N. C. van de Giesen

Model complexity control for hydrologic prediction

A common concern in hydrologic modeling is overparameterization of complex models given limited and noisy data. This leads to problems of parameter nonuniqueness and equifinality, which may negatively affect prediction uncertainties. A systematic way of controlling model complexity is therefore needed. We compare three model complexity control methods for hydrologic prediction, namely, cross validation (CV), Akaikes information criterion (AIC), and structural risk minimization (SRM). Results show that simulation of water flow using non-physically-based models (polynomials in this case) leads to increasingly better calibration fits as the model complexity (polynomial order) increases. However, prediction uncertainty worsens for complex non-physically-based models because of overfitting of noisy data. Incorporation of physically based constraints into the model (e.g., storage-discharge relationship) effectively bounds prediction uncertainty, even as the number of parameters increases. The conclusion is that overparameterization and equifinality do not lead to a continued increase in prediction uncertainty, as long as models are constrained by such physical principles. Complexity control of hydrologic models reduces parameter equifinality and identifies the simplest model that adequately explains the data, thereby providing a means of hydrologic generalization and classification. SRM is a promising technique for this purpose, as it (1) provides analytic upper bounds on prediction uncertainty, hence avoiding the computational burden of CV, and (2) extends the applicability of classic methods such as AIC to finite data. The main hurdle in applying SRM is the need for an a priori estimation of the complexity of the hydrologic model, as measured by its Vapnik-Chernovenkis (VC) dimension. Further research is needed in this area.

Feasibility of soil moisture estimation using passive distributed temperature sensing

Through its role in the energy and water balances at the land surface, soil moisture is a key state variable in surface hydrology and land?atmosphere interactions. Point observations of soil moisture are easy to make using established methods such as time domain reflectometry and gravimetric sampling. However, monitoring large?scale variability with these techniques is logistically and economically infeasible. Here passive soil distributed temperature sensing (DTS) will be introduced as an experimental method of measuring soil moisture on the basis of DTS. Several fiber?optic cables in a vertical profile are used as thermal sensors, measuring propagation of temperature changes due to the diurnal cycle. Current technology allows these cables to be in excess of 10 km in length, and DTS equipment allows measurement of temperatures every 1 m. The passive soil DTS concept is based on the fact that soil moisture influences soil thermal properties. Therefore, observing temperature dynamics can yield information on changes in soil moisture content. Results from this preliminary study demonstrate that passive soil DTS can detect changes in thermal properties. Deriving soil moisture is complicated by the uncertainty and nonuniqueness in the relationship between thermal conductivity and soil moisture. A numerical simulation indicates that the accuracy could be improved if the depth of the cables was known with greater certainty.

Corruption of accuracy and efficiency of Markov chain Monte Carlo simulation by inaccurate numerical implementation of conceptual hydrologic models

Conceptual rainfall?runoff models have traditionally been applied without paying much attention to numerical errors induced by temporal integration of water balance dynamics. Reliance on first?order, explicit, fixed?step integration methods leads to computationally cheap simulation models that are easy to implement. Computational speed is especially desirable for estimating parameter and predictive uncertainty using Markov chain Monte Carlo (MCMC) methods. Confirming earlier work of Kavetski et al. (2003), we show here that the computational speed of first?order, explicit, fixed?step integration methods comes at a cost: for a case study with a spatially lumped conceptual rainfall?runoff model, it introduces artificial bimodality in the marginal posterior parameter distributions, which is not present in numerically accurate implementations of the same model. The resulting effects on MCMC simulation include (1) inconsistent estimates of posterior parameter and predictive distributions, (2) poor performance and slow convergence of the MCMC algorithm, and (3) unreliable convergence diagnosis using the Gelman?Rubin statistic. We studied several alternative numerical implementations to remedy these problems, including various adaptive?step finite difference schemes and an operator splitting method. Our results show that adaptive?step, second?order methods, based on either explicit finite differencing or operator splitting with analytical integration, provide the best alternative for accurate and efficient MCMC simulation. Fixed?step or adaptive?step implicit methods may also be used for increased accuracy, but they cannot match the efficiency of adaptive?step explicit finite differencing or operator splitting. Of the latter two, explicit finite differencing is more generally applicable and is preferred if the individual hydrologic flux laws cannot be integrated analytically, as the splitting method then loses its advantage.

Assessment of Gravity Recovery and Climate Experiment (GRACE) temporal signature over the upper Zambezi

The temporal signature of terrestrial storage changes inferred from the Gravity Recovery and Climate Experiment (GRACE) has been assessed by comparison with outputs from a calibrated hydrological model (lumped elementary watershed (LEW)) of the upper Zambezi and surroundings and an inspection of the within?month ground track coverage of GRACE together with spatial?temporal rainfall patterns. The comparison of the hydrological model with GRACE reveals temporal inconsistencies between both data sets. Because the LEW model has been calibrated and validated with independent data sources, we believe that this is a GRACE artifact. The within?month ground track coverage shows an irregular orbit behavior which may well cause aliasing in the GRACE monthly deconvolutions. This aliasing is the most probable cause of observed temporal inconsistencies between GRACE and other data sets.

Locating illicit connections in storm water sewers using fiber-optic distributed temperature sensing

A newly developed technique using distributed temperature sensing (DTS) has been developed to find illicit household sewage connections to storm water systems in the Netherlands. DTS allows for the accurate measurement of temperature along a fiber-optic cable, with high spatial (2m) and temporal (30s) resolution. We inserted a fiber-optic cable of 1300m in two storm water drains. At certain locations, significant temperature differences with an intermittent character were measured, indicating inflow of water that was not storm water. In all cases, we found that foul water from households or companies entered the storm water system through an illicit sewage connection. The method of using temperature differences for illicit connection detection in storm water networks is discussed. The technique of using fiber-optic cables for distributed temperature sensing is explained in detail. The DTS method is a reliable, inexpensive and practically feasible method to detect illicit connections to storm water systems, which does not require access to private property.

Using Diurnal Variation in Backscatter to Detect Vegetation Water Stress

A difference has been detected between the C-band wind scatterometer measurements from the morning (descending) and evening (ascending) passes of the European Remote Sensing (ERS) 1/2 satellite. In the West African savanna, for example, these differences correspond to the onset of vegetation water stress. A literature review of the current state of knowledge regarding the diurnal variation in vegetation dielectric properties and its influence on observed backscatter is presented. A numerical sensitivity study using the Michigan microwave canopy scattering model was performed to investigate whether this difference might be explained by diurnal variation in the dielectric properties of the canopy. For vertically copolarized backscatter, as in the case of the ERS wind scatterometer, the greatest sensitivity is to leaf moisture (and, hence, dielectric constant), but the trunk moisture is significant at low values of leaf moisture content. This suggests that the ERS wind scatterometer may well detect changes in vegetation water status. The impact of leaf, branch, trunk, and soil moisture contents on L-band HH, VV, and HV backscatter was also investigated to explore the implications for the National Aeronautics and Space Administrations upcoming Soil Moisture Active Passive (SMAP) mission. Results suggest that combining the morning and evening passes of the SMAP radar observations might yield valuable insight into water stress in areas otherwise considered too densely vegetated for traditional soil moisture retrieval.

Determining watershed response in data poor environments with remotely sensed small reservoirs as runoff gauges

In the semiarid regions of Africa, there are many small reservoirs used for irrigation. This study explores the practicality of using small reservoirs as runoff gauges by estimating their water storage changes using remote sensing imagery. A simple rainfall-runoff model is developed by observing the surface area and estimating the volume of eight small reservoirs in the Upper East Region of Ghana and in Togo using Envisat advanced synthetic aperture radar satellite images. The model is based on the Thornthwaite-Mather procedure and the assumption that with increasing precipitation, the contributing watershed area increases exponentially. The model parameters were estimated using the 2005 data and were validated using 2006 data. Although the total rainfall amounts were comparable in these 2 years, the rainfall and reservoir filling patterns were quite different. The model results indicate that the overall impact of the reservoirs largely depends on the ratios of reservoir to watershed areas. For this 2 year study, the reservoirs captured on average 34% of quick flow and 15% of overall runoff.

Predictive Control for National Water Flow Optimization in The Netherlands

The river delta in The Netherlands consists of interconnected rivers and large water bodies. Structures, such as large sluices and pumps, are available to control the local water levels and flows. The national water board is responsible for the management of the system. Its main management objectives are: protection against overtopping of dikes due to high river flows and high sea tides, supply of water during dry periods, and navigation. The system is, due to its size, divided into several subsystems that are managed by separate regional divisions of the national water board. Due to changes in local land-use, local climate, and the need for energy savings, the currently existing control systems have to be upgraded from local manual control schemes to regional model predictive control (MPC) schemes. In principle, the national objectives for the total delta require a centralized control approach integrating all regional MPC schemes. However, such centralized control is on the one hand not feasible, due to computational limitations, and on the other hand unwanted, due to the existing regional structure of the organization of the national water board. In this chapter the application of MPC is discussed for both individual regional control and coordinated national control. Results of a local MPC scheme applied to the actual water system of the North Sea Canal/Amsterdam-Rhine Canal are presented and a framework for coordination between several distributed MPC schemes is proposed.

TRANSIENT FLOW TO OPEN DRAINS : COMPARISON OF LINEARIZED SOLUTIONS WITH AND WITHOUT THE DUPUIT ASSUMPTION

A solution of the Laplace equation with linearized boundary conditions is presented for unsteady flow through a rectangular aquifer. The results are compared with those of the linearized Boussinesq equation. The linearized solution based on the Laplace equation is as, easy to use as Boussinesqs solution, has a wider range of application, and allows accurate computation of streamlines.

Tree rainfall interception measured by stem compression

A method for measuring whole-tree interception of precipitation is presented which employs mechanical displacement sensors to measure trunk compression caused by the water captured by the tree. This direct and nondestructive method is demonstrated to be sensitive to less than 5 kg of interception field tests in Netherlands and Ghana.