the combination of both sensors provides an excellent tool for the evaluation of available rainfall detection and estimation techniques as well as for new developments. The difficult microwave signal interpretation over land surfaces has favoured somewhat the implementation of empirical algorithms which make use of co-located satellite and ground based (radar) observations to derive a calibration of satellite measurements by reference data (e.g. Ferraro and Marks, 1995). For large scale regional or even global applications this approach is hampered by the limited representativity of available calibration data sets. Thus co-located radiometric and radar measurements from TRMM provide an outstanding data source covering the tropical and subtropical latitudes over various climatological regimes. The technique used in this paper follows the ideas of Conner and Petty (1998) and uses the methodology described in Bauer et al. (2001a) to combine TMI and PR measurements by using Heidke Skill score diagrams. Section 2 provides a brief summary of the methodology and describes the calibration of the precipitation index (PI) to a rain intensity by using PR data. Section 3 examines the application of the algorithm to a case of a meso-scale convective cluster over northwest Africa. The derived product is compared to the TRMM standard product 2A12 which delivers surface rainfall and 3D structure of hydrometeors and latent heating over the TMI swath (Kummerow et al., 2000). Additionally, the calibrated PI is compared to the calibration source (2A25) which gives an estimate of the remaining errors after the calibration. All data used in this study are version 5 data, so the TMI brightness temperatures are calibrated as described in Kummerow et al. (2000). The paper is concluded by a summary and discussion. In the following, rainfall intensity is always treated in terms of rain liquid water content (LWC) to avoid uncertainties imposed by the somewhat uncertain drop size distributions and the dependence of rainfall rate calculations on fallspeed parameterisation. Additionally, both scattering

4 ( D 6 ) and emission ( D 3 ) are closer related to liquid water and ice volume densities (where D denotes the particle diameter). 2. Methodology The methodology used has been described in detail in Bauer et al. (2001a). Fig. 1 is showing a flow chart depicting the main features of the algorithm. The technique used here makes use of a first order approach to remove seasonally varying surface contributions from instantaneous TMI measurements by generating maps of clear sky temporal averages of brightness temperatures using the screening technique of Ferraro et al. (1998) over 5 different regions, i.e. Africa, South America, North America, India, and Australia. The averages are running 10 day means up to the day for which the rainfall should be estimated, e.g. the average for the first July includes the last nine days in June and the first of July. The averaging was carried out for a period of 10 month (March October) in the year 2000 and the resulting brightness temperatures are mapped onto a grid with a spatial resolution of 0.4 x 0.4. Features of the background maps are rather smooth with variations introduced by water surfaces and snow in the mountains as well as undetected clouds and precipitation. To restrict the investigation to homogenous surfaces only those pixels are used for which the standard deviation at GHz is less than 10 K. Brightness temperatures (TB) at different wavelengths are usually positively correlated in particular over land surfaces where the background signal is rather strong. Only in case of scattering by precipitating ice the higher frequency measurements are negatively correlated to those at lower frequencies. The full set of available channels carries therefore some redundant information. Thus, the dimension of the input data set (9 for the TMI) may be reduced by means of principal components. The collection of TB vectors from the observations was therefore decomposed into independent vectors by calculation of the covariance matrix of differences between the TBs and their background values (equation (1) in Fig. 1). From this a matrix of eigenvectors can be computed. The major advantage of EOFs is that they are orthogonal to each other in vector space while brightness temperatures are not. Moreover, the associated eigenvalues provide the contribution to the total variance in decreasing order. The first EOF represents the largest contribution, the second EOF the second largest and so on. In case of TMI TBs, the eigenvalues of the first three EOFs usually sum up to more than 98% of the total variability. Figure 1. TMI algorithm flow, details are described in the text. Bars over symbols denote temporal averages and [ ] denote inner products.

5 Figure 2. Time series (March October 2000) of explained variances for the first three eigenvectors e p for five different regions. The idea of surface effect correction by generating datasets where either temperature or moisture dominate the signal and which are subtracted from the actual observation signal by orthogonalization follows the approach by Conner and Petty (1998) (equation (2) in Fig. 1). Bauer et al. (2001a) used radiative transfer simulations to derive the correction eigenvectors e t and e m. This approach is followed here because both eigenvectors are supposed to show only the signature of either temperature or moisture. If the correction data sets are constructed from measurements as in Conner and Petty (1998) then they may contain unscreened precipitation which would suppress the precipitation signal in later analysis. The first eigenvectors with respect to temperature and moisture explain 89% and 86% of the variance in either simulation so only those are used for the correction. After this correction, eigenvectors e p which are assumed now to contain the precipitation signal can be computed. As Bauer et al. (2001a) already showed, e p has the common feature to decrease with frequency in the first EOF which is fairly independent of time and region. This finding is confirmed by computing all e p for the ten month period March October 2000.

6 Figure 3. Heidke skill score diagrams for the period 09/11/ /20/2000 used for the calibration on 09/20/2000 for four different regions. However, if the explained variance of the first EOF is considered as a function of time a strong dependence on region and period is obvious. Fig. 2 shows time series of the explained variances for the first three eigenvectors for all five regions. Over all regions, except India the explained variance of the first EOF is rather high (~80%) with the smoothest time series over South America because of the most homogenous terrain. The eigenvector for India shows a clear depression during the Indian summer monsoon where the explained variance of the first eigenvector drops down to 60%, whereas that of the second is enhanced to 30%. A possible explanation is the high variability in cloud water and water vapour which is indicated by positive e p at lower frequencies and negative e p at 85.5 GHz for the second eigenvector. The highest explained variances are found over Australia reaching values up to 90% during the winter months July and August. Finally, the precipitation signal can be obtained from e p by equation (3) in Fig. 1, where PI represents an index (in units of K) which is positively correlated to rain intensity (rather to ice water path). For the calibration of the PI into rain water contents a co-location procedure of TMI and PR pixel values which are recorded along different scan geometries and resolutions is performed. For the TMI a reference resolution was defined which is set to the resolution of the 19 GHz channel. The effective field of view (EFOV) is enlarged by a factor of 2.5 to cover the area of which ~98% of the signal is received. The EFOVs are approximated by ellipses and the antenna gain function by Gaussian functions following the orientation of the real EFOVs along the TMI scan. PR pixels at a height of 2 km with valid PR retrievals covering more than 80% of the TMI EFOV were used to minimise sampling problems. Before the averaging a parallax correction (Bauer et al., 2001a) is applied if the centre of gravity of the weighting function gives values larger than 5 km. This is important because in those cases where the signal contribution originates from higher altitudes, the comparison to radar data at the TMI nadir location may lead to errors in the calibration data set. As in Bauer et al. (2001a) Heidke skill scores were employed to quantify the accuracy of rain detection from both TMI and PR and to give a calibration tool. The skill scores are computed for classes of rain intensity with a lower threshold resulting in skill score diagrams as presented in Fig. 3 for an example period of 10 days in September To build up statistics it is necessary to sample at least ten days of data to fill the diagram which is important for a stable calibration. Thus it is chosen that the skill score diagrams where build for each day and region sampling the nine

7 days before and the day of the actual TMI overpass. Comparing those diagrams for different regions exhibit some common features like there is almost no skill in determining rain water contents less than 0.03 g m-3. The skill over India is generally ~ 0.1 smaller due to the less explained variance in the first eigenvector. Differences can also be seen at the high end where a maximum index in Africa is related to a PR-derived rain water content of 0.8 g m-3 whereas it is only 0.6 g m-3 over South America. However, examining 10 months of data it was decided to use a polynomial fit along the maximum Heidke skill score to convert the precipitation index into rain water content. This was done for each 10 day running mean Heidke skill score diagram in each region ending up with a fit for each day and region. The errors of the fit itself are varying with time between 0.02 g m-3 and 0.06 g m-3 where higher errors occur if singular events dominate the skill score diagram. Figure 4. Distributions of retrieved rain water content for orbit on 28. July 2000 over Benin and Nigeria from (a) 2A12 V.5 algorithm, (b) PR estimates averaged to TMI reference resolution, (c) calibrated estimates from PI, and (d) pixels where the Ferraro et al. (1998) scattering index indicates rain.

8 Figure 5. Scatter plots of (a) calibrated PI estimates versus 2A12 V.5 estimates, (b) calibrated PI estimates versus averaged PR estimates, (c) 2A12 V.5 versus averaged PR estimates, and (d) remaining standard deviation between calibrated PI and averaged PR pixels for the same case as in Fig Examples and uncertainty estimation Fig. 4 presents a typical example of the results obtained by using the polynomial fits to calibrate the PI into rain water contents. The case represents the passage of a mesoscale convective cluster over southern parts of northwest Africa. The measurement was taken in the decaying stage of most of the convective cells. Comparing the 2A12 with the 2A25 product it is obvious that 2A12 doesn t detect rain water contents lower than 0.2 g m -3 which lead to a significant smaller rain area. The calibrated precipitation index represents the PR swath data relatively well, e.g. between 8 E and 10 E and N. However, it is also not able to detect the very small rain water contents in the south western part of this scene. In the Ferraro scattering index only the convective cores are well represented. Compared to 2A12 the calibrated PI shows a very similar structure at medium and high rain intensities but it exhibits a large negative bias in the convective cores which is introduced by the use of the PR as the calibration source. Fig. 5 shows scatter plots for the orbit considered in Fig 4. In Fig. 5 (a) the scatter between 2A12 and the calibrated PI is increasing with decreasing rain water content. Other cases not shown here reveal that the spatial correlation between 2A12 and PI is relatively high (>0.7) for rain water contents larger than 0.1 g m -3 but the negative bias for the PI was found in any case considered. This bias is also obvious in Fig 5 (c) showing the comparison between 2A12 and 2A25 where also the scatter is considerable larger than between 2A12 and the PI. The comparison of PI to its calibration source in Fig 5 (b) and (d) shows an overestimation of the PI at rain water contents lower than 0.03 g m -3 which is a common feature of all investigated cases. For greater rain water contents there is almost no bias but still a large scatter. This is also obvious in the remaining rms

9 error between 2A25 and the PI which is still around 100% at rain water contents below 0.1 g m -3 and decreasing to 25-50% above 0.1 g m -3. The large scatter around values of 0.1 g m -3 is potentially caused by the large area chosen to build the Heidke skill score diagrams for the calibration. Together with the time average over 10 days variability is suppressed finally causing the scatter in the comparison. A second dynamical calibration like in the PATER ocean algorithm (Bauer et al., 2001b) could be envisaged but is not necessarily expected to improve the calibration very much. Figure 6. Time series of error measures for the African region, (a) percentage of pixels falling outside the calibrated PI range [-20, 180], (b) bias between calibrated PI estimates and averaged PR estimates, (c) efficiency, and (d) rms error. To consider the development of errors over time, Fig. 6 is showing 4 error measures for the period March September 2000 for Africa. Fig. 6 (a) shows the relative number of pixels which fell outside the valid range of the PI and are therefore not to calibrate. This is varying between almost zero to a maximum of 4% where most values were below -20 K and only few above 180 K. The bias shown in Fig. 6 (b) as the ratio of rain water content PR to rain water content PI is varying between 93% and 107% showing largest biases at the beginning and the end of the rain season in northwest Africa. Fig 6 (c) shows the efficiency, defined as: N i= 1 ( LWC i= 1 LWC E = 1 (4) N which is giving an estimate of the explained variability of the PR pixels by the calibrated PI values. E is showing values between 0.55 and 0.75 with the most values located around 65%. The largest PR LWC 2 PR PI 2 )

10 variations are from April to May and in July and August where the low efficiencies probably reflect events with low rain water contents distributed over large areas. The overall rms error Fig. 6 (d) is around 0.03 g m -3 which is dominated by the concentration of the pixel values at low rain water contents and may be somewhat misleading for judging the error at higher intensities as Fig 5 (d) has shown. 4. Summary and conclusions The presented method corrects brightness temperature departures from running 10 day rain free averages for small scale influences by surface temperature and moisture. Heidke skill scores were used to calibrate the resulting precipitation index into a rain water content. For different regions and seasons the same type of calibration can be used. However, the coefficients of the calibration have to be adjusted every day using Heidke skill score diagrams accumulated over the same ten days as the background map. Comparisons of the calibrated PI to TRMM standard products reveal a better potential for detecting low rain water contents than standard indices like SI and the 2A12 product. The calibrated PI usually exhibits a low bias in convective cores when compared to 2A12 but only a small positive bias at rain water contents below 0.04 g m -3 to 2A25. The PI shows a larger rain area than 2A12, mostly due to the improved detection of light rain. Otherwise the spatial features of 2A12 and PI are very similar. Remaining rms errors between the calibrated PI and PR are around 100% for rain water contents below 0.1 g m -3 but decreasing to 25-50% for larger rain water contents. Due to the use of large areas and running ten day averages for the calibration a large part of the variability given in the PR data is not captured. This might be improved by choosing smaller areas and a longer integration time. A more detailed error analysis should analyse the resulting probability density functions of the different products and their errors. Also a stratification of errors in terms of different meteorological regimes with the help of rain gauge and radar data in Benin will help to characterise the errors better. Further improvements can be expected from the consideration of rain and cloud classification as well as the additional use of microphysical properties of clouds derived from measurements of the SEVIRI instrument onboard of the Meteosat Second Generation satellite. Further studies will focus on finding ways how the algorithm can be transferred to other passive microwave instruments, e.g. SSM/I, SSMIS, and AMSR to produce an inter-calibrated passive microwave multi-satellite product which is needed for the calibration of geostationary satellite data. This strategy is targeting at the planned Global Precipitation Mission which consists of a core satellite carrying a radar and a passive microwave radiometer which is accompanied by a constellation of several drone satellites carrying only passive microwave radiometers. This mission will deliver passive microwave rain estimates every three hours at any place on earth. It is planned by NASA and NASDA and will be supported by ESA with one Earth Explorer Opportunity Mission called EGPM. Acknowledgments - The authors are grateful for free access to TRMM data through the NASA TRMM program. This research was supported by the Federal German Ministry of Education and Research (BMBF) under grant No. 07 GWK 02 and by the Ministry of Education, Science and Research (MSWF) of the federal state of Northrine-Westfalia under grant No

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