Simon Zwieback

Recent advances in (soil moisture) triple collocation analysis

Abstract To date, triple collocation (TC) analysis is one of the most important methods for the global-scale evaluation of remotely sensed soil moisture data sets. In this study we review existing implementations of soil moisture TC analysis as well as investigations of the assumptions underlying the method. Different notations that are used to formulate the TC problem are shown to be mathematically identical. While many studies have investigated issues related to possible violations of the underlying assumptions, only few TC modifications have been proposed to mitigate the impact of these violations. Moreover, assumptions, which are often understood as a limitation that is unique to TC analysis are shown to be common also to other conventional performance metrics. Noteworthy advances in TC analysis have been made in the way error estimates are being presented by moving from the investigation of absolute error variance estimates to the investigation of signal-to-noise ratio (SNR) metrics. Here we review existing error presentations and propose the combined investigation of the SNR (expressed in logarithmic units), the unscaled error variances, and the soil moisture sensitivities of the data sets as an optimal strategy for the evaluation of remotely-sensed soil moisture data sets.

Estimating error cross‐correlations in soil moisture data sets using extended collocation analysis

Global soil moisture records are essential for studying the role of hydrologic processes within the larger earth system. Various studies have shown the benefit of assimilating satellite-based soil moisture data into water balance models or merging multisource soil moisture retrievals into a unified data set. However, this requires an appropriate parameterization of the error structures of the underlying data sets. While triple collocation (TC) analysis has been widely recognized as a powerful tool for estimating random error variances of coarse-resolution soil moisture data sets, the estimation of error cross covariances remains an unresolved challenge. Here we propose a method—referred to as extended collocation (EC) analysis—for estimating error cross-correlations by generalizing the TC method to an arbitrary number of data sets and relaxing the therein made assumption of zero error cross-correlation for certain data set combinations. A synthetic experiment shows that EC analysis is able to reliably recover true error cross-correlation levels. Applied to real soil moisture retrievals from Advanced Microwave Scanning Radiometer-EOS (AMSR-E) C-band and X-band observations together with advanced scatterometer (ASCAT) retrievals, modeled data from Global Land Data Assimilation System (GLDAS)-Noah and in situ measurements drawn from the International Soil Moisture Network, EC yields reasonable and strong nonzero error cross-correlations between the two AMSR-E products. Against expectation, nonzero error cross-correlations are also found between ASCAT and AMSR-E. We conclude that the proposed EC method represents an important step toward a fully parameterized error covariance matrix for coarse-resolution soil moisture data sets, which is vital for any rigorous data assimilation framework or data merging scheme.

Frozen Soil Detection Based on Advanced Scatterometer Observations and Air Temperature Data as Part of Soil Moisture Retrieval

Surface soil moisture is one of the operational products derived from Advanced Scatterometer (ASCAT) data. The reliability of its estimation depends on the detection of predominantly frozen conditions of the landscape (including soil and vegetation) and the presence of wet snow, which would otherwise impede the estimation. As the robust determination of the freeze/thaw (F/T) state using exclusively scatterometer measurements on a global basis is complicated due to the myriad of different climatic and land cover conditions; we propose to support the retrieval using ERA Interim temperature data. The approach is based on a probabilistic time series model, whereby backscatter and temperature data are combined to estimate the freeze/thaw state. The method is assessed with proxy F/T states derived from modeled and in situ air and soil temperature data on a global basis. These analyses show an improved consistency compared to a previously published ASCAT F/T algorithm, with typical agreements between the external data and the results of the algorithm exceeding 80%. The quantitative interpretation of these comparisons is, however, hampered by discrepancies between the F/T state derived from temperature data and the one pertinent to radar remote sensing, as the former does not account for, e.g., wet snow conditions. The inclusion of the ERA Interim temperature data can improve the accuracy of the algorithm by more than 10 percentage points in regions where freezing conditions are rare.

Estimation of the temporal autocorrelation structure by the collocation technique with an emphasis on soil moisture studies

Abstract The collocation technique has become a popular tool in oceanography and hydrology for estimating the error variances of different data sources such as in situ sensors, models and remote sensing products. It is also possible to determine calibration constants, for example to account for an off-set between the data sources. So far, the temporal autocorrelation structure of the errors has not been studied, although it is known that it has detrimental effects on the results of the collocation technique, in particular when calibration constants are also determined. This paper shows how the (triple) collocation estimators can be adapted to retrieve the autocovariance functions; the statistical properties as well as the structural deficencies are described. The coupling between the autocorrelation of the error and the estimation of calibration constants is studied in detail, due to its importance for analysing temporal changes. In soil moisture applications, such time variations can be induced, for example, by seasonal changes in the vegetation cover, which affect both models and remote sensing products. The limitations of the proposed technique associated with these considerations are analysed using remote sensing and in situ soil moisture data. The variability of the inter-sensor calibration and the autocovariance are shown to be closely related to temporal patterns of the data. Editor D. Koutsoyiannis Citation Zwieback, S., Dorigo, W., and Wagner, W., 2013. Estimation of the temporal autocorrelation structure by the collocation technique with an emphasis on soil moisture studies. Hydrological Sciences Journal, 58 (8), 1729–1747.

A Polarimetric First-Order Model of Soil Moisture Effects on the DInSAR Coherence

Changes in soil moisture between two radar acquisitions can impact the observed coherence in differential interferometry: both coherence magnitude |Υ| and phase Φ are affected. The influence on the latter potentially biases the estimation of deformations. These effects have been found to be variable in magnitude and sign, as well as dependent on polarization, as opposed to predictions by existing models. Such diversity can be explained when the soil is modelled as a half-space with spatially varying dielectric properties and a rough interface. The first-order perturbative solution achieves–upon calibration with airborne L band data–median correlations ρ at HH polarization of 0.77 for the phase Φ, of 0.50 for |Υ|, and for the phase triplets ≡ of 0.56. The predictions are sensitive to the choice of dielectric mixing model, in particular the absorptive properties; the differences between the mixing models are found to be partially compensatable by varying the relative importance of surface and volume scattering. However, for half of the agricultural fields the Hallikainen mixing model cannot reproduce the observed sensitivities of the phase to soil moisture. In addition, the first-order expansion does not predict any impact on the HV coherence, which is however empirically found to display similar sensitivities to soil moisture as the co-pol channels HH and VV. These results indicate that the first-order solution, while not able to reproduce all observed phenomena, can capture some of the more salient patterns of the effect of soil moisture changes on the HH and VV DInSAR signals. Hence it may prove useful in separating the deformations from the moisture signals, thus yielding improved displacement estimates or new ways for inferring soil moisture.

Influence of Vegetation Growth on the Polarimetric Zero-Baseline DInSAR Phase Diversity—Implications for Deformation Studies

The polarization diversity of the phase causes ambiguities in the estimation of displacements using differential interferometry. Over natural surfaces such as vegetated areas, the magnitude of these ambiguities is potentially related to complex dynamic processes such as vegetation growth. As the properties and possible origins of such diversity (besides noiselike influences) over changing vegetation canopies are virtually unknown, we propose to investigate them empirically using an L-band zero-baseline data set covering one growing season over different agricultural crops. We frequently observe HH-VV phase differences exceeding 0.5π, corresponding to a displacement discrepancy of 3 cm. The HH-VV phase difference and other properties of the polarimetric coherence regions (e.g., the shape and the relation to the in situ observed biomass) vary with the crop type. The observations over wheat and barley and, to a lesser extent, rape suggest the presence of birefringence within the canopy. By contrast, those over maize and sugar beet, while also showing phase diversity, cannot be explained by birefringence or similarly simple models. Irrespective of the origin of this dependence, its presence and systematic nature indicate the potential importance of vegetation effects in differential interferometry, which may limit the accuracy of the estimated deformations over vegetated areas.

A Statistical Test of Phase Closure to Detect Influences on DInSAR Deformation Estimates Besides Displacements and Decorrelation Noise: Two Case Studies in High-Latitude Regions

Displacements of the Earths surface can be estimated using differential interferometric synthetic aperture radar. The estimates are derived from the phase difference between two radar acquisitions. When at least three such acquisitions are available, one can compute the displacement between the first and the third acquisition and compare it with the sum of the two intermediate displacements. These two are expected to be equal for a piston-like spatially uniform deformation. However, this is not necessarily the case in measured data. Such lack of phase closure can be due to decorrelation noise alone. It has also been attributed to complex scattering processes such as soil moisture changes or multiple scattering sources. However, the nature of these nonrandom effects is only poorly understood in cold regions, as the role of snow and freeze/thaw processes has not been studied to date. To distinguish the noise-like and the systematic effects, an asymptotic Wald significance test is proposed. It detects situations when the observed closure error cannot solely be explained by noise. Such situations with p <; 0.05 are observed at the Ku-band during snow metamorphism and melt and following a summer precipitation event in Sodankylä, Finland. They can also be prevalent (> 25%) in the X-band observations of ice-rich permafrost regions in the Lena Delta, Russia, indicating the presence of processes that can have systematic and deleterious impacts on the estimation of surface movements. Satellite-based monitoring of these displacements is thus possibly subject to complex error sources in high-latitude regions.

The Impact of Quadratic Nonlinear Relations between Soil Moisture Products on Uncertainty Estimates from Triple Collocation Analysis and Two Quadratic Extensions

AbstractThe error characterization of soil moisture products, for example, obtained from microwave remote sensing data, is a key requirement for using these products in applications like numerical weather prediction. The error variance and root-mean-square error are among the most popular metrics: they can be estimated consistently for three datasets using triple collocation (TC) without assuming any dataset to be free of errors. This technique can account for additive and multiplicative biases; that is, it assumes that the three products are linearly related. However, its susceptibility to nonlinear relations (e.g., due to sensor saturation and scale mismatch) has not been addressed. Here, a simulation study investigates the impact of quadratic relations on the TC error estimates [also when the products are first rescaled using the nonlinear cumulative distribution function (CDF) matching technique] and on those by two novel methods. These methods—based on error-in-variables regression and probabilistic ...

Temporal error variability of coarse scale soil moisture products - case study in central Spain

The triple collocation technique, which retrieves the error variances of three sets of measurements of the same parameter, is applied to soil moisture records in central Spain: ASCAT remote sensing observations, REMEDHUS in-situ probes, and the ERA Interim model. The objective is the estimation of the temporal variability of the error of ASCAT. The three data sets have to be calibrated with respect to each other as they show different mean values and dynamic ranges. The time-variant estimation of both the error and the calibration parameters is shown to be very sensitive to the extents of the temporal windows used and the calibration procedure. Due to the temporal fluctuations of the calibration constants, artefacts such as seasonal variations and extreme values are introduced. This case study shows that the temporal analysis of the errors using the collocation technique can lead to spurious results when the data sets have to be referenced with respect to one another.

Thaw Subsidence of a Yedoma Landscape in Northern Siberia, Measured In Situ and Estimated from TerraSAR-X Interferometry

In permafrost areas, seasonal freeze-thaw cycles result in upward and downward movements of the ground. For some permafrost areas, long-term downward movements were reported during the last decade. We measured seasonal and multi-year ground movements in a yedoma region of the Lena River Delta, Siberia, in 2013–2017, using reference rods installed deep in the permafrost. The seasonal subsidence was 1.7 ± 1.5 cm in the cold summer of 2013 and 4.8 ± 2 cm in the warm summer of 2014. Furthermore, we measured a pronounced multi-year net subsidence of 9.3 ± 5.7 cm from spring 2013 to the end of summer 2017. Importantly, we observed a high spatial variability of subsidence of up to 6 cm across a sub-meter horizontal scale. In summer 2013, we accompanied our field measurements with Differential Synthetic Aperture Radar Interferometry (DInSAR) on repeat-pass TerraSAR-X (TSX) data from the summer of 2013 to detect summer thaw subsidence over the same study area. Interferometry was strongly affected by a fast phase coherence loss, atmospheric artifacts, and possibly the choice of reference point. A cumulative ground movement map, built from a continuous interferogram stack, did not reveal a subsidence on the upland but showed a distinct subsidence of up to 2 cm in most of the thermokarst basins. There, the spatial pattern of DInSAR-measured subsidence corresponded well with relative surface wetness identified with the near infra-red band of a high-resolution optical image. Our study suggests that (i) although X-band SAR has serious limitations for ground movement monitoring in permafrost landscapes, it can provide valuable information for specific environments like thermokarst basins, and (ii) due to the high sub-pixel spatial variability of ground movements, a validation scheme needs to be developed and implemented for future DInSAR studies in permafrost environments.