Algorithm Theoretical Baseline Document (ATBD) Surface Soil Moisture ASCAT Data Record Time Series

Transcription

1 Page: 1/31 EUMETSAT Satellite Application Facility on Support to Operational Hydrology and Water Management Algorithm Theoretical H25, H108 H111

2 Page: 2/31 Revision History Revision Date Author(s) Description /08/06 S. Hahn First draft. Adopted content from H25 ATBD /01/19 S. Hahn Update annex, add product table list /07/07 S. Hahn Modifications according to review item discrepancies (RIDs) from the data record readiness review (DRR) /10/12 S. Hahn Modifications according to review from EU- METSAT Secretariat.

3 Page: 3/31 Table of Contents 1. Executive summary 8 2. Introduction Purpose of the document Targeted audience Related H SAF surface soil moisture products ASCAT on-board Metop Introduction Instrument description Geometry and coverage Product processing Soil moisture retrieval algorithm Model assumptions and requirements Model limitations and caveats Vegetation Snow Frozen soil Surface water Topographic complexity Long-term land cover changes Estimated standard deviation of backscatter Azimuth and incidence angle dependency of backscatter Azimuthal anisotropy Incidence angle modelling and normalization Vegetation characterization Dry and wet reference estimation Dry correction Wet correction Soil moisture computation WARP Processing steps Re-sampling to a Discrete Global Grid (DGG) Calculation of azimuthal correction coefficients Calculated ESD Estimation of slope and curvature Incidence angle normalization Calculation of dry and wet reference Wet correction Computation of soil moisture Side note on error propagation Limitations and caveats Processing modes

4 Page: 4/ Input data Level 2 output data Surface soil moisture and its noise Processing and correction flags References 27 Appendices 29 A. Introduction to H SAF 29 B. Purpose of the H SAF 29 C. Products / Deliveries of the H SAF 30 D. System Overview 31

5 Page: 5/31 List of Tables 2.1. List of soil moisture products produced related to this ATBD List of Figures 3.1. ASCAT swath geometry for a Metop minimum orbit height (822 km). The dimensions are symmetric with respect to the satellite ground track [1] Functional overview of the ASCAT Level 1 ground processing chain [2] Crossover angle concept Overview of the WARP processing steps A.1. Conceptual scheme of the EUMETSAT Application Ground Segment A.2. Current composition of the EUMETSAT SAF Network

6 Page: 6/31 List of Acronyms ASAR Advanced Synthetic Aperture Radar (on Envisat) ASAR GM ASAR Global Monitoring ASCAT Advanced Scatterometer ATBD Algorithm Theoretical Baseline Document BUFR Binary Universal Form for the Representation of meteorological data DORIS Doppler Orbitography and Radiopositioning Integrated by Satellite (on Envisat) ECMWF European Centre for Medium-range Weather Forecasts Envisat Environmental Satellite ERS European Remote-sensing Satellite (1 and 2) ESA European Space Agency EUM Short for EUMETSAT EUMETCast EUMETSAT s Broadcast System for Environment Data EUMETSAT European Organisation for the Exploitation of Meteorological Satellites FTP File Transfer Protocol H SAF SAF on Support to Operational Hydrology and Water Management Météo France National Meteorological Service of France Metop Meteorological Operational Platform NRT Near Real-Time NWP Near Weather Prediction PRD Product Requirements Document PUM Product User Manual PVR Product Validation Report SAF Satellite Application Facility SAR Synthetic Aperture Radar SRTM Shuttle Radar Topography Mission TU Wien Technische Universität Wien (Vienna University of Technology) WARP Soil Water Retrieval Package

7 Page: 7/31 WARP H WARP Hydrology WARP NRT WARP Near Real-Time ZAMG Zentralanstalt für Meteorologie und Geodynamic (National Meteorological Service of Austria)

8 Page: 8/31 1. Executive summary The Algorithm Theoretical provides a detailed description of the algorithm used to retrieve surface soil moisture information. The concept of the Level 2 surface soil moisture retrieval method developed at the Vienna University of Technology (TU Wien) for use with C-band scatterometers is a physically motivated change detection method. The first realization of the concept was based on ERS-1/2 satellite data sets [3 6] and later the approach was successfully transferred to Advanced Scatterometer (ASCAT) data onboard the Metop-A satellite [7 9]. The soil moisture retrieval algorithm is implemented within a software package called soil WAter Retrieval Package (WARP) and, for near real-time (NRT) applications, in a software package called WARP NRT. WARP is implemented in IDL/Python, whereas WARP NRT is a software package written in C++. In contrast to WARP, which processes several years of Metop ASCAT Level 1b data and produces both a model parameter database and soil moisture time series, WARP NRT processes single orbits and produces soil moisture in the original Level 1b orbit geometry. 2. Introduction 2.1. Purpose of the document The Algorithm Theoretical is intended to provide a detailed description of the scientific background and theoretical justification for the algorithms used to produce the Metop ASCAT soil moisture data sets Targeted audience This document mainly targets: 1. Remote sensing experts interested in the retrieval and error characterization of satellite soil moisture data sets. 2. Users of the remotely sensed soil moisture data sets who want to obtain a more in-depth understanding of the algorithms and sources of error Related H SAF surface soil moisture products In the framework of the H SAF project several soil moisture products, with different timeliness (e.g. NRT, offline, data records), spatial resolution, format (e.g. time series, swath orbit geometry) or the representation of the water content in various soil layers (e.g. surface, root-zone), are generated on a regular basis and distributed to users. A list of all available soil moisture products, as well as other H SAF products (such as precipitation or snow) can be looked up on the H SAF website 1. The following Table 2.1 gives an overview of the instances of surface soil moisture (SSM) products, which are related to this ATBD. 1

9 Page: 9/31 Table 2.1: List of soil moisture products produced related to this ATBD. ID Product Name H25 Metop ASCAT DR2015 SSM time series 12.5 km sampling H108 Metop ASCAT DR2015 EXT SSM time series 12.5 km sampling H109 Metop ASCAT DR2016 SSM time series 12.5 km sampling H110 Metop ASCAT DR2016 EXT SSM time series 12.5 km sampling H111 Metop ASCAT DR2017 SSM time series 12.5 km sampling 3. ASCAT on-board Metop 3.1. Introduction The European contribution within the framework of the Initial Joint Polar System (IJPS) is the EUMETSAT Polar System (EPS). The space segment of the EPS programme is envisaged to contain three sun-synchronous Meteorological Operational Platforms (Metop-A, Metop-B and Metop-C) jointly developed by ESA and EUMETSAT. Each satellite has a nominal lifetime in orbit of about 5 years, with a planned 6 month overlap between consecutive satellites. The first satellite Metop-A, was launched on 19 October 2006, Metop-B was launched on 17 September Metop-C is planned to be launched approximately in The Advanced Scatterometer (ASCAT) is one of the instruments carried on-board the series of Metop satellites Instrument description ASCAT is a real aperture radar system operating in C-band (VV polarization) and provides day- and night-time measurement capability, which is almost unaffected by cloud cover. The instrument design and performance specification is based on the experience of the Scatterometer flown on the ERS-1 and ERS-2 satellite. It can basically work in two different modes: Measurement or Calibration. The Measurement Mode is the only mode that generates science data for users. The instrument uses a pulse compression method called chirp, at which long pulses with linear frequency modulation were generated at a carrier frequency of GHz. After receiving and de-chirping of the ground echoes, a Fourier transform is applied in order to relate different frequencies in the signal to slant range distances. A pre-processing of the noise and echo measurements is done already on board to reduce the data rate to the ground stations, e.g. various averaging takes place reducing the raw data by a factor of approximately 25. Within each pulse repetition interval, after all pulse echoes have been decayed, the contribution of the thermal noise is monitored in order to perform a measurement noise subtraction during the ground processing. A side effect of on board processing is a degree of spatial correlation between different and within received echoes, but this is taken into account later on by the Level 1b processing. The radar pulse repetition frequency (PRF) is approximately Hz, which yields to 4.71 Hz for the beam pulse repetition frequency in the sequence fore-, mid- and aft beam [10]. The Calibration Mode is used during external calibration campaigns (29 days every 13 months), when the platform passes over three different ground transponders located in central Turkey. The objective of such calibration campaigns is to verify that the backscatter measurements from a target is correct for the whole incidence angle range. In other words, the absolute and relative

10 Page: 10/31 calibration will be monitored and checked. A stable radar cross section and an accurately known position on the Earth s surface are the basic and important requirements for each transponder. After receiving a pulse from ASCAT, the active transponder send a delayed pulse back, which in turn can be recorded by ASCAT. A comparison between the localised transponder position and the expected data allows to estimate three depointing angles and gain correction values for each antenna. An east-west distribution with a displacement of approximately 150 km, will allow to obtain transponder measurements from most of the incidence angles for each antenna beam. This high sampling is necessary in order to reconstruct the characteristics of each antenna gain pattern for the whole incidence angle range and achieve an appropriate relative calibration. Such a calibration set up allows to establish a reference system in order to evaluate and monitor the instrument performance on regular basis [11] Geometry and coverage The Metop satellites are flying in sun-synchronous 29 day repeat cycle orbit with an ascending node at 9:30 p.m. and a minimum orbit height of 822 km. This implies that the satellite will make a little more than 14 orbits per day. The advanced measurement geometry of ASCAT allows twice the coverage, compared to its predecessors flying on ERS-1 and ERS-2. Thus, the daily global coverage increased from 41% to 82%. The spatial resolution was also improved from 50 km to km, still reaching the same radiometric accuracy compared to the ERS-1/2 scatterometer. The advanced global coverage capability is accomplished by two sets of three fan-beam antennas, compared to only one set at the ERS satellites. The fan-beams are arranged broadside and ±45 of broadside, thus, allowing to observe three azimuthal directions in each of its two 550 km swaths (see Figure 3.1). The swaths are separated from the satellite ground track by about 360 km for the minimum orbit height. Each point on the Earth s surface that falls within one of the two swaths, will be seen by all three antennas and a so-called σ triplet can be observed. The incidence angles for those two antennas which are perpendicular to the flight direction intersect the surface between 25 and 53.3, whereas the other four antennas have an incidence angle range from 33.7 to 64.5 [1] Product processing Global data products are often classified into different levels according to their processing progress. In case of ASCAT the different product levels can be summarized as follows: Level 0: Unprocessed raw instrument data from the spacecraft. These are transmitted to the ground stations in binary form. Level 1a: Reformatted raw data together with already computed supplementary information (radiometric and geometric calibration) for the subsequent processing. Level 1b: Calibrated, georeferenced and quality controlled backscatter coefficients in full resolution or spatially averaged. It includes also ancillary engineering and auxiliary data. Level 2: Geo-referenced measurements converted to geophysical parameters, at the same spatial and temporal resolution as the Level 1b data.

11 Page: 11/31 fore beam left swath right swath fore beam 64.5 mid beam antenna look angles antenna incidence angles mid beam aft beam satellite ground track aft beam SZR SZO 41 nodes/12.5 km grid 21 nodes/25 km grid 360 km 550 km Figure 3.1: ASCAT swath geometry for a Metop minimum orbit height (822 km). The dimensions are symmetric with respect to the satellite ground track [1]. Level 3: Geophysical products derived from Level 2 data, which are either re-sampled or gridded points. The raw data arriving at the ground processing facility are passed into the Level 1 ground processor (see Figure 3.2). This data driven processing chain generates radiometrically calibrated Level 1b backscatter coefficients. It also includes an external calibration processing chain in order to support the localization and normalisation process of the measurement power echoes. Before satellite launch, it is only possible to estimate parameters characterising the expected instrument performance, since some of them depend on in-flight conditions. But once the satellite is his orbit, these parameters can be assessed during a calibration campaign. The first intermediate product generated just before the swath node generation and spatial averaging steps, is called Level 1b full resolution product. The main geophysical parameter in this product is the normalized backscatter coefficient σ. Along each antenna beam 256 σ values are projected on the Earth s surface. The footprint size is about km of various shapes and orientations, depending on the Doppler pattern over the surface [12]. The radiometric accuracy and the inter-beam radiometric stability is expected to be lass then 0.5 db peak-to-peak, whereas the georeferencing accuracy is about 4 km. In addition a number of quality flags are computed associated with every individual σ sample along each antenna beam. The other two products generated within the Level 1b processing are averaged σ values at

12 Page: 12/31 Figure 3.2: Functional overview of the ASCAT Level 1 ground processing chain [2]. two different spatial grids. A two-dimensional Hamming window function centered at every grid node is used in both cases for spatial filtering. This weighting function is based on a cosine function, which will basically attenuate the contribution of values with increasing distance. The window width is deciding the magnitude of spatial resolution and which values contribute to the weighted result. This means, values beyond the window width are disregarded. The spatial resolution is then defined as the distance when the window function reaches 50% of its peak intensity. This spatial averaging is used in the along- and across-track direction, with the objective to generate a set of σ triplets for each grid node of each swath at the desired radiometric resolution. The first product generated with this approach is called the nominal product and has a spatial resolution of 50 km for each grid point. The grid spacing is 25 km with 21 nodes at each swath per line. The higher resolution product has a spatial resolution ranging from 25 to 34 km. This variability is the result of a trade-off between spatial resolution and the desired radiometric accuracy, which lead to an alternating Hamming window width across the swath for the different beams. In this case the grid spacing is only 12.5 km, with 41 nodes at each swath per line. 4. Soil moisture retrieval algorithm 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 an iterative adjustment process. As a result, it is also quite straight forward to perform an error propagation to estimate the retrieval error for each location on the land surface [8]. A disadvantage of the

13 Page: 13/31 change detection model is that it is a lumped representation of the measurement process. The different contributions to the observed total backscatter from the soil, vegetation, and soilvegetation-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 Model assumptions and requirements The basic assumptions of the TU Wien change detection method are: 1. The relationship between the backscattering coefficient σ expressed in decibels (db) and the surface soil moisture content is linear. 2. The backscattering coefficient σ depends strongly on the incidence angle θ. The relationship is characteristic by roughness conditions and 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 (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 d and θ w ) and where the backscattering coefficient is stable despite seasonal changes in above ground vegetation biomass for dry and wet conditions. 5. Vegetation phenology influences backscatter σ on a seasonal scale. Local short-term fluctuations are suppressed at the scale of the scatterometer measurements. In order to be able to apply the TU Wien soil moisture change detection algorithm, the following requirements needs to be fulfilled: 1. Regular measurements (every 1-3 days), 2. Backscatter measurements from various incidence angles (approx ) 3. Sufficiently long time period (> 2 years). If all of these requirements are met, it is possible to derive robust model parameters, such as the characterization of the incidence angle vs backscatter behaviour, correction coefficients for azimuthal effects and estimation of the dry and wet reference.

14 Page: 14/ Model limitations and caveats Vegetation The influence of vegetation on the backscatter signal is currently accounted for using a seasonal correction. The so-called cross-over angle concept (section 4.4.3) allows to determine the dry/wet reference at incidence angles where the backscattering coefficient is stable despite seasonal changes in the above ground biomass. Inter-annual variability is not accounted for at the moment. In densely vegetated areas (such as Tropical rainforests) the C-band microwaves are not able to penetrate to the ground. Hence, a soil moisture signal from the soil surface is not contained in the backscatter measurements, which is typically characterized by a very low signal variation. However, it is possible to determine these cases with the error propagation, since the signal sensitivity plays an important role Snow Depending on the physical parameters of the snow layer (i.e. liquid water content, roughness of the air-snow interface, depth and layering of the snow pack, grain size and shape) different scattering mechanisms characterize the overall backscatter signal. Snow scattering phenomena are not treated in the TU Wien model and snow covered periods needs to be masked based on auxiliary information Frozen soil At temperatures below 0 C microwave backscatter drops, because of the inability of the soil water molecules to align themselves to the external electromagnetic field. The effect of freezing is more complex in case of vegetation, because plants have adaptive mechanisms to withstand the cold winter weather. Like for snow, handling backscatter from soil freezing periods is not covered by the TU Wien model and affected time periods needs to be masked based on auxiliary information Surface water Backscatter characteristics are primarily controlled by the roughness of the water surface, which is related to the short penetration depth of C-band microwaves (< 1-2 mm). A calm water surface acts like a mirror scattering almost the complete signal into the forward direction. Waves caused by near surface winds increase the backscatter looking at up- and downwind direction, and reduces the signal normal to the wind direction. As a result, open water can have a disturbing influence on the retrieval of soil moisture, if the area covered is large compared to the overall footprint size. Locations with (temporary) standing water needs to be treated carefully Topographic complexity A high variability of backscatter can be observed in mountainous areas which is not necessarily coupled with soil moisture changes. Hence, the surface topography directly influences the scattering behavior, which is not considered in the TU Wien model. A reduced soil moisture retrieval performance can be expected in topographic complex areas.

15 Page: 15/ Long-term land cover changes Long-term land cover changes are not treated in the TU Wien model at the moment. For example, if urbanization or desertification take place on a larger scale, the long-term backscatter signal can be influenced Estimated standard deviation of backscatter The Estimated Standard Deviation (ESD) of backscatter is derived from the measurements of the for and aft beam. This is based on the following observation: all three beams observe the same region and due to the observation geometry the for 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 := E σf σa should be 0, and its variance should be twice the variance of one of the beams (i.e Var [δ] = 2 Var [σ ]). This can be derived using error propagation ( ) [ ] 2 ( ) ( ) δ δ 2 ( ) δ δ Var [δ] Var σf σf + Var [σa] σa + 2 Cov(σf, σa) σf σa +... The first two terms should dominate, whereas the third term is 0 under the assumption of i.i.d. (independent and identically distributed random variables). [ ] Var [δ] Var σf (1) 2 + Var [σa] ( 1) (2) Under the assumption of homoscedasticity (a vector of random variables is homoscedastic if all random variables in the sequence or vector have the same finite variance) the variances are equal and the equation reads [ ] Var [δ] Var σf + Var [σa] = 2 Var [σ ] (3) The previous equation can be re-written to find the final formula for the ESD (1) Var [σ Var [δ] ] = 2 ESD [σ Var [δ] ] = 2 (4) (5) 4.4. Azimuth and incidence angle dependency of backscatter The backscattering coefficient changes as a function of the observed surface properties, most importantly surface dielectric properties, roughness and vegetation. However, the overall magnitude also strongly depends on the measurement geometry, i.e. the incidence angle θ as well

16 Page: 16/31 as the azimuth angle φ. Only measurements based on the same observation geometry can be compared directly Azimuthal anisotropy In some dedicated regions azimuthal effects on the backscattering coefficient are very strong. This azimuthal anisotropy is accounted for by applying a polynomial correction term to the backscatter signal as suggested by [13]. For ASCAT on board Metop, the azimuth angle under which a location is seen depends on the beam (for-, mid- or aft-beam), the swath (left or right) and the orbit direction (ascending or descending), resulting in twelve different azimuth configurations (i.e. φ i with i [1, 12]). For each of these configurations the incidence angle vs backscatter dependency is modeled as a second order polynomial p i (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 0 (θ) is fitted to all observations, resulting in a total of 3 13 = 39 coefficients. The following Equation 6 describes the application of the azimuthal correction σ b i,ac = σ b i (θ) + p 0 (θ) p i (θ) (6) where subscript b i stands for the beam (i.e. for, mid, aft) considered at the current configuration and the subscript ac denotes the backscatter corrected for azimuthal anistropy. The last term in Equation 6 corrects the incidence angle vs. backscatter dependency for the individual characteristics of a certain configuration p i (θ) and references it to an overall average behavior p 0 (θ) Incidence angle modelling and normalization A second order polynomial is also used for the incidence angle normalization (Equation 7), with a reference incidence angle defined as θ r = 40. Such a formulation can be considered as a second-order Taylor polynomial with an expansion point at θ r. Taylor polynomials at a given point are finite order truncation of its Taylor series, which completely determines the function in some neighbourhood of the point. The reference incidence angle of 40 has been chosen in order to minimize interpolation errors [3]. σ θ (t) = σ r (t) + σ r (t) (θ θ r ) σ r (t) (θ θ r ) 2 (7) In Equation 7 the zero-order coefficient σr (t) represents the normalized backscatter at the reference incidence angle θ r, and the first- and second-order coefficients and are referred to as slope σ r and curvature σ r parameters, characterizing surface roughness and the phenological cycle of the vegetation. The TU Wien model assumes that vegetation changes have a direct impact on the sensitivity of the backscatter signal (e.g. for sparse vegetation, the backscatter vs. incidence angle relationship tends to drop off rapidly, while for fully grown vegetation, it becomes less steep, almost horizontal in the case of rain forest), whereas changes in soil moisture are expected to have a minimal influence on the sensitivity (or in other words the incidence angle behaviour stays the same, except for on offset). Slope and curvature are determined as the coefficients of a straight line fitted to the so called local slopes σ l. A local slope is estimated by the first derivative of the backscatter vs incidence

17 Page: 17/31 angle dependency and are computed as difference quotients between for and mid beam, as well as aft and mid beam. σ l (θ l ) = σ (8) θ Specifically, each backscatter triplet (σf, σ m, σa) taken at their respective incidence angle (θ f, θ m, θ a ) yields to local slope estimates. σ fm σ am ( ) θm + θ f 2 ( ) θm + θ a 2 = σ m σ f θ m θ f (9) = σ m σ a θ m θ a (10) These local slopes are taken as estimates of the second derivative of the following equation: σ θ = σ r + σ r (θ θ r ) (11) The number of local slopes used for fitting a regression line, in order to determine slope and curvature at the reference incidence angle, are selected on a time-window basis Vegetation characterization Typically, a distinct backscatter signal can be observed over a range of incidence angles. The characteristic behaviour is mainly influenced by vegetation, soil roughness, dielectric properties and land cover. The dominant scattering mechanisms of vegetation are volume scattering in the vegetation canopy and surface scattering from the underlying soil surface [14]. A distinctly different behaviour can normally be observed between volume and surface scattering. The backscattering coefficient rapidly decreases with the incidence angle, with the exception of very rough surfaces [15]. By taking into consideration the model assumptions (e.g. roughness and land cover are stable), a simple concept can be formulated explaining the backscatter incidence angle relationship in relation to vegetation and soil moisture changes. Such a concept is outlined in Figure 4.1, which shows the backscatter signal over the incidence angle for two different states of vegetation (dormant and fully developed) and soil moisture (dry and wet soil). It is noticeable that for both soil conditions there is a crossover angle indicating that backscatter is rather stable despite vegetation growth. If these cross-over angles are chosen correctly, it is possible to compensate for vegetation effects. In the current formulation of the TU Wien backscatter model, θ d and θ w are set to 25 and 40, respectively Dry and wet reference estimation The estimation of the dry and wet backscatter reference is based upon the average of the extreme lowest (driest) and highest (wettest) measurements for a given location that have ever been recorded. An explicit uncertainty range, defined as a 95% 2-sided confidence interval, is used to separate the extreme low and high values [9]. The definition of the confidence interval considers the noise of dry and wet reference, which has been estimated using error propagation: Confidence Interval = ±1.96 σ n (θ) (12)

18 Page: 18/31 Backscatter [db] wet soil fully developed vegetation dormant vegetation dry soil fully developed vegetation dormant vegetation Incidence angle [degree] Figure 4.1: Crossover angle concept. The value 1.96 represents the 97.5 percentile of the standard normal distribution, which is often rounded to 2 for simplicity. After separation of the extreme observations, a transformation to the presumed cross-over angles is needed. The cross-over angels are distinct incidence angles θ d and θ w, where the backscattering coefficient is stable despite seasonal changes in above ground vegetation biomass for dry and wet conditions, respectively. Rearranging Equation 7 will transform the normalized backscatter values to the respective dry and wet cross-over angles: σ d (t) = σ r (t) + σ r (t) (θ d θ r ) σ r (t) (θ d θ r ) 2 (13) σ w (t) = σ r (t) + σ r (t) (θ w θ r ) σ r (t) (θ w θ r ) 2 (14) Once the number of extreme measurements for the lower (N b ) and upper (N u ) limits are known and the transformation to respective cross-over angles is completed, the dry and wet references are calculated as the mean value. N b C d = 1 σd,j (15) N b j=1 N u C w = 1 σw,j (16) N u Knowing the dry and wet references at their cross-over angles, an inverse transformation to j=1

19 Page: 19/31 the normalisation angle is necessary to obtain the final references. σ d r (t) = C d σ r (t) (θ d θ r ) 1 2 σ r (t) (θ d θ r ) 2 (17) σ w r (t) = C w σ r (t) (θ w θ r ) 1 2 σ r (t) (θ w θ r ) 2 (18) Dry correction In the current formulation of the algorithm no dry correction is involved Wet correction A problem related to the correct estimation of the wet reference is that in some regions truly saturated conditions are never captured simply due to the prevailing climate. Hence, a correction needs to be applied simulating wet conditions allowing to estimate a wet reference. The application of the correction is described in section Soil moisture computation Soil moisture computation is a change detection algorithm which compares the observed normalized backscatter to the highest (wettest) and lowest (driest) values ever observed at a certain location. Under the assumption of a linear relationship between normalized backscatter and surface soil moisture, the latter can be estimated using: S d (t) = σ r (t) σr d (t) σr w (t) σr d 100 (19) (t) The estimated surface soil moisture represents the topmost soil layer (< 5 cm) and is given in degree of saturation (S d ), ranging from 0% (dry) to 100% (wet). S d, given in %, can be converted into (absolute) volumetric units m 3 m 3 with the help of soil porosity information. Θ (t) = p Sd (t) 100 where Θ is absolute soil moisture in m 3 m 3, p is porosity in m 3 m 3. As it can be seen in Equation 20, the accuracy of soil porosity is as much as important as the relative soil moisture content. (20) 5. WARP The TU Wien soil moisture retrieval algorithm is implemented within a software package called soil WAter Retrieval Package (WARP), which processes several years of Metop ASCAT Level 1b data and produces both a model parameter database and soil moisture time series data records. An flowchart of the WARP processing steps is shown in Figure 5.1.

20 Page: 20/31 Figure 5.1: Overview of the WARP processing steps Processing steps The following subsections describe the implementation of the individual processing steps in WARP Re-sampling to a Discrete Global Grid (DGG) The task of re-sampling is to interpolate 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 (GP) 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 re-sampling is a time series of interpolated measurements at each GP over land. The WARP 5 is discussed in more detail in [16]. The three beams on each side of ASCAT are indicated as for, mid and aft beam. For each point in the orbit grid, all GPs within an 18 km radius are determined by a nearest-neighbour

21 Page: 21/31 (NN) search, from which the interpolated values for the backscatter for each of the three beams (and other such as incidence angle) are obtained as weighted average, with weighting coefficients computed according to the Hamming window function: ( w (x) = cos 2π δx ) d whereby δx denotes the distance between the actual GPI and the orbit grid points in the diameter d of the search radius. The Hamming window has been chosen for interpolation, because it is also used in the creation of the Level 1b product. The result of the re-sampling step for each of the GPIs is a time series ts gpi, containing N gpi records. (21) ts gpi [i] = σ b,i, θ b,i, φ b,i, t i 1 i N gpi (22) each consisting of a time stamp t i and measurement triples for backscatter σ b,i, incidence angle θ b,i and azimuth angle φ b,i. The subscript b {f, m, a} distinguishes between the for, mid and aft beam. Note that the following processing steps are applied for each GPI individually and based on the re-sampled time series Calculation of azimuthal correction coefficients As described in section in some dedicated areas azimuthal effects on the backscattering coefficient are very strong. In this step correction coefficients are computed based on a polynomial fit estimated for each individual look configuration (12 combinations possible: 2 swaths, 3 beams and 2 orbit directions), which is subtracted by a polynomial fit calculated from all look configurations. This way, the individual incidence angle vs backscatter characteristics are adjusted to a mean relationship canceling static azimuthal effects. The correction coefficients are stored for each grid point and always used to correct the resampled backscatter beforehand Calculated ESD This step initializes the error propagation in the soil moisture retrieval algorithm. computed as ESD is δ i = σ f,i σ a,i (23) ESD [σ ] = Var [δ i ] 2 after strong outliers (defined as 3 IQR) are masked out of the distribution of δ. (24) Estimation of slope and curvature The slope and curvature parameters are determined as the coefficients of a straight line fitted to the so called local slopes (see Equation 11). Local slopes are estimates of the first derivative of the backscatter vs. incidence angle dependency, and are computed as difference quotients between for and mid beam, and aft and mid beam, respectively.

22 Page: 22/31 In order to increase the precision of the estimates, the fit for a given day is computed from the local slopes not only for a day, but from a time window of several days centred at the day under question. 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. In order to (i) address the issue of time window length and (ii) 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 [8] 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 and corresponding noise estimates 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). The slope and curvature day-of-year parameter needs to be converted into time series by mapping the time t i to the respective day of year. σ r,i = σ r (doy (t i )) (25) Incidence angle normalization σ r,i = σ r (doy (t i )) (26) The incidence angle normalization is computed by inverting Equation 7 and using the already estimated slope σ r and curvature σ r parameter. In order to make use of the slope and curvature parameter, they need to be converted into a time series from their original day-of-year format. As a result, a backscatter measurement taken at an arbitrary incidence angle θ the corresponding value at the reference angle θ r will be calculated. Letting wet get x = [ ] σθ,b,i, σ r,i, σ r,i (27) f (x) : σ r,b,i = σ θ,b,i σ r,i θ b,i 1 2 σ r,i ( θ b,i ) 2 (28) with θ b,i = θ b,i θ r. If we assume that the errors of the normalized backscatter, slope and curvature are uncorrelated, the covariance matrix of x is simply ESD [σ ] Cov x = 0 Var [σ r] i 0 (29) 0 0 Var [σ r ] i

23 Page: 23/31 The Jacobian J of f (x) is obtained as J = ( ) δf = δx [1, θ b,i, 1 2 ( θ b,i) 2 ] Thus, the noise variance of the normalized backscatter for beam b is (30) Var [σ r] b,i = ESD [σ ] 2 + Var [ σ r ]i ( θ b,i) Var [ σ r ] i ( θ b,i) 4 (31) Finally, the three beams (now having been shifted to a common reference angle) are averaged σ r,i = 1 3 The corresponding variance is given by Var [ σ r] i = 1 9 b {f,m,a} b {f,m,a} σ r,b,i (32) Var [σ r] b,i (33) 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 [4] Calculation of dry and wet reference For a given grid point, the dry σr d and wet σr w 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 arrays indexed by the day of year, just as slope and curvature. Hence, also in this case the parameters needs to be transformed to time series. σ d r,i = σ d r (doy (t i )) (34) σ d r,i = σ w r (doy (t i )) (35) In the TU Wien backscatter model it is 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. The wet crossover angle θ w assumed to be at 40 (which is identical to the reference incidence angle θ r ) and the dry crossover angle θ d is located at 25. Both parameters have been determined empirically [4]. The importance of the crossover angle concept lies in the fact that the crossover angles, vegetation has no effect on backscatter [5]. In order to determine the lowest backscatter value irrespective of the vegetation conditions, the normalized backscatter measurements are first shifted to the dry crossover angle using Equation 36. σ d,i = σ r,i + σ r,i ( θ d ) σ r,i ( θ d ) 2 (36) with θ d = (θ d θ r ), and corresponding noise estimate

24 Page: 24/31 Var [σ d] i = Var [ σ r] i + Var [ σ r ]i ( θ d) Var [ σ r ] i ( θ d) 4 (37) From the resulting empirical distribution, an explicit uncertainty range, defined as a 95% 2-sided confidence interval, is used to separate the extreme low and high values. The average of the N b smallest values is used as an estimate of the lowest backscatter value at the dry crossover angle. N b C d = 1 σ N (38) d, {j} b j=1 whereby is a permutation that sorts the time series in ascending order w.r.t. the backscatter values. Since the normalized backscatter values have different noise variances (depending on the day and incidence angle), 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 [C d] = 1 Nb 2 N b Var [σd] {j} (39) Finally, for each day t, C d has to be shifted back to the reference incidence angle along its corresponding vegetation curve, in order to obtain σ d,i. The noise is given by j=1 σ d r,i = C d σ r,i ( θ d ) 1 2 σ r,i ( θ d ) 2 (40) [ [ Var σr d ]i = Var C d] Var [ σ r ]i ( θ d) Var [ σ r ] i ( θ d) 4 (41) This is the final estimate of the noise variance for the dry reference. The estimates of the wet reference σ w r,i = C w σ r,i ( θ w ) 1 2 σ r,i ( θ w ) 2 (42) where θ w = θ w θ r and its corresponding noise Var [σ w r ] i = Var [C w ] Var [ σ r ]i ( θ w) Var [ σ r ] i ( θ w) 4 (43) are obtained in a completely analogue fashion, but instead the N u values are averaged at the wet crossover angle θ w in order to compute C w. It is worth mentioning that due the selection of the crossover angles, which are fixed to 25 for σ d r and 40 for σ w r globally, the dry reference is changing over time, whereas σ w r is constant (i.e. it does not depend on the day). This is because the wet crossover angel is equal to the reference angle, and thus θ w = Wet correction The application of wet correction is based on an external climate data set [17], since scatterometer measurements alone are not sufficient to locate these regions. The wet correction is done in

25 Page: 25/31 two steps: first the lowest level of the wet reference is set to -10 db and subsequently, in regions with rarely saturated soil moisture conditions σr w values are raised until a sensitivity (defined as σr w σr d ) of at least 5 db has been reached [9] Computation of soil moisture Under the assumption of a linear relationship between normalized backscatter and surface soil moisture, the latter can be estimated using: S d,i = σ r,i σd r,i σr,i w 100 (44) σd r,i By proceeding with the derivation of the error propagation, we obtain the following noise estimate of the soil moisture Var [S d ] i = Var [ σ r] i ( 1 ) σr,i w σd r,i 2 [ ] + Var σr d σ r,i σw r,i ( ) i σr,i w σd r,i + Var [σr w ] i σ r,i σd r,i ( σr,i w σd r,i ) (45) 5.2. Side note on error propagation Let x = [x 1,, x p ] be a p-dimensional observation vector. x is assumed to be an instance of 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), 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 q p, b R q, then the covariance transforms like Σ y = AΣ x A T (46) whereby A T denotes the transpose of A. If, on the other hand, f is a non-linear mapping, we first linearise it by replacing its first order Taylor approximation about the operation point x 0 : whereby ( ) δf y = f (x) f (x 0 ) + (x x 0 ) (47) δx ( ) δf δx is the Jacobian J of f. Putting everything together we finally obtain ( ) ( ) δf δf T Σ y = Σ x (48) δx δx

26 Page: 26/31 for the variance of y under the mapping f. Equation 48 is the workhorse of the WARP error propagation scheme Limitations and caveats The soil moisture algorithm is applied on a global basis (i.e. for each grid point over land), but in certain situations, for example when dense forest, snow cover, frozen soil, open water or topographic complex area dominates the satellite footprint, the retrieval of soil moisture is heavily impacted or not possible at all. In addition, not each case (e.g. frozen soil, snow cover, open water) can be modeled by the error propagation and thus, it is even more important to reliably mask affected measurements. Advisory and processing flags indicate such critical cases, but it is left to the user to judge whether the soil moisture data is meaningful or not. Users are advised to to use the best auxiliary data available to improve the flagging of snow, frozen soil and (temporally) standing water. However, under the following conditions a surface soil moisture retrieval from Metop ASCAT should be most suited: low to moderate vegetation regimes, unfrozen and no snow, low to moderate topographic variations, no wetlands and coastal areas Processing modes The software package WARP can operate in two modes: full re-processing and extension. The difference between the two modes is that in latter case no new model parameters are computed and new Level 1b are re-sampled, normalized and transformed to soil moisture based on preexisting model parameters. These model parameters have to be derived from the same Level 1b (i.e. same calibration, resolution, etc.) used for the extension Input data The input data is described in detail in the Product User Manual (PUM) [18] Level 2 output data The following parameters are part of the Level 2 output data. A more detailed list with data type and data format can be found in the Product User Manual (PUM) [18] Surface soil moisture and its noise The surface soil moisture estimate represents the topmost soil layer (< 5 cm) and is given in degree of saturation (S d ), ranging from 0% (dry) to 100% (wet). S d can be converted into (absolute) volumetric units with the help of soil porosity information (see Equation 20). In extreme cases, the interpolated backscatter at θ r may exceed the dry or the wet backscatter reference. In these cases, the value is less than 0% or more than 100%. When this happens, the values are artificially set to 0% and 100% respectively. At the same time, the relevant correction flags are set.

27 Page: 27/ Processing and correction flags These flags indicate several conditions of interest. Processing flags are set to flag the reason for a soil moisture value not being provided in the product and correction flags are set to flag a soil moisture value provided in the product, but that has been modified after the retrieval for different reasons, according to quality criteria based on the data itself. 6. References [1] J. Figa-Saldana, J. J. W. Wilson, E. Attema, R. Gelsthorpe, M. R. Drinkwater, and A. Stoffelen, The Advanced Scatterometer (ASCAT) on the Meteorological Operational (MetOp) Platform: A follow on for European Wind Scatterometers, Canadian Journal of Remote Sensing, vol. 28, no. 3, pp , [2] ASCAT Product Guide, Tech. Rep. Doc. No: EUM/OPS-EPS/MAN/04/0028, v5, [3] W. Wagner, G. Lemoine, M. Borgeaud, and H. Rott, A study of vegetation cover effects on ERS scatterometer data, vol. 37, no. 2II, pp [4] W. Wagner, G. Lemoine, and H. Rott, A method for estimating soil moisture from ERS scatterometer and soil data, vol. 70, no. 2, pp [5] W. Wagner, J. Noll, M. Borgeaud, and H. Rott, Monitoring soil moisture over the canadian prairies with the ERS scatterometer, vol. 37, pp [6] K. Scipal, W. Wagner, M. Trommler, and K. Naumann, The global soil moisture archive from ERS scatterometer data: first results, vol. 3. IEEE, pp [7] Z. Bartalis, W. Wagner, V. Naeimi, S. Hasenauer, K. Scipal, H. Bonekamp, J. Figa, and C. Anderson, Initial soil moisture retrievals from the METOP-a advanced scatterometer (ASCAT), vol. 34. [8] V. Naeimi, Model improvements and error characterization for global ERS and METOP scatterometer soil moisture data, phd dissertation. [9] V. Naeimi, K. Scipal, Z. Bartalis, S. Hasenauer, and W. Wagner, An improved soil moisture retrieval algorithm for ERS and METOP scatterometer observations, vol. 47, no. 7, pp [10] R. V. Gelsthorpe, E. Schied, and J. J. W. Wilson, ASCAT - MetOp s Advanced Scatterometer, ESA Bull. ISSN , vol. 102, pp , [11] J. J. W. Wilson, C. Anderson, M. A. Baker, H. Bonekamp, J. F. Saldana, R. G. Dyer, J. A. Lerch, G. Kayal, R. V. Gelsthorpe, M. A. Brown, E. Schied, S. Schutz-Munz, F. Rostan, E. W. Pritchard, N. G. Wright, D. King, and U. Onel, Radiometric Calibration of the Advanced Wind Scatterometer Radar ASCAT Carried Onboard the METOP-A Satellite, IEEE Transactions on Geoscience and Remote Sensing, vol. 48, pp , [12] R. D. Lindsley, C. Anderson, J. Figa-Saldana, and D. G. Long, A Parameterized ASCAT Measurement Spatial Response Function, IEEE Transactions on Geoscience and Remote Sensing, pp. 1 10, 2016.

28 Page: 28/31 [13] Z. Bartalis, K. Scipal, and W. Wagner, Azimuthal anisotropy of scatterometer measurements over land, vol. 44, no. 8, pp [14] A. K. Fung, Microwave scattering and emission models and their applications. Artech House. [15] F. T. Ulaby, R. K. Moore, and A. K. Fung, Microwave Remote Sensing: Active and Passive. Vol. III - Volume Scattering and Emission Theory, Advanced Systems and Applications. Artech House, Inc. [16] WARP 5 Grid, Tech. Rep. v0.3, [17] M. Kottek, J. Grieser, C. Beck, B. Rudolf, and F. Rubel, World map of the köppen-geiger climate classification updated, vol. 15, pp [18] Product User Manual (PUM) Soil Moisture Data Records, Metop ASCAT Soil Moisture Time Series, Tech. Rep. Doc. No: SAF/HSAF/CDOP2/PUM, v0.3, 2016.

29 Page: 29/31 Appendices A. Introduction to H SAF H SAF is part of the distributed application ground segment of the European Organization for the Exploitation of Meteorological Satellites (EUMETSAT). The application ground segment consists of a Central Application Facilities located at EUMETSAT Headquarters, and a network of eight Satellite Application Facilities (SAFs), located and managed by EUMETSAT Member States and dedicated to development and operational activities to provide satellite-derived data to support specific user communities (see Figure A.1): Figure A.1: Conceptual scheme of the EUMETSAT Application Ground Segment. Figure A.2 here following depicts the composition of the EUMETSAT SAF network, with the indication of each SAF s specific theme and Leading Entity. B. Purpose of the H SAF The main objectives of H SAF are: a) to provide new satellite-derived products from existing and future satellites with sufficient time and space resolution to satisfy the needs of operational hydrology, by generating, centralizing, archiving and disseminating the identified products: precipitation (liquid, solid, rate, accumulated); soil moisture (at large-scale, at local-scale, at surface, in the roots region);

30 Page: 30/31 Figure A.2: Current composition of the EUMETSAT SAF Network. snow parameters (detection, cover, melting conditions, water equivalent); b) to perform independent validation of the usefulness of the products for fighting against floods, landslides, avalanches, and evaluating water resources; the activity includes: downscaling/upscaling modelling from observed/predicted fields to basin level; fusion of satellite-derived measurements with data from radar and raingauge networks; assimilation of satellite-derived products in hydrological models; assessment of the impact of the new satellite-derived products on hydrological applications. C. Products / Deliveries of the H SAF For the full list of the Operational products delivered by H SAF, and for details on their characteristics, please see H SAF website hsaf.meteoam.it. All products are available via EUMETSAT data delivery service (EUMETCast 2 ), or via ftp download; they are also published in the H SAF website 3. All intellectual property rights of the H SAF products belong to EUMETSAT. The use of these products is granted to every interested user, free of charge. If you wish to use these products, EUMETSAT s copyright credit must be shown by displaying the words copyright (year) EUMETSAT on each of the products used