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

Estimation of aquifer lower layer hydraulic conductivity values through base flow hydrograph rising limb analysis

The estimation of catchment-averaged aquifer hydraulic conductivity values is usually performed through a base flow recession analysis. Relationships between the first time derivatives of the base flow and the base flow values themselves, derived for small and large values of time, are used for this purpose. However, in the derivation of the short-time equations, an initially fully saturated aquifer without recharge with sudden drawdown is assumed, which occurs very rarely in reality. It is demonstrated that this approach leads to a nonnegligible error in the parameter estimates. A new relationship is derived, valid for the rising limb of a base flow hydrograph, succeeding a long rainless period. Application of this equation leads to accurate estimates of the aquifer lower layer saturated hydraulic conductivity. Further, it has been shown analytically that, if base flow is modeled using the linearized Boussinesq equation, the base flow depends on the effective aquifer depth and the ratio of the saturated hydraulic conductivity to the drainable porosity, not on these three parameters separately. The results of the new short-time expression are consistent with this finding, as opposed to the use of a traditional base flow recession analysis. When base flow is modeled using the nonlinear Boussinesq equation, the new expression can be used, without a second equation for large values of time, to estimate the aquifer lower layer hydraulic conductivity. Overall, the results in this paper suggest that the new methodology outperforms a traditional recession analysis for the estimation of catchment-averaged aquifer hydraulic conductivities

Local sensitivity analysis for compositional data with application to soil texture in hydrologic modelling

Compositional data, such as soil texture, are hard to deal with in the geosciences as standard statistical methods are often inappropriate to analyse this type of data. Especially in sensitivity analysis, the closed character of the data is often ignored. To that end, we developed a method to assess the local sensitivity of a model output with resect to a compositional model input. We adapted the finite difference technique such that the different parts of the input are perturbed simultaneously while the closed character of the data is preserved. This method was applied to a hydrologic model and the sensitivity of the simulated soil moisture content to local changes in soil texture was assessed. Based on a high number of model runs, in which the soil texture was varied across the entire texture triangle, we identified zones of high sensitivity in the texture triangle. In such zones, the model output uncertainty induced by the discrepancy between the scale of measurement and the scale of model application, is advised to be reduced through additional data collection. Furthermore, the sensitivity analysis provided more insight into the hydrologic model behaviour as it revealed how the model sensitivity is related to the shape of the soil moisture retention curve

Soil moisture retrieval through a merging of multi-temporal L-band SAR data and hydrologic modelling

he objective of the study is to investigate the potential of retrieving superficial soil moisture content (m(v)) from multi-temporal L-band synthetic aperture radar (SAR) data and hydrologic modelling. The study focuses on assessing the performances of an L-band SAR retrieval algorithm intended for agricultural areas and for watershed spatial scales (e. g. from 100 to 10 000 km(2)). The algorithm transforms temporal series of L-band SAR data into soil moisture contents by using a constrained minimization technique integrating a priori information on soil parameters. The rationale of the approach consists of exploiting soil moisture predictions, obtained at coarse spatial resolution ( e. g. 1530 km2) by point scale hydrologic models ( or by simplified estimators), as a priori information for the SAR retrieval algorithm that provides soil moisture maps at high spatial resolution (e. g. 0.01 km(2)). In the present form, the retrieval algorithm applies to cereal fields and has been assessed on simulated and experimental data. The latter were acquired by the airborne E-SAR system during the AgriSAR campaign carried out over the Demmin site (Northern Germany) in 2006. Results indicate that the retrieval algorithm always improves the a priori information on soil moisture content though the improvement may be marginal when the accuracy of prior mv estimates is better than 5%

Consistency between hydrological model, large aperture scintillometer and remote sensing based evapotranspiration estimates for a heterogeneous catchment

The catchment averaged actual evapotranspiration rate is a hydrologic model variable that is difficult to quantify. Evapotranspiration rates - up till present - cannot be continuously observed at the catchment scale. The objective of this paper is to estimate the evapotranspiration rates (or its energy equivalent, the latent heat fluxes LE) for a heterogeneous catchment of 102.3 km(2) in Belgium using three fundamentally different algorithms. One possible manner to observe this variable could be the continuous measurement of sensible heat fluxes (H) across large distances (in the order of kilometers) using a large aperture scintillometer (LAS), and converting these observations into evapotranspiration rates. Latent heat fluxes are obtained through the energy balance equation using a series of sensible heat fluxes measured with a LAS over a distance of 9.5 km in the catchment, and point measurements of net radiation (R-n) and ground heat flux (G) upscaled to catchment average through the use of TOPLATS, a physically based land surface model. The resulting LE-values are then compared to results from the remote sensing based surface energy balance algorithm ETLook and the land surface model. Firstly, the performance of ETLook for the energy balance terms has been assessed at the point scale and at the catchment scale. Secondly, consistency between daily evapotranspiration rates from ETLook, TOPLATS and LAS is shown

On the Use of Adaptive Ensemble Kalman Filtering to Mitigate Error Misspecifications in GRACE Data Assimilation

The ensemble Kalman filter (EnKF) has been proved as a useful algorithm to mergecoarse-resolution Gravity Recovery and Climate Experiment (GRACE) data with hydrologic model results.However, in order for the EnKF to perform optimally, a correct forecast error covariance is needed. TheEnKF estimates this error covariance through an ensemble of model simulations with perturbed forcingdata. Consequently, a correct specification of perturbation magnitude is essential for the EnKF to workoptimally. To this end, an adaptive EnKF (AEnKF), a variant of the EnKF with an additional componentthat dynamically detects and corrects error misspecifications during the filtering process, has been applied.Due to the low spatial and temporal resolutions of GRACE data, the efficiency of this method could bedifferent than for other hydrologic applications. Therefore, instead of spatially or temporally averaging theinternal diagnostic (normalized innovations) to detect the misspecifications, spatiotemporal averaging wasused. First, sensitivity of the estimation accuracy to the degree of error in forcing perturbations wasinvestigated. Second, efficiency of the AEnKF for GRACE assimilation was explored using two syntheticand one real data experiment. Results show that there is considerable benefit in using this method toestimate the forcing error magnitude and that the AEnKF can efficiently estimate this magnitude.Ashkan Shokri acknowledges the support from Monash University in the form of a Monash Graduate Scholarship (MGS) and Monash International Postgraduate Research Scholarship (MIPRS). Valentijn Pauwels was supported through an ARC Future Fellowship Grant (FT130100545). The research is supported through an ARC Discovery Grant (DP140103679). This research is also supported in part by the Monash eResearch Centre and eSolutions-Research Support Services through the use of the Monash Campus HPC Cluster