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Derivation and characterization of a new filter for nonlinear high-dimensional data assimilation
(2015)
Data assimilation (DA) combines model forecasts with real-world observations to achieve an optimal estimate of the state of a dynamical system. The quality of predictions in nonlinear and chaotic systems such as atmospheric or oceanic circulation is strongly sensitive to the initial conditions. Therefore, beyond the consistent reconstruction of past states, a primary relevance of advanced DA methods concerns the proper model initialization. The ensemble Kalman filter (EnKF) and its deterministic variants, mostly square root filters such as the ensemble transform Kalman filter (ETKF), represent a popular alternative to variational DA schemes. They are applied in a wide range of research and operations. Their forecast step employs an ensemble integration that fully respects the nonlinear nature of the analyzed system. In the analysis step, they implicitly assume the prior state and observation errors to be Gaussian. Consequently, in nonlinear systems, the mean and covariance of the analysis ensemble are biased and these filters remain suboptimal. In contrast, the fully nonlinear, non-Gaussian particle filter (PF) relies on Bayes' theorem without further assumptions, which guarantees an exact asymptotic behavior. However, it is exposed to weight collapse, particularly in higher-dimensional settings, known as the curse of dimensionality.
This work presents a new method to obtain an analysis ensemble with mean and covariance that exactly match the corresponding Bayesian estimates. This is achieved by a deterministic matrix square root transformation of the forecast ensemble, and subsequently a suitable random rotation that significantly contributes to filter stability while preserving the required second-order statistics. The forecast step remains as in the ETKF. The algorithm, which is fairly easy to implement and computationally efficient, is referred to as the nonlinear ensemble transform filter (NETF). The limitation with respect to fully-nonlinear filtering is that the NETF only considers the mean and covariance of the Bayesian analysis density, neglecting higher-order moments.
The properties and performance of the proposed algorithm are investigated via a set of experiments. The results indicate that such a filter formulation can increase the analysis quality, even for relatively small ensemble sizes, compared to other ensemble filters in nonlinear, non-Gaussian scenarios. They also confirm that localization enhances the applicability of this PF-inspired scheme in larger-dimensional systems. Finally, the novel filter is coupled to a large-scale ocean general circulation model with a realistic observation scenario. The NETF remains stable with a small ensemble size and shows a consistent behavior. Additionally, its analyses exhibit low estimation errors, as revealed by a comparison with a free ensemble integration and the ETKF. The results confirm that, in principle, the filter can be applied successfully and as simple as the ETKF in high-dimensional problems. No further modifications are needed, even though the algorithm is only based on the particle weights. Thus, it is able to overcome the curse of dimensionality, even in deterministic systems. This proves that the NETF constitutes a promising and user-friendly method for nonlinear high-dimensional DA.
In the past sixty years, excessive water consumption and dam construction have significantly influenced natural flow regimes and surface freshwater ecosystems throughout China, and thus resulted in serious environmental problems. In order to balance the competing water demands between human and environment and provide knowledge on sustainable water management, assessments on anthropogenic flow alterations and their impacts on aquatic and riparian ecosystems in China are needed.
In this study, the first evaluation on quantitative relationships between anthropogenic flow alterations and ecological responses in eleven river basins and watersheds in China was performed based on the data that could be obtained from published case studies. Quantitative relationships between changes in average annual discharge, seasonal low flow and seasonal high flow and changes in ecological indicators (fish diversity, fish catch and vegetation cover, etc.) were analyzed. The results showed that changes in riparian vegetation cover as well as changes in fish diversity and fish catch were strongly correlated with the changes in flow magnitude (r = 0.77, 0.66), especially with changes in average annual river discharge. In addition, more than half of the variations in vegetation cover could be explained by changes in average annual river discharge (r² = 0.63) and roughly 50 % changes in fish catch in arid and semi-arid region and 60% changes of fish catch in humid region could be related to alterations in average annual river discharge (r² = 0.53, 0.58).
In a supplementary analysis of this study, the first estimation on quantitative relationships between decreases in native fish species richness and anthropogenic flow alterations in 34 river basins and sub-basins in China was conducted. Linear relationships between losses of native fish species and five ecologically relevant flow indicators were analyzed by single and multiple regression models. For the single regression analysis, significant linear relationships were detected for the indicators of long-term average annual discharge (ILTA) and statistical low flow Q90 (IQ90). For the multiple regressions, no indicator other than ILTA has significant relationships with changes in number of fish species mainly due to collinearity. Two conclusions emerged from the analysis: 1) losses of fish species were positively correlated with changes in ILTA in China and 2) indicator of ILTA was dominant over other flow indicators included in this research for the given dataset. These results provide a guideline for the sustainable water resources management in rivers with high risk of fish extinction in China.
In situ rainwater harvesting has a long history in arid and semi-arid regions of the world buffering water shortages for human consumption and agriculture. In the context of an Integrated Water Resource Management (IWRM) in the Cuvelai Basin in northern Namibia, roof top rainwater harvesting is being introduced to a rural community for the irrigation of household scale gardens for the cultivation of horticulture products. This study elaborates how harvested rainwater can be used for garden irrigation in a sustainable manner evaluating ecologic, economic and social implications. Considering local conditions eight cropping scenarios were designed, including different criteria as well as one and two annual planting seasons. These schemes were tested under present climate conditions and under three future climate change scenarios for 2050 with the help of a tank model designed to model monthly tank inflows and outflows. Special attention was laid on risk and uncertainty aspects of varying inter-annual and interseasonal precipitation and future climate change. A framework for the assessment of sustainability was adapted to the purposes of this study and indicators have been developed in order to assess the cropping and irrigation schemes for sustainability.
The study found that with the given tank size of 30 m³, depending on crop scenario, under optimized conditions a garden area of 60 to 90 m³ can be irrigated. The choice of crops highly impacts water use efficiency and economic profitability, compared to the considerably lower impact of amount of annual planting seasons and future climate change. In the case of worsening future climate conditions, adaptation measures need to be taken as especially the economic as well as the environmental situation are expected to exacerbate due to expected decreases in yields and revenues. Already under present conditions however, the economic dimension represents the most limiting factor to sustainability, particularly due to the excessive investment costs of the rainwater harvesting and gardening facility. Nonetheless, rainwater harvesting in combination with gardening can be regarded as successful in securing household nutrition, providing sufficient horticulture products for household consumption or market sale. At the same time with the optimal choice of crops the investment costs can be recovered within the end of the lifespan of the facility.
Long-term average groundwater recharge representing the sustainable groundwater resources is modeled as a 0.5° by 0.5° grid on global scale by the WaterGAP Global Hydrology Model. Due to uncertainties of estimating groundwater recharge, especially in semiarid and arid regions, independent estimates are used for calibrating the model. This work compiled a new set of independent groundwater recharge estimates based on a work of Scanlon et al. (2006). The 59 independent estimates, together with an already existing independent estimates compilation, are used for the evaluation of two WGHM variants; one variant is modeling with an improved more realistically distributed daily precipitation dataset.
The objective of this thesis is the evaluation of the modeled data of the WaterGAP Global Hydrology Model (WGHM). The analysis of the impact of the new Watch Forcing Data (WFD) precipitation dataset on the modeled groundwater recharge tends to result in lower values in humid and higher values in (semi-)arid regions compared to the WGHM standard variant. Comparing both WGHM variants to the independent estimates compilations, representing (semi-)arid regions, the WGHM variant shows over- and underestimations especially of the low values and the WGHM WFD variant shows a bias toward overestimation especially for values below 4 mm/yr. The analysis of texture, hydrogeology and vegetation/ land cover could not give satisfying explanations for the discrepancies, but derived from the groundwater recharge measurement methods analysis indirect/ localized recharge seems to be a significant factor causing underestimations, as resulted in the comparison of the independent estimates based on Scanlon et al. 2006 with the WGHM variants.
The design of rainwater harvesting based gardens requires considering current climate but also climate change during the lifespan of the facility. The goal of this study is to present an approach for designing garden variants that can be safely supplied with harvested rainwater, taking into account climate change and adaptation measures. In addition, the study presents a methodology to quantify the effects of climate change on rainwater harvesting based gardening. Results of the study may not be accurate due to the assumptions made for climate projections and may need to be further refined. We used a tank flow model and an irrigation water model. Then we established three simple climate scenarios and analyzed the impact of climate change on harvested rain and horticulture production for a semi-arid region in northern Namibia. In the two climate scenarios with decreased precipitation and medium/high temperature increase; adaptation measures are required to avoid substantial decreases in horticulture production. The study found that the most promising adaptation measures to sustain yields and revenues are a more water efficient garden variant and an enlargement of the roof size. The proposed measures can partly or completely compensate the negative impacts of climate change.
Bayesian Networks are computer-based environmental models that are frequently used to support decision-making under uncertainty. Under data scarce conditions, Bayesian Networks can be developed, parameterized, and run based on expert knowledge only. However, the efficiency of expert-based Bayesian Network modeling is limited by the difficulty in deriving model inputs in the time available during expert workshops. This thesis therefore aimed at developing a simple and robust method for deriving conditional probability tables from expert estimates in a time-efficient way. The design and application of this new elicitation and conversion method is demonstrated using a case study in Xinjiang, Northwest China. The key characteristics of this method are its time-efficiency and the approach to use different conversion tables based on varying levels of confidence. Although the method has its limitations, e.g. it can only be applied for variables with one conditioning variable; it provides the opportunity to support the parameterization of Bayesian Networks which would otherwise remain half-finished due to time constraints. In addition, a case study in the Murray-Darling Basin, Australia, is used to compare Bayesian Network types and software to improve the presentation clarity of large Bayesian Networks. Both case studies aimed at gaining insights on how to improve the applicability of Bayesian Networks to support environmental management.
Irrigation intensifies land use by increasing crop yield but also impacts water resources. It affects water and energy balances and consequently the microclimate in irrigated regions. Therefore, knowledge of the extent of irrigated land is important for hydrological and crop modelling, global change research, and assessments of resource use and management. Information on the historical evolution of irrigated lands is limited. The new global Historical Irrigation Dataset (HID) provides estimates of the temporal development of the area equipped for irrigation (AEI) between 1900 and 2005 at 5 arc-minute resolution. We collected subnational irrigation statistics from various sources and found that the global extent of AEI increased from 63 million ha (Mha) in 1900 to 112 Mha in 1950 and 306 Mha in 2005. We developed eight gridded versions of time series of AEI by combining subnational irrigation statistics with different data sets on the historical extent of cropland and pasture. Different rules were applied to maximize consistency of the gridded products to subnational irrigation statistics or to historical cropland and pasture data sets. The HID reflects very well the spatial patterns of irrigated land in the western United States as shown on historical maps. Mean aridity on irrigated land increased and river discharge decreased from 1900–1950 whereas aridity decreased from 1950–2005. The dataset and its documentation are made available in an open data repository at https://mygeohub.org/publications/8 (doi:10.13019/M2MW2G).
The three-dimensional quantification of small-scale processes in the upper troposphere and lower stratosphere is one of the challenges of current atmospheric research and requires the development of new measurement strategies. This work presents the first results from the newly developed Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA) obtained during the ESSenCe (ESa Sounder Campaign) and TACTS/ESMVal (TACTS: Transport and composition in the upper troposphere/lowermost stratosphere, ESMVal: Earth System Model Validation) aircraft campaigns. The focus of this work is on the so-called dynamics-mode data characterized by a medium-spectral and a very-high-spatial resolution. The retrieval strategy for the derivation of two- and three-dimensional constituent fields in the upper troposphere and lower stratosphere is presented. Uncertainties of the main retrieval targets (temperature, O3, HNO3, and CFC-12) and their spatial resolution are discussed. During ESSenCe, high-resolution two-dimensional cross-sections have been obtained. Comparisons to collocated remote-sensing and in situ data indicate a good agreement between the data sets. During TACTS/ESMVal, a tomographic flight pattern to sense an intrusion of stratospheric air deep into the troposphere was performed. It was possible to reconstruct this filament at an unprecedented spatial resolution of better than 500 m vertically and 20 × 20 km horizontally.
Ternary aerosol nucleation experiments were conducted in the CLOUD chamber at CERN in order to investigate the influence of ions on new particle formation. Neutral and ion-induced nucleation experiments, i.e., with and without the presence of ions, were carried out under precisely controlled conditions. The sulphuric acid concentration was measured with a Chemical Ionization Mass Spectrometer (CIMS) during the new particle formation experiments. The added ternary trace gases were ammonia (NH3), dimethylamine (DMA, C2H7N) or oxidised products of pinanediol (PD, C10H18O2). When pinanediol was introduced into the chamber, an increase in the mass spectrometric signal used to determine the sulphuric acid concentration (m/z 97, i.e., HSO4−) was observed due to ions from the CLOUD chamber. The enhancement was only observed during ion-induced nucleation measurements by using either galactic cosmic rays (GCR) or the proton synchrotron (PS) pion beam for the ion generation, respectively. The ion effect typically involved an increase in the apparent sulphuric acid concentration by a factor of ~2 to 3 and was qualitatively verified by the ion measurements by an Atmospheric Pressure interface-Time Of Flight (APi-TOF) mass spectrometer. By applying a high voltage (HV) clearing field inside the CLOUD chamber the ion effect on the CIMS measurement was completely eliminated since, under these conditions, small ions are swept from the chamber in about one second. In order to exclude the ion effect and to provide corrected sulphuric acid concentrations during the GCR and PS beam nucleation experiments, a parameterisation was derived that utilizes the trace gas concentrations and the UV light intensity as input parameters. Atmospheric sulphuric acid measurements with a CIMS showed an insignificant ion effect.
Ternary aerosol nucleation experiments were conducted in the CLOUD chamber at CERN in order to investigate the influence of ions on new particle formation. Neutral and ion-induced nucleation experiments, i.e. without and with the presence of ions, respectively, were carried out under precisely controlled conditions. The sulfuric acid concentration was measured with a chemical ionisation mass spectrometer (CIMS) during the new particle formation experiments. The added ternary trace gases were ammonia (NH3), dimethylamine (DMA, C2H7N) or oxidised products of pinanediol (PD, C10H18O2). When pinanediol was introduced into the chamber, an increase in the mass spectrometric signal used to determine the sulfuric acid concentration (m/z 97, i.e. HSO4−) was observed due to ions from the CLOUD chamber. The enhancement was only observed during ion-induced nucleation measurements by using either galactic cosmic rays (GCRs) or the proton synchrotron (PS) pion beam for the ion generation, respectively. The ion effect typically involved an increase in the apparent sulfuric acid concentration by a factor of ~ 2 to 3 and was qualitatively verified by the ion measurements with an atmospheric-pressure interface-time of flight (APi-TOF) mass spectrometer. By applying a high-voltage (HV) clearing field inside the CLOUD chamber, the ion effect on the CIMS measurement was completely eliminated since, under these conditions, small ions are swept from the chamber in about 1 s. In order to exclude the ion effect and to provide corrected sulfuric acid concentrations during the GCR and PS beam nucleation experiments, a parameterisation was derived that utilises the trace gas concentrations and the UV light intensity as input parameters. Atmospheric sulfuric acid measurements with a CIMS showed an insignificant ion effect.