Kaighin A. McColl

Extended triple collocation: Estimating errors and correlation coefficients with respect to an unknown target

Calibration and validation of geophysical measurement systems typically require knowledge of the true value of the target variable. However, the data considered to represent the true values often include their own measurement errors, biasing calibration, and validation results. Triple collocation (TC) can be used to estimate the root-mean-square-error (RMSE), using observations from three mutually independent, error-prone measurement systems. Here, we introduce Extended Triple Collocation (ETC): using exactly the same assumptions as TC, we derive an additional performance metric, the correlation coefficient of the measurement system with respect to the unknown target, rho(t,Xi). We demonstrate that rho(2)(t,Xi) is the scaled, unbiased signal-to-noise ratio and provides a complementary perspective compared to the RMSE. We apply it to three collocated wind data sets. Since ETC is as easy to implement as TC, requires no additional assumptions, and provides an extra performance metric, it may be of interest in a wide range of geophysical disciplines.

Uncertainty Analysis of Soil Moisture and Vegetation Indices Using Aquarius Scatterometer Observations

Simple functions of radar backscatter coefficients have been proposed as indices of soil moisture and vegetation, such as the radar vegetation index, i.e., RVI, and the soil saturation index, i.e., ms. These indices are ratios of noisy and potentially miscalibrated radar measurements and are therefore particularly susceptible to estimation errors. In this study, we consider uncertainty in satellite estimates of RVI and ms arising from two radar error sources: noise and miscalibration. We derive expressions for the variance and bias in estimates of RVI and ms due to noise. We also derive expressions for the sensitivity of RVI and ms to calibration errors. We use one year (September 1, 2011 to August 31, 2012) of Aquarius scatterometer observations at three polarizations ( σHH, σVV, and σHV) to map predicted error estimates globally, using parameters relevant to the National Aeronautics and Space Administration Soil Moisture Active and Passive satellite mission. We find that RVI is particularly vulnerable to errors in the calibration offset term over lightly vegetated regions, resulting in overestimates of RVI in some arid regions. ms is most sensitive to calibration errors over regions where the dynamic range of the backscatter coefficient is small, including deserts and forests. Noise induces biases in both indices, but they are negligible in both cases; however, it also induces variance, which is large for highly vegetated regions (for RVI) and areas with low dynamic range in backscatter values (for ms). We find that, with appropriate temporal and spatial averaging, noise errors in both indices can be reduced to acceptable levels. Areas sensitive to calibration errors will require masking.

How Many Parameters Can Be Maximally Estimated From a Set of Measurements

Remote sensing algorithms often invert multiple measurements simultaneously to retrieve a group of geophysical parameters. In order to create a robust retrieval algorithm, it is necessary to ensure that there are more unique measurements than parameters to be retrieved. If this is not the case, the inversion might have multiple solutions and be sensitive to noise. In this letter, we introduce a methodology to calculate the number of (possibly fractional) “degrees of information” in a set of measurements, representing the number of parameters that can be retrieved robustly from that set. Since different measurements may not be mutually independent, the amount of duplicate information is calculated using the information-theoretic concept of total correlation (a generalization of mutual information). The total correlation is sensitive to the full distribution of each measurement and therefore accounts for duplicate information even if multiple measurements are related only partially and nonlinearly. The method is illustrated using several examples, and applications to a variety of sensor types are discussed.

Sensitivity of Aquarius active and passive measurements temporal covariability to land surface characteristics

Active and passive microwave observations over land are affected by surface characteristics in different ways. L-band radar backscatter and radiometer measurements each have distinct advantages and problematic issues when applied to surface soil moisture estimation. Spaceborne radiometry has the advantage of better sensitivity to the geophysical parameter but suffers from coarse spatial resolution given limitations on antenna dimensions. Active sensing has the advantage of higher spatial resolution, but the measurements are, relative to radiometry, more affected by the confounding influences of scattering by vegetation and rough surfaces. Active and passive measurements can potentially span different scales and allow the combining of the relative advantages of the two sensing approaches. This strategy is being implemented in the NASA Soil Moisture Active Passive (SMAP) mission, which relies on the relationship between active and passive measurements to provide 9-km surface soil moisture estimates. The aim of this paper is to study the sensitivity of spaceborne L-band active and passive temporal covariations to land surface characteristics, in preparation for SMAP. A significant linear relationship (with slope β) is obtained between NASAs Aquarius scatterometer and radiometer observations across major global biomes. The error in β estimation is found to increase with land cover heterogeneity and to be unaffected by vegetation density (up to moderate densities). Results show that β estimated with two to eight months of Aquarius measurements (depending on vegetation seasonality) reflect local vegetation cover conditions under surfaces with complex mixture of vegetation, surface roughness, and dielectric constant.

Mean-velocity profile of smooth channel flow explained by a cospectral budget model with wall-blockage

A series of recent studies has shown that a model of the turbulent vertical velocity variance spectrum (Fvv) combined with a simplified cospectral budget can reproduce many macroscopic flowproperties of turbulent wall-bounded flows, including various features of the mean-velocity profile (MVP), i.e., the “law of the wall”. While the approach reasonably models the MVP’s logarithmic layer, the buffer layer displays insufficient curvature compared to measurements. The assumptions are re-examined here using a direct numerical simulation (DNS) dataset at moderate Reynolds number that includes all the requisite spectral and co-spectral information. Starting with several hypotheses for the cause of the “missing” curvature in the buffer layer, it is shown that the curvature deficit is mainly due to mismatches between (i) the modelled and DNS-observed pressure-strain terms in the cospectral budget and (ii) the DNS-observed Fvv and the idealized form used in previous models. By replacing the current parameterization for the pressure-strain term with an expansive version that directly accounts for wall-blocking effects, the modelled and DNS reported pressure-strain profiles match each other in the buffer and logarithmic layers. Forcing the new model with DNS-reported Fvv rather than the idealized form previously used reproduces the missing buffer layer curvature to high fidelity thereby confirming the “spectral link” between Fvv and the MVP across the full profile. A broad implication of this work is that much of the macroscopic properties of the flow (such as the MVP) may be derived from the energy distribution in turbulent eddies (i.e., Fvv) representing the microstate of the flow, provided the link between them accounts for wall-blocking.

Soil Salinity Impacts on L-Band Remote Sensing of Soil Moisture

The recently launched Soil Moisture and Ocean Salinity (SMOS) satellite is providing soil moisture observations at continental scales by measuring L-band microwave radiation emitted from the land surface. While its retrieval algorithms will correct for factors such as vegetation and surface roughness, it will not correct for soil salinity. This letter tests the assumption that soil salinity will have a negligible impact on L-band brightness temperature (Tb) at SMOS scales using field data; airborne Tb observations were collected in a saline groundwater discharge area near Nilpinna Station, South Australia. At the 500-m scale, the airborne observations of Tb could not be reproduced using the baseline algorithm of the SMOS Level 2 retrieval scheme, without accounting for soil salinity in the model. The analysis in this letter shows that soil moisture retrieval errors of at least 0.04 m3 m-3 (i.e., the entire SMOS error budget) will occur due to salinity alone in SMOS footprints with saline coverage as low as 25% (possibly even much less). Consequently, fractional salinity coverage cannot be considered a negligible factor by microwave soil moisture satellite missions.

L-Band Radar Soil Moisture Retrieval Without Ancillary Information

A radar-only retrieval algorithm for soil moisture mapping is applied to L-band scatterometer measurements from the Aquarius. The algorithm is based on a nonlinear relation between L-band backscatter and volumetric soil moisture and does not require ancillary information on the surface, e.g., land classification, vegetation canopy, surface roughness, etc. It is based on the definition of three limiting cases or end-members: 1) smooth bare soil; 2) rough bare soil; and 3) maximum vegetation condition. In this study, an estimation method is proposed for the end-member parameters that is iterative and only uses space-borne measurements. The major advantages of the algorithm include an analytic formulation (direct inversion possible), and the fact that there is no requirement for ancillary information. Ancillary data often misclassify the surface and the parameterizations linking surface classification to model parameter values are often highly uncertain. The retrieval algorithm is tested using 3 years of space-borne scatterometer observations from the Aquarius/SAC-D. Retrieved soil moisture accuracy is assessed in several ways: comparison of global spatial patterns with other available soil moisture products (two reanalysis modeling products and retrievals based on the Aquarius radiometer), extended triple collocation (ETC) and time series analysis over selected target areas. In general, low bias and standard deviation are observed with levels comparable to independent radiometer-based retrievals. The errors, however, increase across areas with high vegetation density. The results are promising and applicable to forthcoming L-band radar missions such as SMAP-NASA (2015) and SAOCOM-CONAE (2016).

Relationship Between Vegetation Microwave Optical Depth and Cross-Polarized Backscatter From Multiyear Aquarius Observations

Soil moisture retrieval algorithms based on passive microwave remote sensing observations need to account for vegetation attenuation and emission, which is generally parameterized as vegetation optical depth (VOD). This multisensor study tests a new method to retrieve VOD from cross-polarized radar backscattering coefficients. Three years of Aquarius/SAC-D data were used to establish a relationship between the cross-polarized backscattering coefficient σHV and VOD derived from a multitemporal passive dual-channel algorithm (VODMT). The dependence of the correspondence is analyzed for different land use classes. There are no systematic differences in the slope for woody versus nonwoody vegetation, resulting in a strong correlation (80% explained-variance) and a global linear relationship when all classes are combined. The relationship is stable over the years of observations. The comparison of the Aquarius-derived VODMT to Soil Moisture and Ocean Salinitys multi-angular VOD estimates shows similar spatial patterns and temporal behavior, evident in high correlations. However, VODMT has considerably higher mean values, but lower dynamic range globally. Most of the differences can be attributed to differences in instrument sampling. The main result of this study, a relationship between backscatter and VOD, will permit high-resolution mapping of VOD with synthetic aperture radar measurements. These maps allow future studies of scaling and heterogeneity effects of vegetation on soil moisture retrieval at the coarser scales of land microwave radiometry. The study shows that VOD based on passive measurements and predicted by active measurements are comparable globally and that the breakdown by land cover classification does not affect the relationship appreciably.

Multi-temporal microwave retrievals of Soil Moisture and vegetation parameters from SMAP

The NASA Soil Moisture Active Passive (SMAP) mission aims at producing low (36 km) and high-resolution (9 km) global maps of surface soil moisture based on L-band radiometer and radar/radiometer measurements, respectively. In this research study, results of applying a novel retrieval algorithm, the so-called Multi-Temporal Dual Channel Algorithm (MT-DCA) to the first year of SMAP observations are presented. MT-DCA allows retrieving not only soil moisture, but also vegetation optical depth (VOD) and scattering albedo estimates, from passive microwave measurements alone and without reliance of a priori information. At L-band, VOD is proportional to total vegetation water content and albedo accounts for structural changes. The analysis of these parameters at different temporal and spatial scales will reveal the full potential of L-band microwave for global ecology studies.

Implications of non-local transport and conditionally-averaged statistics on Monin-Obukhov Similarity Theory and Townsend’s attached eddy hypothesis

AbstractAccording to Townsend’s hypothesis, so-called wall-attached eddies are the main contributors to turbulent transport in the atmospheric surface layer (ASL). This is also one of the main assu...