METOP ASCAT Soil Moisture Time Series

Transcription

1 Page: 1/26 EUMETSAT Satellite Application Facility on Support to Operational Hydrology and Water Management Algorithm Theoretical (ATBD) for product H25/SM-OBS-4 METOP ASCAT Soil Moisture Time Series 1

2 Page: 2/26 DOCUMENT CHANGE RECORD Issue / Revision Date Author Description /10/2013 Sebastian Hahn, Thomas Melzer, Christoph Paulik, Christoph Reimer Draft version prepared /10/2013 Sebastian Hahn, Stefan Hasenauer Revising section 2 and /10/2013 Stefan Hasenauer Revising chapter /10/2013 Stefan Hasenauer, Caroline Steiner Revising chapter 4 and 6 2

3 Page: 3/26 Algorithm Theoretical Product SM-OBS-4 Metop ASCAT soil moisture time series INDEX 1 The EUMETSAT Satellite Application Facilities and H-SAF Introduction to product SM-OBS Principle of the product Overview of Processing Steps Algorithms description Resampling Azimuthal Normalisation Estimate Noise of Backscatter Measurements Model Incidence Angle Dependence and Vegetation Correction Incidence Angle Normalisation of Backscatter Determination of Dry and Wet References Wet reference correction Soil Moisture Calculation Error Propagation Validation activities of SM-OBS-4 product Reference documents References

4 Page: 4/26 Acronyms AMSU AMSU-A Advanced Microwave Sounding Unit (on NOAA and MetOp) Advanced Microwave Sounding Unit - A (on NOAA and MetOp) AMSU-B Advanced Microwave Sounding Unit - B (on NOAA up to 17) ATDD AU BfG CAF CDOP CESBIO CM-SAF CNMCA CNR CNRS DMSP DPC EARS ECMWF EDC EUM EUMETCast EUMETSAT FMI FTP GEO GRAS-SAF HDF HRV H-SAF IDL IFOV IMWM IPF IPWG IR IRM ISAC ITU LATMOS LEO LSA-SAF Météo France METU MHS Algorithms Theoretical Definition Document Anadolu University (in Turkey) Bundesanstalt für Gewässerkunde (in Germany) Central Application Facility (of EUMETSAT) Continuous Development-Operations Phase Centre d'etudes Spatiales de la BIOsphere (of CNRS, in France) SAF on Climate Monitoring Centro Nazionale di Meteorologia e Climatologia Aeronautica (in Italy) Consiglio Nazionale delle Ricerche (of Italy) Centre Nationale de la Recherche Scientifique (of France) Defense Meteorological Satellite Program Dipartimento Protezione Civile (of Italy) EUMETSAT Advanced Retransmission Service European Centre for Medium-range Weather Forecasts EUMETSAT Data Centre, previously known as U-MARF Short for EUMETSAT EUMETSAT s Broadcast System for Environmental Data European Organisation for the Exploitation of Meteorological Satellites Finnish Meteorological Institute File Transfer Protocol Geostationary Earth Orbit SAF on GRAS Meteorology Hierarchical Data Format High Resolution Visible (one SEVIRI channel) SAF on Support to Operational Hydrology and Water Management Interactive Data Language Instantaneous Field Of View Institute of Meteorology and Water Management (in Poland) Institut für Photogrammetrie und Fernerkundung (of TU-Wien, in Austria) now Department of Geodesy and Geoinformation International Precipitation Working Group Infra Red Institut Royal Météorologique (of Belgium) (alternative of RMI) Istituto di Scienze dell Atmosfera e del Clima (of CNR, Italy) İstanbul Technical University (in Turkey) Laboratoire Atmosphères, Milieux, Observations Spatiales (of CNRS, in France) Low Earth Orbit SAF on Land Surface Analysis National Meteorological Service of France Middle East Technical University (in Turkey) Microwave Humidity Sounder (on NOAA 18 and 19, and on MetOp) 4

5 Page: 5/26 MSG Meteosat Second Generation (Meteosat 8, 9, 10, 11) MVIRI Meteosat Visible and Infra Red Imager (on Meteosat up to 7) MW Micro Wave NESDIS National Environmental Satellite, Data and Information Services NMA National Meteorological Administration (of Romania) NOAA National Oceanic and Atmospheric Administration (Agency and satellite) NWC-SAF SAF in support to Nowcasting & Very Short Range Forecasting NWP Numerical Weather Prediction NWP-SAF SAF on Numerical Weather Prediction O3M-SAF SAF on Ozone and Atmospheric Chemistry Monitoring OMSZ Hungarian Meteorological Service ORR Operations Readiness Review OSI-SAF SAF on Ocean and Sea Ice PDF Probability Density Function PEHRPP Pilot Evaluation of High Resolution Precipitation Products Pixel Picture element PMW Passive Micro-Wave PP Project Plan PR Precipitation Radar (on TRMM) PUM Product User Manual PVR Product Validation Report RMI Royal Meteorological Institute (of Belgium) (alternative of IRM) RR Rain Rate RU Rapid Update SAF Satellite Application Facility SEVIRI Spinning Enhanced Visible and Infra-Red Imager (on Meteosat from 8 onwards) SHMÚ Slovak Hydro-Meteorological Institute SSM/I Special Sensor Microwave / Imager (on DMSP up to F-15) SSMIS Special Sensor Microwave Imager/Sounder (on DMSP starting with S-16) SYKE Suomen ympäristökeskus (Finnish Environment Institute) T BB TKK TMI TRMM TSMS TU-Wien U-MARF UniFe URD UTC VIS ZAMG Equivalent Blackbody Temperature (used for IR) Teknillinen korkeakoulu (Helsinki University of Technology) TRMM Microwave Imager (on TRMM) Tropical Rainfall Measuring Mission UKMO Turkish State Meteorological Service Technische Universität Wien (in Austria) Unified Meteorological Archive and Retrieval Facility University of Ferrara (in Italy) User Requirements Document Universal Coordinated Time Visible Zentralanstalt für Meteorologie und Geodynamik (of Austria) 5

6 Page: 6/26 List of symbols θ Incidence angle (degree), generic θ i,b Observed incidence angle of beam b {f, m, a} (fore-, mid-, aft-beam) of i-th record in the time series of the current GPI φ, φ i,b Azimuth angle (degree), generic and observed σ 0 0, σ i,b Radar cross-section, backscattering coefficient m2 or db, generic and observed m2 t, t i Time, generic and observed d = doy(t), d i Day of year, d N, 1 d 366, as function of t (t i ) σ 0 (θ, d) Backscatter, modelled as function of incidence angle, with the model depending on the day of year d (i.e., d indexes one instance of the model class) 0 (θ i ) Observed backscatter, represented in terms of the model σ i,b σ (θ, d) σ θ ref, d σ (θ, d) σ θ ref, d σ 0 i θ ref θ dry σ dry θ ref, d θ wet σ wet θ ref, d First derivative of σ 0 (θ, d) First derivative ( slope ) at reference angle, parameter array Second derivative of σ 0 (θ, d) Second derivative ( curvature ) at reference angle, parameter array Normalised backscatter at reference angle, averaged over the beams, of the i-th record in the time series Dry crossover angle Dry reference at reference angle, parameter array Wet crossover angle Wet reference at reference angle, parameter array 6

7 Page: 7/26 1 The EUMETSAT Satellite Application Facilities and H-SAF The EUMETSAT Satellite Application Facility on Support to Operational Hydrology and Water Management (H-SAF) is part of the distributed application ground segment of the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT). The application ground segment consists of a Central Application Facility (CAF) and a network of eight Satellite Application Facilities (SAFs) dedicated to development and operational activities to provide satellitederived data to support specific user communities. See next figure: Figure 1 Conceptual scheme of the EUMETSAT application ground segment Next figure reminds the current composition of the EUMETSAT SAF network (in order of establishment). Nowcasting & Very Short Range Forecasting Ocean and Sea Ice Ozone & Atmospheric Chemistry Monitoring Climate Monitoring Numerical Weather Prediction GRAS Meteorology Land Surface Analysis Operational Hydrology & Water Management Figure 2 Current composition of the EUMETSAT SAF network (in order of establishment) Conceptual scheme of the EUMETSAT application ground segment The H-SAF was established by the EUMETSAT Council on 3 July 2005; its Development Phase started on 1 st September 2005 and ended on 31 August Its first Continuous Development and Operations Phase (CDOP) started on 28 September 2010 and ended on 28 February The SAF is now in its Second Continuous Development and Operations Phase (CDOP-2) started on 1 March 2012 and will end on 28 February

8 Page: 8/26 2 Introduction to product SM-OBS Principle of the product The concept of the Level 2 surface soil moisture retrieval model developed at the Vienna University of Technology (TU Wien) for use with C-band Scatterometers is a physically motivated change detection method. The first realisation of the concept was based on ERS 1/2 satellite data sets (Wagner et al. 1999a; Wagner et al. 1999b; Wagner et al. 1999c) and later the approach was successfully transferred to Advanced Scatterometer (ASCAT) data onboard the METOP-A satellite (Bartalis et al. 2007; Naeimi et al. 2008; Naeimi et al. 2009). The soil moisture retrieval algorithm is implemented within a software package called Soil Water Retrieval Package (WARP). The TU Wien change detection algorithm is from a mathematical point of view less complex than a radiative transfer model and can be inverted analytically. Therefore soil moisture can be estimated directly from the Scatterometer measurements without the need for iterative adjustment process. Because of this it is also quite straight forward to perform an error propagation to estimate the retrieval error for each land surface pixel (Naeimi et al. 2009). A disadvantage of the change detection model is that it is a lumped representation of the measurement process. Therefore, the different contributions to the observed total backscatter from the soil, vegetation, and soil-vegetation-interaction effects cannot be separated as would be the case for radiative transfer modelling approaches. It also means that it is necessary to calibrate its model parameters using long backscatter time series to implicitly account for land cover, surface roughness, and many other effects. The basic assumptions of the TU Wien change detection model are: 1. The relationship between the backscattering coefficient σ 0 expressed in decibels (db) and the surface soil moisture content is linear. 2. The backscattering coefficient σ 0 depends strongly on the incidence angle θ. The relationship σ 0 - θ is characteristic of the roughness conditions and the land cover, but is not affected by changes in the soil moisture content. 3. At the spatial scale of the Scatterometer measurements roughness and land cover are stable in time. 4. When vegetation grows, backscatter may decrease or increase, depending on whether the attenuation of the soil contribution is more important than the enhanced contribution from the vegetation canopy, or vice versa. Because the relative magnitude of these effects depends on the incidence angle, the curve σ 0 - θ changes with vegetation phenology over the year. This effect can be exploited to correct for the impact of vegetation phenology in the soil moisture retrieval by assuming that there are distinct incidence angles θ dry and θ wet, where the backscattering coefficient σ 0 is stable despite seasonal changes in above ground vegetation biomass for dry and wet conditions. 5. Vegetation phenology influences σ 0 on a seasonal scale. Local short-term fluctuations are suppressed at the scale of the Scatterometer measurements. Overall, the results obtained in experimental validation studies for both ERS-1/2 SCAT and METOP ASCAT showed that these assumptions are in general quite good. Also, they have received support from new theoretical studies. For example, the linearity assumption (point 1 above) has been held to be in contradiction to the Integral Equation Model (IEM) that suggests a non-linear relationship. But, as 8

9 Page: 9/26 recently demonstrated by Zribi (personal communication), this contradiction disappears when IEM is coupled with an air-soil transition model as first proposed for the SMOS retrieval (Schneeberger et al. 2004). With respect to seasonal vegetation effects, a recent study by Crow et al. (2010) shows that the change detection model is better able to describe the soil moisture retrieval skill over a larger range of incidence angles than the widely used Cloud Model (Attema and Ulaby 1978) in combination with the IEM (Fung 1994; Hsieh et al. 1997). But of course, there are instances where one or more of these assumptions break down. Currently the biggest problem appears to be that under extremely dry conditions, as might be found in deserts or semi-arid environments during the dry season, backscatter decreases when the soil becomes slightly wet. 2.2 Overview of Processing Steps In the software package WARP the TU Wien change detection model is applied to ERS 1/2 AMI and METOP ASCAT measurements in a sequence of processing steps (see Figure 3 for an overview): 1. Resampling of data: The Scatterometer measurements in orbit geometry are resampled to a fixed Discrete Global Grid (DGG), called WARP 5 grid. 1. Azimuthal normalisation: Backscatter values are normalised in terms of their acquisition azimuth angle, based on look-up tables with long-term mean values. 2. Estimate noise of σ 0 : Estimate the standard deviation (ESD) of σ 0 due to instrument noise, speckle and residual azimuthal effects based on the measurements of the fore- and aft antennas. 3. Model incidence angle dependency: Determine the mean annual cycle of the incidence angle behaviour of σ 0 by making use of the fact that the Scatterometer provides instantaneous measurements at two different incidence angles. The incidence angle dependency is described by a second order polynomial determined by the slope and the curvature. The slope and the curvature show a distinct annual cycle, determined by vegetation growth and decay. Slope and curvature parameters are determined by fitting a first degree polynomial to each group of local slope values. The results are the first and second derivatives of backscatter at 40 for each day of year. The final slope and curvature values are the result of averaging these derivative values over several periods with different duration (14-84 days). Corresponding noise values are also calculated. 4. Normalisation of backscatter measurements: Extrapolate all σ 0 taken over the entire incidence angle range to a reference angle of θ ref = 40 and calculate the average σ 0 θ ref based on the backscatter triplet. 5. Estimate noise of σ 0 θ ref : Based on the rules of error propagation the estimated standard deviation of σ 0 θ ref is calculated. 6. Detect frost and snow conditions: Use decision tree trained by historical temperature data to detect freeze/thawing events [RD-2]. 7. Determine dry and wet references: After σ 0 has been normalised with respect to the incidence angle, vegetation phenology effects and σ 0 θ ref outliers have been removed, dry and wet soil backscatter reference curves, σ dry θ ref, d and σ wet θ ref, d are determined. These maximum and minimum σ 0 θ ref are determined by statistical methods of noise analysis. 8. Wet reference correction: In dry climates the wet reference estimation can be biased given that there may never be enough rainfall to thoroughly wet the soil surface layer (Wagner and Scipal 9

10 Page: 10/ ). To correct biased σ wet θ ref, d in such dry climates, Koeppen climate classification data (Kottek et al. 2006) is used in conjunction with the sensitivity to soil moisture (defined in turn as the difference between the dry and wet parameters derived in the previous step). 9. Calculate surface soil moisture: Calculate the surface soil moisture by comparing σ 0 θ ref to the seasonally varying dry and wet reference values. 10. Estimate retrieval error of surface soil moisture: Calculate the estimated standard deviation of the surface soil moisture by rules of error propagation. Figure 3: Overview of the processing steps in WARP. In the following section, the single processing steps will be explained in detail. 10

11 Page: 11/26 3 Algorithms description 3.1 Resampling The task of resampling is to interpolate L1b Scatterometer measurements, given in the orbit grid, to a fixed Earth grid. For this purpose a Discrete Global Grid (DGG) has been developed by TU Wien and is called WARP 5 grid. The WARP 5 grid contains grid points with an equal spacing of 12.5 km in longitude and latitude. Each of the grid points is identified by a unique grid point index (GPI). The result of the resampling is a time series of interpolated measurements at each GPI over land (Figure 4). The DGG is discussed in more detail in [RD-1]. Figure 4: Orbit grid (dots) and WARP 5 grid (crosses) over Italy. The geometry of the ASCAT instrument is described in Figure 5, where the three satellite beams are indicated as fore, mid and aft beam. For each point in the orbit grid, all GPIs within an 18 km radius are determined by a nearest neighbour search, from which the interpolated values for the backscatter sigma naught σ 0 for each of the three beams (and other attributes such as incidence angle) are obtained as weighted average, with weighting coefficients computed according to the Hamming window function: w(x) = cos 2π δx r whereby δx denotes the distance between the actual GPI and the orbit grid point, and r the diameter of the search radius. We chose the Hamming window function for interpolation, because it is also used in the creation of the L1b product. Also two other window functions are currently supported, namely Lanczos and Inverse Distance Weighting, but the relative merits of the respective functions have yet to be evaluated. The result of the resampling step is, for each land GPI, a time series ts gpi, containing N gpi records ts gpi [i] = σ 0 i,b, θ i,b, φ i,b, t i, 1 i N gpi 11

12 Page: 12/26 each consisting of a time stamp t i and measurement triples for backscatter σ 0 i,b, incidence angle θ i,b and azimuth angle φ i,b. The subscript b {f, m, a} distinguishes between the fore, mid-, and aft-beam. Note that in the processing chain described below, the time-series are processed for each GPI separately. 3.2 Azimuthal Normalisation In some regions backscatter σ 0 varies strongly with azimuth or look angle, an effect known as azimuthally anisotropy. These azimuthal effects are accounted for by applying a polynomial correction term to the backscatter values. In this step, the coefficients of the polynomials are computed from the backscatter time series. For ASCAT on board METOP, the azimuth angle under which a location is seen depends on the beam (fore-, mid- or aft-beam), the swath (left or right) and the satellite direction (ascending or descending), resulting in 12 different azimuth configurations. For each of these configurations c, the σ 0 - θ dependency is modelled as a second order polynomial p c (θ). The coefficients of these polynomials are determined by fitting the model to all observations falling into the respective configuration category. Furthermore, an overall model p o (θ) is fitted to all observations, resulting in a total of 3 x 13 = 39 parameters. During the subsequent steps, a correction bias is applied to each backscatter value σ 0 i,b, depending on its azimuthal configuration: 0 σ i,b σ 0 i,b + p o θ i,b p c θ i,b This approach has been suggested, and is justified and described in more detail in Bartalis et al. (2006). Figure 5: Metop ASCAT geometry, introducing swaths, beams and nodes. 12

13 Page: 13/ Estimate Noise of Backscatter Measurements This step initialises the error propagation in the algorithm. It estimates the random noise of a single beam measurement σ 0. This is based on the following observation: all three beams observe the same region (soil moisture), and the fore- and aft-beam have the same incidence angle. Thus, as long as there are no azimuthal effects, the measurements of the for- and aft-beam are comparable, i.e., statistically speaking, they are instances of the same distribution. Hence, the expectation of the difference: δ = σ f 0 σ a 0 should be 0, and its variance should be twice the variance of one of the beams (assuming, the measurements are independent): var[δ] = 2 var[σ 0 ] By taking the square root and re-arranging, this gives us an estimate of the standard deviation of σ 0, which is called estimated standard deviation (ESD, see also Figure 6): ESD = std[σ 0 ] = std[δ] 2 whereby std[δ] is obtained as empirical standard deviation of δ over the whole time series. Figure 6: Global distribution of ESD. 3.4 Model Incidence Angle Dependence and Vegetation Correction The key equation of the model expresses the observed backscatter σ 0 (θ, t) as a function of the incidence angle θ at day d, more precisely as a second order polynomial about the reference angle θ ref = 40 o (Wagner et al. 1999b): σ 0 (θ, d) = σ 0 θ ref, d + σ θ ref, d θ θ ref σ θ ref, d θ θ ref 2 Eqn

14 Page: 14/26 whereby the 0th-order coefficient σ 0 θ ref, d is the normalised backscatter at the 40 o reference incidence angle, and the 1st and 2nd order coefficients σ θ ref, d and σ θ ref, d are referred to as slope and curvature parameters (see Figure 7). Slope and curvature mediate the effect of vegetation on the functional relationship between σ 0 and θ: for sparse vegetation, the curve tends to drop off rapidly, while for fully grown vegetation, it becomes less steep, almost horizontal in the case of rain forest (Figure 7b). In the model, we assume that the vegetation state is always the same at the same day of the year, i.e. it does not change inter-annually, and is thus a function of the day-of-year d. Hence, for each GPI, there will be 366 vegetation curves, each determined by a slope/curvature pair σ θ ref, d, σ θ ref, d. The slope and curvature parameters, which determine, in conjunction with the incidence angle, the effect of vegetation on the backscatter, are estimated during this step. Figure 7: Backscatter as function of the incidence angle. In WARP, it is assumed that an increase in soil moisture simply shifts the curve upwards (a), while a change in vegetation affects its shape, i.e., higher order moments (b).. Slope and curvature are determined as the coefficients of a straight line fitted to the so called local slopes. Local slopes are estimates of the first derivative of the backscatter - incidence angle dependency, and are computed as difference quotients between fore-and mid-beam, and aft- and mid-beam, respectively: σ local (θ, t) = σ0 θ To be more specific, each backscatter beam-triple [σ i,f, σ i,m, σ i,a ] (fore-, mid-, and aft-beam measurements) taken at incidence angles [θ i,f, θ i,m, θ i,a ] yields two local slope estimates at day d i : σ i,f θ i,m + θ i,f, d 2 i = σ i,m σ i,f θ i,m θ i,f σ i,a θ i,m + θ i,a, d 2 i = σ i,m σ i,a θ i,m θ i,a These local slopes are taken as instances of the first derivative of Eqn

15 Page: 15/26 σ (θ, d) = σ θ ref, d + σ θ ref, d θ θ ref Eqn.3.2 Thus, the slope and curvature parameters can be retrieved as the intercept and slope of a linear function (note that the normalized backscatter σ 0 (θ ref, d), which depends on the unknown soil moisture, has vanished in the first derivative), by fitting a line to the local slopes. In order to increase the precision of the estimates, the fit for a given day d is computed from the local slopes not only for day d, but from a time window of several days centred at d. Note that for the slope and curvature parameters, we do not use the i, b subscripts, because slope/curvature pertain to the whole time series - not only a single observation - and also equally to all beams. Figure 8: The effect of the time window size on the slope estimate. The width of the window is crucial for the quality of the estimates, since a window that is too short will lead to poor precision of the estimates, while a time window that is too long will tend to smooth local details or even average measurements taken from different vegetation periods (see Figure 8). In order to a) address the issue of time window length and b) to compute noise estimates for the parameters (which are difficult to obtain by error propagation in this case), a Monte Carlo approach has been implemented (Naeimi et al. 2009): the original time series is contaminated with independent and identically distributed (i.i.d.) Gaussian noise, resulting in 50 noisy instances of the original time series. Also, for each of these instances, a window width in a range of 2-12 is randomly assigned. Now, for a subset of 27 equidistant days, the slope and curvature parameters are estimated for each of the 50 training sets, and their final values σ θ ref, d, σ θ ref, d and corresponding noise estimates var[σ θ ref, d ], var[ σ θ ref, d are obtained as mean and variance, respectively, of the empirical distribution of the 50 values. Finally, a full complement of 366 parameter and noise values (one per day) is obtained from the 27 computed ones by cubic spline interpolation (this approach has been chosen in order to save processing time). 3.5 Incidence Angle Normalisation of Backscatter Backscatter measurements taken at different incidence angles are not directly comparable. Having retrieved the slope and curvature parameters, we can invert the model Eqn.3.2 in order to compute from 15

16 Page: 16/26 a backscatter measurement taken at an arbitrary incidence angle the corresponding value at the reference angle. Letting we get Eqn.3.3 x = σ 0 i,b (θ i ), σ θ ref, d i, σ θ ref, d i, f(x) = σ 0 i,b θ ref = σ 0 i,b (θ i ) σ θ ref, d i Δθ i 1 2 σ θ ref, d i (Δθ i ) 2 Eqn.3.3 Note that we have not included the day of year d i as parameter of the backscatter σ 0 i,b (θ i ) for several reasons. First, in the model the backscatter for a given day is thought of a function of the incidence angle, but not of time. It does depend on time, though not in a direct functional sense, but indirectly, through d i s effect on the slope and curvature, which it indexes. Second, the time parameter can always be retrieved from the time series via the index i, so adding it to the parameter list is redundant. Third, the notation becomes more concise. However, we must use d i as argument to the slope and curvatures parameters, since it is used as index into these parameter arrays. If we assume that the errors of the normalised backscatter, slope and curvature i.e., the components of x - are uncorrelated, the covariance matrix of x is simply The Jacobian of f is obtained as: Cov x = I 3x3 ESD 2, var σ θ ref, d i, var σ θ ref, d i T f x = [1, Δθ i, 0.5(Δθ i ) 2. ] Thus, according to Eqn.3.6, the noise variance of the normalised backscatter for beam b is Eqn.3.4: var σ 0 i,b θ ref = ESD 2 + var σ θ ref, d i (Δθ i ) var σ θ ref, d i (Δθ i ) 4 Eqn.3.4 Finally, the three beams now having been shifted to a common reference angle are averaged: σ i 0 θ ref = 1 3 The corresponding noise variance is given by var[σ i 0 θ ref ] = 1 9 b {f,m,a} b {f,m,a} σ 0 i,b θ ref var[σ 0 i,b θ ref ] As can be seen, averaging over the three beams has the effect that the variance of the noise due to instrument noise, speckle and azimuthal effects is lowered by a factor of three. It does, however, not lower the error due to the lack of fit of the slope model (Wagner 1998). 16

17 Page: 17/ Determination of Dry and Wet References For a given GPI, the dry σ dry θ ref, d and wet σ wet (θ ref, d) reference are the historically lowest and highest normalized backscatter values, respectively, measured at this location at a given day d. The dry and wet references are stored as parameter arrays indexed by the time, just as slope and curvature. The WARP model assumes that the vegetation (i.e., backscatter-vs.-incidence angle) curves for dormant and full vegetation intersect, and that the point of intersection depends on the soil moisture conditions: the intersection points for the driest and wettest conditions are called dry and wet crossover angles, respectively (Figure 9). The wet crossover angle θ wet is at 40 degrees (which is also the reference angle), while the dry crossover angle θ dry is located at 25 degrees (these values have been determined empirically). The importance of the crossover angle concept lies in the fact that at the crossover angles, vegetation has no effect on backscatter (Wagner 1998). Figure 9: Cross-over angle concept for vegetation correction. In order to determine the lowest backscatter value irrespective of the vegetation conditions, the normalised backscatter measurements are first shifted to the dry crossover angle: σ i 0 θ dry = σ i 0 θ ref + σ θ ref, d i Δθ dry σ θ ref, d i Δθ dry 2, with Δθ dry = θ dry θ ref,, and corresponding noise estimate var[σ i 0 θ dry ] = var[σ i 0 ] θ ref ] + var[σ θ ref, d i ] Δθ dry var[σ θ ref, d i ] Δθ dry 4. Eqn.3.5 Note the similarity to Eqn.3.3 and Eqn.3.4, but in this case, we are not shifting from the individual incidence angle to the reference angle, but from the reference angle to the dry crossover angle. From the resulting empirical distribution, the average of the M = N gpi 2.5% smallest values is used as an estimate of the lowest backscatter value at the dry crossover angle: σ dry θ dry = 1 M σ 0 Π{i} θ dry, M i=1 17

18 Page: 18/26 whereby Π is a permutation that sorts the timeseries in ascending order w.r.t. the backscatter values. Since the normalised backscatter values have different noise variances (depending on the day and incidence angle of acquisition), there exists no simple general expression for the noise variance of the average, but we have (assuming the noise contributions of the measurements are uncorrelated): var[σ dry θ dry ] = 1 M 2 var[σ 0 Π{i} θ dry ]. Finally, for each day t, σ dry θ dry has to be shifted back to the reference angle along its corresponding vegetation curve, in order to obtain σ dry θ ref, d : The noise is given by σ dry θ ref, d = σ dry θ dry σ θ ref, d Δθ dry 1 2 σ θ ref, d Δθ dry 2 var[σ dry θ ref, d ] = var[σ dry θ dry ] + var[σ θ ref, d Δθ dry 2 ] M i= var[ σ θ ref, d ] Δθ dry 4 This is the final estimate of the noise variance for the dry reference. The estimates for the wet reference σ wet θ ref, t = σ wet (θ wet ) σ θ ref, d (Δθ wet ) 1 2 σ θ ref, d (Δθ wet ) 2 (where Δθ wet = θ wet θ ref and its corresponding noise var[σ wet θ ref, d ] = var[σ wet (θ wet )] + var[σ θ ref, d (Δθ wet ) 2 ] var[ σ θ ref, d ](Δθ wet ) 4 are obtained in a completely analogue fashion, but instead of the 2.5 % lowest values at θ dry, the 2.5 % highest values have to be averaged at the wet crossover angle θ wet in order to compute σ wet (θ wet ). It is worth mentioning that due to the selection of the cross-over angles, which are fixed at 25 for σ 0 0 dry and 40 for σ wet globally, the dry reference is changing over time, whereas σ wet θ ref, d is constant (i.e., it does not depend on the day). This is because the wet crossover angle is equal to the reference angle, and thus Δθ wet 0 (see Figure 10). A global map of abovementioned references is given in Figure

19 Page: 19/26 Figure 10: Example of the dry and wet reference characteristics at a GPI near Salamanca, Spain. Figure 11: Example of wet backscatter reference (a), lowest dry backscatter reference (b) and sensitivity (c) derived from METOP-A ASCAT ( ). 19

20 Page: 20/ Wet reference correction It is possible that a region has never been captured in a truly saturated condition, which could be simply due to the fact that there were none, or that it did not occur during a satellite overpass. Thus, the assumption that the highest measured backscatter value represents a saturated condition is not valid. In order to correct for the first issue a so-called wet reference correction will be applied in affected regions. However, it is not possible to identify those regions relying only on Scatterometer measurements. Therefore, an external climate classification dataset will be used (Kottek et al. 2006). The utilisation of the wet reference correction is done in 2 steps: first the lowest level of the wet reference is set to -10 db, globally. Subsequently, in regions with rarely saturated soil moisture conditions (predominantly dry and hot climate zones) the wet reference is further raised until the sensitivity reaches at least 5 db (see Figure 12). Figure 12: Wet correction (a) and its effect on sensitivity (b) globally. 3.8 Soil Moisture Calculation The surface soil moisture detection algorithm is a change detection algorithm which basically compares the observed normalised backscatter to the highest (wettest) and lowest (driest) values ever observed at the grid point at day t. Under the assumption of a linear relationship between the backscatter in db and surface soil moisture, the latter can be estimated as (Wagner 1998): ssm(i) = σ i 0 θ ref σ dry θ ref, d i σ wet θ ref, d i σ dry θ ref, d i. 100 = σ i 0 θ ref σ dry θ ref, d i sens

21 Page: 21/26 Note that ssm(i) is expressed in percent. The difference between wet and dry reference in the denominator is known as sensitivity (sens). By proceeding along the lines of the derivation of Eqn.3.4, we obtain the following noise estimate for the soil moisture var[ssm(i)] = var σ i 0 θ ref sens 2 + var[σ dry θ ref, t ] σ i 0 θ ref, d i σ wet θ ref, d i sens var[σ wet θ ref, t ] σ i 0 θ ref, d i σ dry 2 θ ref, d i sens Error Propagation Let x = [x 1,, x p ] be a p-dimensional observation vector. x is assumed to be an instance of a p- dimensional random variable, with known covariance matrix Σ x. We are interested in how the covariance transforms under a mapping : R p R q, y = f(x), transforms, i.e., given x and f, we would like to know the covariance of y, Σ y. If f is a linear mapping of the form y = Ax + b, A R qxp, b R q, then the covariance transforms like whereby A T denotes the transpose of A. Σ y = AΣ x A T, If, on the other hand, f is a non-linear mapping, we first linearise it by replacing it by its first order Taylor approximation about the operation point x o : y = f(x) f(x 0 ) + f x (x x o) whereby f is the Jacobian of f. x Putting everything together, we finally obtain Eqn.3.6 Σ y = f x Σ x f T Eqn.3.6 x for the variance of y under the mapping f. Eqn.3.6 is the workhorse of the WARP error propagation scheme. 21

22 Page: 22/26 4 Validation activities of SM-OBS-4 product A detailed review of the ASCAT soil moisture product (validation results as well as issues) is given in (Wagner et al. 2013). In the following, a chronological overview of validation highlights within the last few years is given. One of the first studies that evaluated off-line soil moisture from METOP-A is (Bartalis et al. 2007). This study used commissioning phase data with model parameters that stem from historical ERS data ( ). Comparisons between ASCAT SSM and corresponding proxies of rainfall and NDVI showed a good qualitative agreement. In preparation of soil moisture data assimilation into weather models, (Scipal et al. 2007) evaluated the potential of ASCAT soil moisture data for numerical weather prediction at ECMWF by applying a nudging experiment using ECMWF's Integrated Forecast System (IFS). A comparison between ASCAT soil moisture and data from higher resolution ENVISAT ASAR (1 km) over Australia's Murray Darling basin gave insight that spatial patterns were well represented and that ASCAT SM compared to ASAR SM with a correlation of 0.91 for cropland (Sabel et al. 2008). A quantitative approach is the contribution of (Naeimi et al. 2009) who compared ERS and ASCAT data for consistency. They found that the shift of incidence angle between the two instruments was not significant for the soil moisture retrieval and could show relatively high correlation coefficients (0.90) between the two datasets (RMSE of 8.5). One of the first dedicated validation studies was (Brocca, Melone, Moramarco, Wagner & Hasenauer 2010) who compared the product over a site in Central Italy using both in situ and simulated soil moisture data. Two years of ASCAT data ( ) were used. The product was used for generating a Soil Water Index (SWI) and then compared to in situ and model data with correlation coefficients higher than 0.92 and 0.8 respectively. (Albergel et al. 2010) evaluated ASCAT time series and modelled surface soil moisture over the SMOSMANIA network and a SMOSREX station at a depth of 5 cm and 0-6 cm, respectively. Significant correlation values could be observed between ASCAT and in situ measurements, with an RMSE of m3/m3. Another important study (Brocca et al. 2011) compared the product to three AMSR-E products over 17 sites located in Italy, Spain, France and Luxemburg. The overall performance of the ASCAT product was very good, typically better or comparable with the best of the three AMSR-E products which were derived with the Land Parameter Retrieval Model (LPRM) (Jeu et al. 2008; Owe et al. 2008). A data assimilation experiment of ASCAT into a continuous rainfall-runoff model over the Upper Tiber River catchment in Italy (Brocca, Melone, Moramarco, Wagner, Naeimi, et al. 2010) indicated that by assimilating the SWI (representing the root zone layer) leads to potentially improved flood predictions, especially in case of highly uncertain initial soil moisture conditions. The SWI was found strongly correlated with the simulated saturation degree (R² higher than 0.90, RMSE less than 0.014m³/m³). Another follow-up study is (Brocca et al. 2012), where also root-zone soil moisture was assimilated. The ASCAT product served as input to long-term soil moisture datasets and has therefore been validated against other microwave datasets. In one study, (Dorigo et al. 2010) used ASCAT, AMSR-E, ERA two model datasets, ERA-Interim and GLDAS-NOAH, for cross-comparison by applying the triple collocation method. The focus of the study lies on revealing trends in uncertainty related to different observation principles, frequencies and the choice of the reference. The results show reasonable errors and patterns reflecting the known 22

23 Page: 23/26 performance issues of the respective datasets. Furthermore, improvements of ASCAT compared to ERS-2 can be shown. Another important study (Liu et al. 2011) compared the ASCAT product with AMSR-E data (VUA- NASA algorithm) and merged the two datasets in order to produce an improved soil moisture product with better spatial coverage and an increased number of observations. A CDF matching against GLDSA-Noah soil moisture estimates adapts the scales without effectively changing the temporal pattern of the respective products. The merged product then is used for sparsely and moderately vegetated regions. Important results were obtained by (Matgen et al. 2012) who validated the product over a much more densely vegetated study site over the Bibeschbach experimental catchment in Luxembourg. In their study the SWI compared very well to Antecedent Precipitation Index (API) and modelled data. Given the fact that about 46% of the catchment is covered by forests, still correlation values higher than 0.8 and RMSE values less than 0.04m³m-³ were obtained. (Parrens et al. 2012) compared soil moisture measurements of 21 SMOSMANIA in situ soil moisture network in southern France at a depth of 5 cm and simulations of the ISBA-A-gs model against the ASCAT product. The satellite data were projected onto the ISBA-A-gs grid to compute error metrics regarding absolute correlations and anomalies. The anomaly correlation coefficients between in situ observations and the SMOS product ranged from 0.23 to 0.48, while the ones for ASCAT were ranging from 0.35 to More and more regions in different climates were investigated, for example the semi-arid Kairouan region in Tunisia with a moisture anomaly index (Amri et al. 2012) where RMSE values m³m-³ between ground measurements and ASCAT were obtained. For root-zone soil moisture, this value decreased to 0.032m³m-³. The set up of a soil moisture network in the Tibetan Plateau is evaluated by (Su et al. 2011) using the ASCAT soil wetness index product and AMSR-E soil moisture measurements. Results reveal the ability of ASCAT soil moisture products to estimate the soil moisture of the area during the monsoon season. For south-east Australia, ASCAT, SMOS and AMSR-E products were evaluated against in situ measurements (Su et al. 2013). 23

24 Page: 24/26 5 Reference documents [RD-1] WARP 5 grid document, version 0.3, 4 October 2013, Vienna University of Technology, Austria. [RD-2] GIO Global Land Algorithm Theoretical Basis Document, Soil Water Index (SWI), issue I1.00, 28 March Available at [RD-3] H-SAF Product User Manual (PUM) H25/SM-OBS-4 Metop ASCAT Soil Moisture Time Series, issue 0.6, 16 October

25 Page: 25/26 6 References Albergel, C. et al., Cross-evaluation of modelled and remotely sensed surface soil moisture with in situ data in southwestern France. Hydrology and Earth System Sciences, 14(11), pp Available at: Amri, R. et al., Analysis of C-Band Scatterometer Moisture Estimations Derived Over a Semiarid Region. IEEE Transactions on Geoscience and Remote Sensing, 50(7), pp Bartalis, Z. et al., Initial soil moisture retrievals from the METOP-A Advanced Scatterometer (ASCAT). Geophysical Research Letters, 34(20), pp.1 5. Available at: [Accessed July 26, 2012]. Brocca, L., Melone, F., Moramarco, T., Wagner, W. & Hasenauer, S., ASCAT soil wetness index validation through in situ and modeled soil moisture data in central Italy. Remote Sensing of Environment, 114(11), pp Available at: Brocca, L. et al., Assimilation of Surface- and Root-Zone ASCAT Soil Moisture Products Into Rainfall Runoff Modeling. IEEE Transactions on Geoscience and Remote Sensing, 50(7), pp Brocca, L., Melone, F., Moramarco, T., Wagner, W., Naeimi, V., et al., Improving runoff prediction through the assimilation of the ASCAT soil moisture product. Hydrology and Earth System Sciences, 14, pp Available at: [Accessed July 20, 2012]. Brocca, L. et al., Soil moisture estimation through ASCAT and AMSR-E sensors: An intercomparison and validation study across Europe. Remote Sensing of Environment, 115(12), pp Available at: [Accessed July 26, 2012]. Dorigo, W.A. et al., Error characterisation of global active and passive microwave soil moisture datasets. Hydrology and Earth System Sciences, 14(12), pp Available at: [Accessed July 26, 2012]. Jeu, R.A.M. et al., Global Soil Moisture Patterns Observed by Space Borne Microwave Radiometers and Scatterometers. Surveys in Geophysics, 29(4-5), pp Available at: [Accessed July 26, 2012]. Liu, Y.Y. et al., Developing an improved soil moisture dataset by blending passive and active microwave satellite-based retrievals. Hydrology and Earth System Sciences, 15(2), pp Available at: Matgen, P. et al., On the potential of MetOp ASCAT-derived soil wetness indices as a new aperture for hydrological monitoring and prediction: a field evaluation over Luxembourg. Hydrological 25

26 Page: 26/26 Processes, 26(15), pp Available at: [Accessed July 19, 2012]. Naeimi, V., Bartalis, Z. & Wagner, W., ASCAT Soil Moisture: An Assessment of the Data Quality and Consistency with the ERS Scatterometer Heritage. Journal of Hydrometeorology, 10(2), pp Available at: [Accessed July 26, 2012]. Owe, M., de Jeu, R. & Holmes, T., Multisensor historical climatology of satellite-derived global land surface moisture. Journal of Geophysical Research, 113(F1), p.f Available at: Parrens, M. et al., Comparing soil moisture retrievals from SMOS and ASCAT over France. Hydrology and Earth System Sciences, 16(2), pp Sabel, D. et al., Synergistic use of scatterometer and ScanSAR data for extraction of surface soil moisture information in Australia. In 2008 EUMETSAT Meteorological Satellite Conference. Darmstadt, Germany: EUMETSAT, pp Scipal, K. et al., Towards the assimilation of scatterometer derived soil moisture in the ECMWF numerical weather prediction system. In Joint 2007 EUMETSAT Meteorological Satellite Conference and the 15th Satellite Meteorology & Oceanography Conference of the American Meteorological Society. Amsterdam, The Netherlands, p. 8. Su, C.-H. et al., Inter-comparison of microwave satellite soil moisture retrievals over the Murrumbidgee Basin, southeast Australia. Remote Sensing of Environment, 134(2013), pp Available at: [Accessed March 22, 2013]. Su, Z. et al., The Tibetan Plateau observatory of plateau scale soil moisture and soil temperature (Tibet-Obs) for quantifying uncertainties in coarse resolution satellite and model products. Hydrology and Earth System Sciences, 15(7), pp Available at: Wagner, W. et al., The ASCAT Soil Moisture Product: A Review of its Specifications, Validation Results, and Emerging Applications. Meteorologische Zeitschrift, 22(1), pp Available at: [Accessed April 29, 2013]. 26