Balaji Devaraju

Large-Scale Runoff from Landmasses: A Global Assessment of the Closure of the Hydrological and Atmospheric Water Balances*

AbstractThe performance of hydrological and hydrometeorological water-balance-based methods to estimate monthly runoff is analyzed. Such an analysis also allows for the examination of the closure of water budgets at different spatial (continental and catchment) and temporal (monthly, seasonal, and annual) scales. For this analysis, different combinations of gridded observations [Global Precipitation Climatology Centre (GPCC), Global Precipitation Climatology Project (GPCP), Climate Prediction Center (CPC), Climatic Research Unit (CRU), and University of Delaware (DEL)], atmospheric reanalysis models [Interim ECMWF Re-Analysis (ERA-Interim), Climate Forecast System Reanalysis (CFSR), and Modern-Era Retrospective Analysis for Research and Applications (MERRA)], partially model-based datasets [Global Land Surface Evaporation: The Amsterdam Methodology (GLEAM), Moderate Resolution Imaging Spectroradiometer (MODIS) Global Evapotranspiration Project (MOD16), and FLUXNET Multi-Tree Ensemble (FLUXNET MTE)], and G...

Estimating Runoff Using Hydro-Geodetic Approaches

Given the continuous decline in global runoff data availability over the past decades, alternative approaches for runoff determination are gaining importance. When aiming for global scale runoff at a sufficient temporal resolution and with homogeneous accuracy, the choice to use spaceborne sensors is only a logical step. In this respect, we take water storage changes from Gravity Recovery And Climate Explorer (grace) results and water level measurements from satellite altimetry, and present a comprehensive assessment of five different approaches for river runoff estimation: hydrological balance equation, hydro-meteorological balance equation, satellite altimetry with quantile function-based stage–discharge relationships, a rudimentary instantaneous runoff–precipitation relationship, and a runoff–storage relationship that takes time lag into account. As a common property, these approaches do not rely on hydrological modeling; they are either purely data driven or make additional use of atmospheric reanalyses. Further, these methods, except runoff–precipitation ratio, use geodetic observables as one of their inputs and, therefore, they are termed hydro-geodetic approaches. The runoff prediction skill of these approaches is validated against in situ runoff and compared to hydrological model predictions. Our results show that catchment-specific methods (altimetry and runoff–storage relationship) clearly outperform the global methods (hydrological and hydro-meteorological approaches) in the six study regions we considered. The global methods have the potential to provide runoff over all landmasses, which implies gauged and ungauged basins alike, but are still limited due to inconsistencies in the global hydrological and hydro-meteorological datasets that they use.

Continental-Scale Basin Water Storage Variation from Global and Dynamically Downscaled Atmospheric Water Budgets in Comparison with GRACE-Derived Observations

AbstractSince 2002, the Gravity Recovery and Climate Experiment (GRACE) has provided gravity-derived observations of variations in the terrestrial water storage. Because of the lack of suitable direct observations of large-scale water storage changes, a validation of the GRACE observations remains difficult. An approach that allows the evaluation of terrestrial water storage variations from GRACE by a comparison with those derived from aerologic water budgets using the atmospheric moisture flux divergence is presented. In addition to reanalysis products from the European Centre for Medium-Range Weather Forecasts and the National Centers for Environmental Prediction, high-resolution regional atmospheric simulations were produced with the Weather Research and Forecast modeling system (WRF) and validated against globally gridded observational data of precipitation and 2-m temperature. The study encompasses six different climatic and hydrographic regions: the Amazon basin, the catchments of Lena and Yenisei, ...

A stochastic framework for inequality constrained estimation

Quality description is one of the key features of geodetic inference. This is even more true if additional information about the parameters is available that could improve the accuracy of the estimate. However, if such additional information is provided in the form of inequality constraints, most of the standard tools of quality description (variance propagation, confidence ellipses, etc.) cannot be applied, as there is no analytical relationship between parameters and observations. Some analytical methods have been developed for describing the quality of inequality constrained estimates. However, these methods either ignore the probability mass in the infeasible region or the influence of inactive constraints and therefore yield only approximate results. In this article, a frequentist framework for quality description of inequality constrained least-squares estimates is developed, based on the Monte Carlo method. The quality is described in terms of highest probability density regions. Beyond this accuracy estimate, the proposed method allows to determine the influence and contribution of each constraint on each parameter using Lagrange multipliers. Plausibility of the constraints is checked by hypothesis testing and estimating the probability mass in the infeasible region. As more probability mass concentrates in less space, applying the proposed method results in smaller confidence regions compared to the unconstrained ordinary least-squares solution. The method is applied to describe the quality of estimates in the problem of approximating a time series with positive definite functions.

What Is the Spatial Resolution of grace Satellite Products for Hydrology

The mass change information from the Gravity Recovery And Climate Experiment (grace) satellite mission is available in terms of noisy spherical harmonic coefficients truncated at a maximum degree (band-limited). Therefore, filtering is an inevitable step in post-processing of grace fields to extract meaningful information about mass redistribution in the Earth-system. It is well known from previous studies that a number can be allotted to the spatial resolution of a band-limited spherical harmonic spectrum and also to a filtered field. Furthermore, it is now a common practice to correct the filtered grace data for signal damage due to filtering (or convolution in the spatial domain). These correction methods resemble deconvolution, and, therefore, the spatial resolution of the corrected grace data have to be reconsidered. Therefore, the effective spatial resolution at which we can obtain mass changes from grace products is an area of debate. In this contribution, we assess the spatial resolution both theoretically and practically. We confirm that, theoretically, the smallest resolvable catchment is directly related to the band-limit of the spherical harmonic spectrum of the grace data. However, due to the approximate nature of the correction schemes and the noise present in grace data, practically, the complete band-limited signal cannot be retrieved. In this context, we perform a closed-loop simulation comparing four popular correction schemes over 255 catchments to demarcate the minimum size of the catchment whose signal can be efficiently recovered by the correction schemes. We show that the amount of closure error is inversely related to the size of the catchment area. We use this trade-off between the error and the catchment size for defining the potential spatial resolution of the grace product obtained from a correction method. The magnitude of the error and hence the spatial resolution are both dependent on the correction scheme. Currently, a catchment of the size ≈63,000 km 2 can be resolved at an error level of 2 cm in terms of equivalent water height.

On the Spatial Resolution of Homogeneous Isotropic Filters on the Sphere

Interest in filtering on the sphere was rejuvenated by the necessity to filter GRACE data, which has led to the development of a variety of filters with a multitude of design methods. Nevertheless, a lacuna exists in the understanding of filters and filtered fields, especially signal leakage due to filtering and resolution of the filtered field. In this contribution, we specifically look into the latter aspect, where we take an intuitive and empirical approach instead of a rigorous mathematical approach. The empirical approach is an adaptation of the technique used in optics and photography communities for determining the resolving power of lenses. This resolution analysis is carried out for the most commonly used homogeneous isotropic filters in the GRACE community. The analysis indicates that a concrete number for the filters can only be specified as an ideal number. Nevertheless, resolution as a concept is described in detail by the modulation transfer function, which also provides some insight into the smoothing properties of the filter.

Describing the Quality of Inequality Constrained Estimates

A key feature of geodetic adjustment theory is the description of stochastic properties of the estimated quantities. A variety of tools and measures have been developed to describe the quality of ordinary least-squares estimates, for example, variance-covariance information, redundancy numbers, etc. Many of these features can easily be extended to a constrained least-squares estimate with equality constraints. However, this is not true for inequality constrained estimates. In many applications in geodesy the introduction of inequality constraints could improve the results (e.g. filter and network design or the regularization of ill-posed problems). This calls for an adequate stochastic modeling accompanying the already highly developed estimation theory in the field of inequality constrained estimation. Therefore, in this contribution, an attempt is made to develop measures for the quality of inequality constrained least-squares estimates combining Monte Carlo methods and the theory of quadratic programming. Special emphasis is placed on the derivation of confidence regions.

Estimating GRACE Monthly Water Storage Change Consistent with Hydrology by Assimilating Hydrological Information

A sequential estimation approach is used for constraining GRACE monthly estimates of mass changes with observed hydrological data, which is available for 20% of the land area, in order to improve the overall quality of the GRACE dataset. It is expected that the hydrological data constrains GRACE by utilising the correlations within the spherical harmonic coefficients, which is described by a simulated covariance matrix. Due to the dependancy of the approach on the stochastic information of GRACE, the influence of different structures of the GRACE covariance matrix were also tested. Initial results show that the hydrology constraints replace GRACE completely in the constrained areas, and contribute only meagrely outside the constrained areas. This hints at better parametrization of the model. The tests with different structures of the GRACE covariance matrix indicate that the block-diagonal structure approximates the full covariance matrix very well.