Multivariate calibration of a water and energy balance model in the spectral domain

The objective of this paper is to explore the possibility of using multiple variables in the calibration of hydrologic models in the spectral domain. A simple water and energy balance model was used, combined with observations of the energy balance and the soil moisture profile. The correlation functions of the model outputs and the observations for the different variables have been calculated after the removal of the diurnal cycle of the energy balance variables. These were transformed to the frequency domain to obtain spectral density functions, which were combined in the calibration algorithm. It has been found that it is best to use the square root of the spectral densities in the parameter estimation. Under these conditions, spectral calibration performs almost equally as well as time domain calibration using least squares differences between observed and simulated time series. Incorporation of the spectral coefficients of the cross-correlation functions did not improve the results of the calibration. Calibration on the correlation functions in the time domain led to worse model performance. When the meteorological forcing and model calibration data are not overlapping in time, spectral calibration has been shown to lead to an acceptable model performance. Overall, the results in this paper suggest that, in case of data scarcity, multivariate spectral calibration can be an attractive tool to estimate model parameters

Multiscale assimilation of Advanced Microwave Scanning Radiometer-EOS snow water equivalent and Moderate Resolution Imaging Spectroradiometer snow cover fraction observations in northern Colorado

Eight years (2002–2010) of Advanced Microwave Scanning Radiometer–EOS (AMSR-E) snow water equivalent (SWE) retrievals and Moderate Resolution Imaging Spectroradiometer (MODIS) snow cover fraction (SCF) observations are assimilated separately or jointly into the Noah land surface model over a domain in Northern Colorado. A multiscale ensemble Kalman filter (EnKF) is used, supplemented with a rule-based update. The satellite data are either left unscaled or are scaled for anomaly assimilation. The results are validated against in situ observations at 14 high-elevation Snowpack Telemetry (SNOTEL) sites with typically deep snow and at 4 lower-elevation Cooperative Observer Program (COOP) sites. Assimilation of coarse-scale AMSR-E SWE and fine-scale MODIS SCF observations both result in realistic spatial SWE patterns. At COOP sites with shallow snowpacks, AMSR-E SWE and MODIS SCF data assimilation are beneficial separately, and joint SWE and SCF assimilation yields significantly improved root-mean-square error and correlation values for scaled and unscaled data assimilation. In areas of deep snow where the SNOTEL sites are located, however, AMSR-E retrievals are typically biased low and assimilation without prior scaling leads to degraded SWE estimates. Anomaly SWE assimilation could not improve the interannual SWE variations in the assimilation results because the AMSR-E retrievals lack realistic interannual variability in deep snowpacks. SCF assimilation has only a marginal impact at the SNOTEL locations because these sites experience extended periods of near-complete snow cover. Across all sites, SCF assimilation improves the timing of the onset of the snow season but without a net improvement of SWE amounts

Assessment and enhancement of MERRA land surface hydrology estimates

The Modern-Era Retrospective Analysis for Research and Applications (MERRA) is a state-of-the-art reanalysis that provides, in addition to atmospheric fields, global estimates of soil moisture, latent heat flux, snow, and runoff for 1979 present. This study introduces a supplemental and improved set of land surface hydrological fields ("MERRA-Land") generated by rerunning a revised version of the land component of the MERRA system. Specifically, the MERRA-Land estimates benefit from corrections to the precipitation forcing with the Global Precipitation Climatology Project pentad product (version 2.1) and from revised parameter values in the rainfall interception model, changes that effectively correct for known limitations in the MERRA surface meteorological forcings. The skill (defined as the correlation coefficient of the anomaly time series) in land surface hydrological fields from MERRA and MERRA-Land is assessed here against observations and compared to the skill of the state-of-the-art ECMWF Re-Analysis-Interim (ERA-I). MERRA-Land and ERA-I root zone soil moisture skills (against in situ observations at 85 U.S. stations) are comparable and significantly greater than that of MERRA. Throughout the Northern Hemisphere, MERRA and MERRA-Land agree reasonably well with in situ snow depth measurements (from 583 stations) and with snow water equivalent from an independent analysis. Runoff skill (against naturalized stream flow observations from 18 U.S. basins) of MERRA and MERRA-Land is typically higher than that of ERA-I. With a few exceptions, the MERRA-Land data appear more accurate than the original MERRA estimates and are thus recommended for those interested in using MERRA output for land surface hydrological studies

The importance of parameter resampling for soil moisture data assimilation into hydrologic models using the particle filter

The Sequential Importance Sampling with Resampling (SISR) particle filter and the SISR with parameter resampling particle filter (SISR-PR) are evaluated for their performance in soil moisture assimilation and the consequent effect on baseflow generation. With respect to the resulting soil moisture time series, both filters perform appropriately. However, the SISR filter has a negative effect on the baseflow due to inconsistency between the parameter values and the states after the assimilation. In order to overcome this inconsistency, parameter resampling is applied along with the SISR filter, to obtain consistent parameter values with the analyzed soil moisture state. Extreme parameter replication, which could lead to a particle collapse, is avoided by the perturbation of the parameters with white noise. Both the modeled soil moisture and baseflow are improved if the complementary parameter resampling is applied. The SISR filter with parameter resampling offers an efficient way to deal with biased observations. The robustness of the methodology is evaluated for 3 model parameter sets and 3 assimilation frequencies. Overall, the results in this paper indicate that the particle filter is a promising tool for hydrologic modeling purposes, but that an additional parameter resampling may be necessary to consistently update all state variables and fluxes within the model

Towards the sequential assimilation of SAR-derived water stages into hydraulic models using the Particle Filter : proof of concept

With the onset of new satellite radar constellations (e.g. Sentinel-1) and advances in computational science (e.g. grid computing) enabling the supply and processing of multimission satellite data at a temporal frequency that is compatible with real-time flood forecasting requirements, this study presents a new concept for the sequential assimilation of Synthetic Aperture Radar (SAR)-derived water stages into coupled hydrologic-hydraulic models. The proposed methodology consists of adjusting storages and fluxes simulated by a coupled hydrologic-hydraulic model using a Particle Filterbased data assimilation scheme. Synthetic observations of water levels, representing satellite measurements, are assimilated into the coupled model in order to investigate the performance of the proposed assimilation scheme as a function of both accuracy and frequency of water level observations. The use of the Particle Filter provides flexibility regarding the form of the probability densities of both model simulations and remote sensing observations. We illustrate the potential of the proposed methodology using a twin experiment over a widely studied river reach located in the Grand-Duchy of Luxembourg. The study demonstrates that the Particle Filter algorithm leads to significant uncertainty reduction of water level and discharge at the time step of assimilation. However, updating the storages of the model only improves the model forecast over a very short time horizon. A more effective way of updating thus consists in adjusting both states and inputs. The proposed methodology, which consists in updating the biased forcing of the hydraulic model using information on model errors that is inferred from satellite observations, enables persistent model improvement. The present schedule of satellite radar missions is such that it is likely that there will be continuity for SAR-based operational water management services. This research contributes to evolve reactive flood management into systematic or quasi-systematic SAR-based flood monitoring services

Assimilating SAR-derived water level data into a hydraulic model: a case study

Satellite-based active microwave sensors not only provide synoptic overviews of flooded areas, but also offer an effective way to estimate spatially distributed river water levels. If rapidly produced and processed, these data can be used for updating hydraulic models in near real-time. The usefulness of such approaches with real event data sets provided by currently existing sensors has yet to be demonstrated. In this case study, a Particle Filter-based assimilation scheme is used to integrate ERS-2 SAR and ENVISAT ASAR-derived water level data into a one-dimensional (1-D) hydraulic model of the Alzette River. Two variants of the Particle Filter assimilation scheme are proposed with a global and local particle weighting procedure. The first option finds the best water stage line across all cross sections, while the second option finds the best solution at individual cross sections. The variant that is to be preferred depends on the level of confidence that is attributed to the observations or to the model. The results show that the Particle Filter-based assimilation of remote sensing-derived water elevation data provides a significant reduction in the uncertainty at the analysis step. Moreover, it is shown that the periodical updating of hydraulic models through the proposed assimilation scheme leads to an improvement of model predictions over several time steps. However, the performance of the assimilation depends on the skill of the hydraulic model and the quality of the observation data