Projected Newton Method for noise constrained Tikhonov regularization

Tikhonov regularization is a popular approach to obtain a meaningful solution for ill-conditioned linear least squares problems. A relatively simple way of choosing a good regularization parameter is given by Morozov's discrepancy principle. However, most approaches require the solution of the Tikhonov problem for many different values of the regularization parameter, which is computationally demanding for large scale problems. We propose a new and efficient algorithm which simultaneously solves the Tikhonov problem and finds the corresponding regularization parameter such that the discrepancy principle is satisfied. We achieve this by formulating the problem as a nonlinear system of equations and solving this system using a line search method. We obtain a good search direction by projecting the problem onto a low dimensional Krylov subspace and computing the Newton direction for the projected problem. This projected Newton direction, which is significantly less computationally expensive to calculate than the true Newton direction, is then combined with a backtracking line search to obtain a globally convergent algorithm, which we refer to as the Projected Newton method. We prove convergence of the algorithm and illustrate the improved performance over current state-of-the-art solvers with some numerical experiments

Numerically Stable Recurrence Relations for the Communication Hiding Pipelined Conjugate Gradient Method

Pipelined Krylov subspace methods (also referred to as communication-hiding methods) have been proposed in the literature as a scalable alternative to classic Krylov subspace algorithms for iteratively computing the solution to a large linear system in parallel. For symmetric and positive definite system matrices the pipelined Conjugate Gradient method outperforms its classic Conjugate Gradient counterpart on large scale distributed memory hardware by overlapping global communication with essential computations like the matrix-vector product, thus hiding global communication. A well-known drawback of the pipelining technique is the (possibly significant) loss of numerical stability. In this work a numerically stable variant of the pipelined Conjugate Gradient algorithm is presented that avoids the propagation of local rounding errors in the finite precision recurrence relations that construct the Krylov subspace basis. The multi-term recurrence relation for the basis vector is replaced by two-term recurrences, improving stability without increasing the overall computational cost of the algorithm. The proposed modification ensures that the pipelined Conjugate Gradient method is able to attain a highly accurate solution independently of the pipeline length. Numerical experiments demonstrate a combination of excellent parallel performance and improved maximal attainable accuracy for the new pipelined Conjugate Gradient algorithm. This work thus resolves one of the major practical restrictions for the useability of pipelined Krylov subspace methods.Comment: 15 pages, 5 figures, 1 table, 2 algorithm

An assessment of wheat (Triticum aestivum L.) genotypes under saline and waterlogged compacted soil conditions, I: grain yield and yield components

A pot experiment was conducted to study effects of salinity and waterlogging under soil compaction conditions on grain yield and yield components of wheat. Treatments were arranged in a factorial layout assigned to a randomized complete design with three replications. Treatment combinations included: two sets of compaction levels, i.e. non-compacted and compacted soil; four abiotic stresses, i.e. non-saline aerobic (untreated silt loam texture soil having ECe = 3 dS m-1); saline × aerobic (S) (ECe 15 dS m-1); saline × waterlogged (S×W); and waterlogged alone (W) were applied; and two Iranian wheat genotypes i.e. Kouhdasht and Tajan. Compaction was achieved by dropping a 5 kg weight, 20 times from 70 cm height on a wooden block placed on top of soil-filled pots. In non-waterlogged treatments, soil water was maintained at 70% of available water holding capacity (AWHC). Waterlogging was achieved by maintaining water up to 110% of the soil’s AWHC for 25 days during tillering stage. Compaction significantly intensified effect of all other treatments, except waterlogging, on grain yield and yield components of wheat genotypes as compared to control. S×W caused significantly higher reduction in grain yield and yield components for both genotypes than other treatments

An assessment of wheat (Triticum aestivum L.) genotypes under saline and waterlogged compacted soil conditions, II: leaf ion concentrations

A pot experiment was conducted to study effects of salinity and waterlogging under soil compaction conditions on grain yield and yield components of wheat. Treatments were arranged in a factorial layout assigned to a randomized complete design with three replications. Treatment combinations included: two sets of compaction levels, i.e. non-compacted and compacted soil; four abiotic stresses, i.e. non-saline aerobic (untreated silt loam texture soil having ECe = 3 dS m-1); saline × aerobic (S) (ECe 15 dS m-1); saline × waterlogged (S×W); and waterlogged alone (W) were applied; and two Iranian wheat genotypes i.e. Kouhdasht and Tajan. Compaction was achieved by dropping a 5 kg weight, 20 times from 70 cm height on a wooden block placed on top of soil-filled pots. In non-waterlogged treatments, soil water was maintained at 70% of available water holding capacity (AWHC). Waterlogging was achieved by maintaining water up to 110% of the soil’s AWHC for 25 days during tillering stage. S×W caused significantly higher reduction in K+ concentration for both genotypes than other treatments. S×W also resulted in higher leaf Na+ and Cl- concentrations in comparison to other treatments. Kouhdasht maintained significantly higher K + concentration and K+: Na+ ratio at S and S×W treatments than that Tajan (under both non-compacted and compacted soil conditions)

Data assimilation of in situ soil moisture measurements in hydrological models: first annual doctoral progress report, work plan and achievements

Water scarcity and the presence of water of good quality is a serious public concern since it determines the availability of water to society. Water scarcity especially in arid climates and due to extreme droughts related to climate change drive water use technologies such as irrigation to become more efficient and sustainable. Plant root water and nutrient uptake is one of the most important processes in subsurface unsaturated flow and transport modeling, as root uptake controls actual plant evapotranspiration, water recharge and nutrient leaching to the groundwater, and exerts a major influence on predictions of global climate models. To improve irrigation strategies, water flow needs to be accurately described using advanced monitoring and modeling. Our study focuses on the assimilation of hydrological data in hydrological models that predict water flow and solute (pollutants and salts) transport and water redistribution in agricultural soils under irrigation. Field plots of a potato farmer in a sandy region in Belgium were instrumented to continuously monitor soil moisture and water potential before, during and after irrigation in dry summer periods. The aim is to optimize the irrigation process by assimilating online sensor field data into process based models. Over the past year, we demonstrated the calibration and optimization of the Hydrus 1D model for an irrigated grassland on sandy soil. Direct and inverse calibration and optimization for both heterogeneous and homogeneous conceptualizations was applied. Results show that Hydrus 1D closely simulated soil water content at five depths as compared to water content measurements from soil moisture probes, by stepwise calibration and local sensivity analysis and optimization the Ks, n and α value in the calibration and optimization analysis. The errors of the model, expressed by deviations between observed and modeled soil water content were, however, different for each individual depth. The smallest differences between the observed value and soil-water content were attained when using an automated inverse optimization method. The choice of the initial parameter value can be optimized using a stepwise approach. Our results show that statistical evaluation coefficients (R2, Ce and RMSE) are suitable benchmarks to evaluate the performance of the model in reproducing the data. The degree of water stress simulated with Hydrus 1D suggested to increase irrigation at least one time, i.e. at the beginning of the simulation period and further distribute the amount of irrigation during the growing season, instead of using a huge amount of irrigation later in the season. In the next year, we will further look for to the best method (using soft data and methods for instance PTFs, EMI, Penetrometer) to derive and predict the spatial variability of soil hydraulic properties (saturated hydraulic conductivity) of the soil and link to crop yield at the field scale. Linear and non-linear pedotransfer functions (PTFs) have been assessed to predict penetrometer resistance of soils from their water status (matric potential, ψ and degree of saturation, S) and bulk density, ρb, and some other soil properties such as sand content, Ks etc. The geophysical EMI (electromagnetic induction) technique provides a versatile and robust field instrument for determining apparent soil electrical conductivity (ECa). ECa, a quick and reliable measurement, is one of ancillary properties (secondary information) of soil, can improve the spatial and temporal estimation of soil characteristics e.g., salinity, water content, texture, prosity and bulk density at different scales and depths. According to previous literature on penetrometer measurements, we determined the effective stress and used some models to find the relationships between soil properties, especially Ks, and penetrometer resistance as one of the prediction methods for Ks. The initial results obtained in the first yearshowed that a new data set would be necessary to validate the results of this part. In the third year, quasi 3D-modelling of water flow at the field scale will be conducted. In this modeling set -up, the field will be modeled as a collection of 1D-columns representing the different field conditions (combination of soil properties, groundwater depth, root zone depth). The measured soil properties are extrapolated over the entire field by linking them to the available spatially distributed data (such as the EMI-images). The data set of predicted Ks and other soil properties for the whole field constructed in the previous steps will be used for parameterising the model. Sensitivity analysis ‘SA’ is essential to the model optimization or parametrization process. To avoid overparameterization, the use of global sensitivity analysis (SA) will be investigated. In order to include multiple objectives (irrigation management parameters, costs, …) in the parameter optimization strategy, multi-objective techniques such as AMALGAM have been introduced. We will investigate multi-objective strategies in the irrigation optimization

Integrated water and soil conservation for food security in Niger, preliminary results

As a result of growing population pressure and limited fertile land availability, Nigerien farmers increasingly rely on marginal lands for food crops production. These degraded lands, however, generally provide poor millet yields due to their low soil nutrient content and imbalanced partitioning of water in the root-zone. This study evaluates the agronomical, hydrological and soil quality parameters of water and soil conservation techniques (i.e. zaï, demi-lunes and no-till with scarification) which tackle these two major crop growth limitations by means of an in situ root-zone water balance experiment. Preliminary results from the first cropping season from June to October 2011 show overall low yields. The 2011 season was characterised by erratic rainfall with a severe dry spell during flowering stage. The control and manure treatment did not yield grain, but simply applying manure did increase dry matter production with a factor of 20. The highest grain yield was produced by the zaï, 134 kg/ha, which was 3 and 9 times better than respectively the grain yield of demi-lunes and no-till with scarification treatments. The zaï treatment moreover reduced cumulative actual evaporation as measured using mini-lysimeters during a 10 day drying cycle. In conclusion, until now the synergistic effect of the water-harvesting practices and the supply of manure show promising potential to rehabilitate and to increase the agronomic efficiency of marginal land in Niger. Future work will focus on the impact of the treatments on yield, soil quality properties and on the root-zone water balance