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Finding behavioral parameterization for a 1-D water balance model by multi-criteria evaluation
(2019)

Evapotranspiration is often estimated by numerical simulation. However, to produce accurate simulations, these models usually require on-site measurements for parameterization or calibration. We have to make sure that the model realistically reproduces both, the temporal patterns of soil moisture and evapotranspiration. In this study, we combine three sources of information: (i) measurements of sap velocities; (ii) soil moisture; and (iii) expert knowledge on local runoff generation and water balance to define constraints for a “behavioral” forest stand water balance model. Aiming for a behavioral model, we adjusted soil moisture at saturation, bulk resistance parameters and the parameters of the water retention curve (WRC). We found that the shape of the WRC influences substantially the behavior of the simulation model. Here, only one model realization could be referred to as “behavioral”. All other realizations failed for a least one of our evaluation criteria: Not only transpiration and soil moisture are simulated consistently with our observations, but also total water balance and runoff generation processes. The introduction of a multi-criteria evaluation scheme for the detection of unrealistic outputs made it possible to identify a well performing parameter set. Our findings indicate that measurement of different fluxes and state variables instead of just one and expert knowledge concerning runoff generation facilitate the parameterization of a hydrological model.

Nonlocal operators are used in a wide variety of models and applications due to many natural phenomena being driven by nonlocal dynamics. Nonlocal operators are integral operators allowing for interactions between two distinct points in space. The nonlocal models investigated in this thesis involve kernels that are assumed to have a finite range of nonlocal interactions. Kernels of this type are used in nonlocal elasticity and convection-diffusion models as well as finance and image analysis. Also within the mathematical theory they arouse great interest, as they are asymptotically related to fractional and classical differential equations.
The results in this thesis can be grouped according to the following three aspects: modeling and analysis, discretization and optimization.
Mathematical models demonstrate their true usefulness when put into numerical practice. For computational purposes, it is important that the support of the kernel is clearly determined. Therefore nonlocal interactions are typically assumed to occur within an Euclidean ball of finite radius. In this thesis we consider more general interaction sets including norm induced balls as special cases and extend established results about well-posedness and asymptotic limits.
The discretization of integral equations is a challenging endeavor. Especially kernels which are truncated by Euclidean balls require carefully designed quadrature rules for the implementation of efficient finite element codes. In this thesis we investigate the computational benefits of polyhedral interaction sets as well as geometrically approximated interaction sets. In addition to that we outline the computational advantages of sufficiently structured problem settings.
Shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations. Here we consider a class of shape optimization problems constrained by nonlocal equations which involve interface-dependent kernels. We derive the shape derivative associated to the nonlocal system model and solve the problem by established numerical techniques.

This thesis considers the general task of computing a partition of a set of given objects such that each set of the partition has a cardinality of at least a fixed number k. Among such kinds of partitions, which we call k-clusters, the objective is to find the k-cluster which minimises a certain cost derived from a given pairwise difference between objects which end up the same set. As a first step, this thesis introduces a general problem, denoted by (||.||,f)-k-cluster, which models the task to find a k-cluster of minimum cost given by an objective function computed with respect to specific choices for the cost functions f and ||.||. In particular this thesis considers three different choices for f and also three different choices for ||.|| which results in a total of nine different variants of the general problem. Especially with the idea to use the concept of parameterised approximation, we first investigate the role of the lower bound on the cluster cardinalities and find that k is not a suitable parameter, due to remaining NP-hardness even for the restriction to the constant 3. The reductions presented to show this hardness yield the even stronger result which states that polynomial time approximations with some constant performance ratio for any of the nine variants of (||.||,f)-k-cluster require a restriction to instances for which the pairwise distance on the objects satisfies the triangle inequality. For this restriction to what we informally refer to as metric instances, constant-factor approximation algorithms for eight of the nine variants of (||.||,f)-k-cluster are presented. While two of these algorithms yield the provably best approximation ratio (assuming P!=NP), others can only guarantee a performance which depends on the lower bound k. With the positive effect of the triangle inequality and applications to facility location in mind, we discuss the further restriction to the setting where the given objects are points in the Euclidean metric space. Considering the effect of computational hardness caused by high dimensionality of the input for other related problems (curse of dimensionality) we check if this is also the source of intractability for (||.||,f)-k-cluster. Remaining NP-hardness for restriction to small constant dimensionality however disproves this theory. We then use parameterisation to develop approximation algorithms for (||.||,f)-k-cluster without restriction to metric instances. In particular, we discuss structural parameters which reflect how much the given input differs from a metric. This idea results in parameterised approximation algorithms with parameters such as the number of conflicts (our name for pairs of objects for which the triangle inequality is violated) or the number of conflict vertices (objects involved in a conflict). The performance ratios of these parameterised approximations are in most cases identical to those of the approximations for metric instances. This shows that for most variants of (||.||,f)-k-cluster efficient and reasonable solutions are also possible for non-metric instances.

This study aims to estimate the cotton yield at the field and regional level via the APSIM/OZCOT crop model, using an optimization-based recalibration approach based on the state variable of the cotton canopy - the leaf area index (LAI), derived from atmospherically corrected Landsat-8 OLI remote sensing images in 2014. First, a local sensitivity and global analysis approach was employed to test the sensitivity of cultivar, soil and agronomic parameters to the dynamics of the LAI. After sensitivity analyses, a series of sensitive parameters were obtained. Then, the APSIM/OZCOT crop model was calibrated by observations over a two-year span (2006-2007) at the Aksu station, combined with these sensitive cultivar parameters and the current understanding of cotton cultivar parameters. Third, the relationship between the observed in-situ LAI and synchronous perpendicular vegetation indices derived from six Landsat-8 OLI images covering the entire growth stage was modelled to generate LAI maps in time and space. Finally, the Particle Swarm Optimization (PSO) and general-purpose optimization approach (based on Nelder-Mead algorithm) were used to recalibrate four sensitive agronomic parameters (row spacing, sowing density per row, irrigation amount and total fertilization) according to the minimization of the root-mean-square deviation (RMSE) between the simulated LAI from the APSIM/OZCOT model and retrieved LAI from Landsat-8 OLI remote sensing images. After the recalibration, the best simulated results compared with observed cotton yield were obtained. The results showed that: (1) FRUDD, FLAI and DDISQ were the major cultivar parameters suitable for calibrating the cotton cultivar. (2) After the calibration, the simulated LAI performed well with an RMSE and mean absolute error (MAE) of 0.45 and 0.33, respectively, in 2006 and 0.46 and 0.41, respectively, in 2007. The coefficient of determination between the observed and simulated LAI was 0.83 and 0.97, respectively, in 2006 and 2007. The Pearson- correlation coefficient was 0.913 and 0.988 in 2006 and 2007, respectively, with a significant positive correlation between the simulated and observed LAI. The difference between the observed and simulated yield was 776.72 kg/ha and 259.98 kg/ha in 2006 and 2007, respectively. (3) Cotton cultivation in 2014 was obtained using three Landsat-8 OLI images - DOY136 (May), DOY 168 (June) and DOY 200 (July) - based on the phenological differences in cotton and other vegetation types. (4) The yield estimation after the assimilation closely approximated the field-observed values, and the coefficient of determination was as high as 0.82, after recalibration of the APSIM/OZCOT model for ten cotton fields. The difference between the observed and assimilated yields for the ten fields ranged from 18.2 to 939.7 kg/ha. The RMSE and MAE between the assimilated and observed yield was 417.5 and 303.1 kg/ha, respectively. These findings provide scientific evidence for the feasibility of coupled remote sensing and APSIM/OZCOT model at the field level. (5) Upscaling from field level to regional level, the assimilation algorithm and scheme are both especially important. Although the PSO method is very efficient, the computational efficiency is also the shortcoming of the assimilation strategy on a regional scale. Comparisons between the PSO and general-purpose optimization method (based on the Nelder-Mead algorithm) were implemented from the RSME, LAI curve and computational time. The general-purpose optimization method (based on the Nelder-Mead algorithm) was used for the regional assimilation between remote sensing and the APSIM/OZCOT model. Meanwhile, the basic unit for regional assimilation was also determined as cotton field rather than pixel. Moreover, the crop growth simulation was also divided into two phases (vegetative growth and reproductive growth) for regional assimilation. (6) The regional assimilation at the vegetative growth stage between the remote sensing derived and APSIM/OZCOT model-simulated LAI was implemented by adjusting two parameters: row spacing and sowing density per row. The results showed that the sowing density of cotton was higher in the southern part than in the northern part of the study area. The spatial pattern of cotton density was also consistent with the reclamation from 2001 to 2013. Cotton fields after early reclamation were mainly located in the southern part while the recent reclamation was located in the northern part. Poor soil quality, lack of irrigation facilities and woodland belts of cotton fields in the northern part caused the low density of cotton. Regarding the row spacing, the northern part was larger than the southern part due to the variation of two agronomic modes from military and private companies. (7) The irrigation and fertilization amount were both used as key parameters to be adjusted for regional assimilation during the reproductive growth period. The result showed that the irrigation per time ranged from 58.14 to 89.99 mm in the study area. The spatial distribution of the irrigation amount is higher in the northern part while lower in southern study area. The application of urea fertilization ranged from 500.35 to 1598.59 kg/ha in the study area. The spatial distribution of fertilization was lower in the northern part and higher in the southern part. More fertilization applied in the southern study area aims to increase the boll weight and number for pursuing higher yields of cotton. The frequency of the RSME during the second assimilation was mainly located in the range of 0.4-0.6 m2/m2. The estimated cotton yield ranged from 1489 to 8895 kg/ha. The spatial distribution of the estimated yield is also higher in the southern part than the northern study area.

High-resolution projections of the future climate are required to assess climate change realistically at a regional scale. This is in particular important for climate change impact studies since global projections are much too coarse to represent local conditions adequately. A major concern is thereby the change of extreme values in a warming climate due to their severe impact on the natural environment, socio-economical systems and the human health. Regional climate models (RCMs) are, however, able to reproduce much of those local features. Current horizontal resolutions are about 18-25km, which is still too coarse to directly resolve small-scale processes such as deep-convection. For this reason, projections of a possible future climate were simulated in this study with the regional climate model COSMO-CLM at horizontal resolutions of 4.5km and 1.3km for the region of Saarland-Lorraine-Luxemburg and Rhineland-Palatinate for the first time. At a horizontal scale of about 1km deep-convection is treated explicitly, which is expected to improve particularly the simulation of convective summer precipitation and a better resolved orography is expected to improve near surface fields such as 2m temperature. These simulations were performed as 10-year long time-slice experiments for the present climate (1991"2000), the near future (2041"2050) and the end of the century (2091"2100). The climate change signals of the annual and seasonal means and the change of extremes are analysed with respect to precipitation and 2m temperature and a possible added value due to the increased resolution is investigated. To assess changes in extremes, extreme indices have been applied and 10- and 20-year return levels were estimated by "peak-over-threshold" models. Since it is generally known that model output of RCMs should not directly be used for climate change impact studies, the precipitation and temperature fields were bias-corrected with several quantile-matching methods. Among them is a new developed parametric method which includes an extension for extreme values and is hence expected to improve the correction. In addition, the impact of the bias-correction on the climate change signals and on the extreme value statistics was investigated. The results reveal a significant warming of the annual mean by about +1.7 -°C until 2041"2050 and +3.7 -°C until 2091"2100, but considerably stronger signals of up to +5 -°C in summer in the Rhine Valley. Furthermore, the daily variability increases by about +0.8 -°C in summer but decreases by about -0.8 -°C in winter. Consequently, hot extremes increase moderately until the mid of the century but strongly thereafter, in particular in the Rhine Valley. Cold extremes warm continuously in the complete domain in the next 100 years but strongest in mountainous areas. The change signals with regard to annual precipitation are of the order -±10% but not significant. Significant, however, are a predicted increase of +32% of the seasonal precipitation in autumn until 2041"2050 and a decrease of -28% in summer until 2091-2100. No significant changes were found for days with intensities > 20 mm/day, but the results indicate that extremes with return periods â‰¤2 years increase as well as the frequency and duration of dry periods. The bias-corrections amplified positive signals but dampened negative signals and considerably reduced the power of detection. Moreover, absolute values and frequencies of extremes were altered by the correction but change signals remained approximately constant. The new method outperformed other parametric methods, in particular with regard to extreme value correction and related extreme indices and return levels. Although the bias correction removed systematic errors, it should be treated as an additional layer of uncertainty in climate change studies. Finally, the increased resolution of 1.3km improved predominantly the representation of temperature fields and extremes in terms of spatial heterogeneity. The benefits for summer precipitation were not as clear due to a severe dry-bias in summer, but it could be shown that in principle the onset and intensity of convection improves. This work demonstrates that climate change will have severe impacts in this investigation area and that in particular extremes may change considerably. An increased resolution provides thereby an added value to the results. These findings encourage further investigations, for other variables as for example near-surface wind, which will be more feasible with growing computing resources. These analyses should, however, be repeated with longer time series, different RCMs and anthropogenic scenarios to determine the robustness and uncertainty of these results more extensively.

The reduction of information contained in model time series through the use of aggregating statistical performance measures is very high compared to the amount of information that one would like to draw from it for model identification and calibration purposes. It is readily known that this loss imposes important limitations on model identification and -diagnostics and thus constitutes an element of the overall model uncertainty as essentially different model realizations with almost identical performance measures (e.g. r-² or RMSE) can be generated. In three consecutive studies the present work proposes an alternative approach towards hydrological model evaluation based on the application of Self-Organizing Maps (SOM; Kohonen, 2001). The Self-Organizing Map is a type of artificial neural network and unsupervised learning algorithm that is used for clustering, visualization and abstraction of multidimensional data. It maps vectorial input data items with similar patterns onto contiguous locations of a discrete low-dimensional grid of neurons. The iterative training of the SOM causes the neurons to form a discrete, data-compressed representation of the high-dimensional input data. Using appropriate visualization techniques, information on distributions, patterns and relationships in complex data sets can be extracted. Irrespective of their potential, SOM applications have earned very little attention in hydrological modelling compared to other artificial neural network techniques. Therefore, the aim of the present work is to demonstrate that the application of Self-Organizing Maps has very high potential to address fundamental issues of model evaluation: It is shown that the clustering and classification of model time series by means of SOM can provide useful insights into model behaviour. In combination with the diagnostic properties of Signature Indices (Gupta et al., 2008; Yilmaz et al., 2008) SOM provides a novel tool for interpreting the model parameters in the hydrological context and identifying parameter sets that simultaneously meet multiple objectives, even if the corresponding model realizations belong to different models. Moreover, the presented studies and reviews also encourage further studies on the application of SOM in hydrological modelling.

Tropospheric ozone (O3) is known to have various detrimental effects on plants, such as visible leaf injury, reduced growth and premature senescence. Flux models offer the determination of the harmful ozone dose entering the plant through the stomata. This dose can then be related to phytotoxic effects mentioned above to obtain dose-response relationships, which are a helpful tool for the formulation of abatement strategies of ozone precursors. rnOzone flux models are dependant on the correct estimation of stomatal conductance (gs). Based on measurements of gs, an ozone flux model for two white clover clones (Trifolium repens L. cv Regal; NC-S (ozone-sensitive) and NC-R (ozone-resistant)) differing in their sensitivity to ozone was developed with the help of artificial neural networks (ANNs). White clover is an important species of various European grassland communities. The clover plants were exposed to ambient air at three sites in the Trier region (West Germany) during five consecutive growing seasons (1997 to 2001). The response parameters visible leaf injury and biomass ratio of NC-S/NC-R clone were regularly assessed. gs-measurements of both clones functioned as output of the ANN-based gs model, while corresponding climate parameters (i.e. temperature, vapour pressure deficit (VPD) and photosynthetic active radiation (PAR)) and various ozone concentration indices were inputs. The development of the model was documented in detail and various model evaluation techniques (e.g. sensitivity analysis) were applied. The resulting gs model was used as a basis for ozone flux calculations, which were related to above mentioned response parameters. rnThe results showed that the ANNs were capable of revealing and learning the complex relationship between gs and key meteorological parameters and ozone concentration indices. The dose-response relationships between ozone fluxes and visible leaf injury were reasonably strong, while those between ozone fluxes and NC-S/NC-R biomass ratio were fairly weak. The results were discussed in detail with respect to the suitability of the chosen experimental methods and model type.

In past years, desertification and land degradation have been acknowledged as a major threat to human welfare world-wide, and their environmental and societal implications have sparked the formulation of the UN Convention to Combat Desertification (UNCCD). Any measure taken against desertification, or the design of dedicated early warning systems, must take into account both the spatial and temporal dimensions of process driving factors. Equally important, past and present reactions of ecosystems to physical and socio-economical disturbances or management interventions need to be understood. In this context, remote sensing and geoinformation processing support the required assessment, monitoring and modelling approaches, and hence provide an essential contribution to the scientific component of the struggle against desertification. Supported by DG Research of the European Commission, the Remote Sensing Department of the University of Trier convened RGLDD to promote scientific exchange between specialists working on the interface of remote sensing, geoinformation processing, desertification/land degradation research and its socio-economic implications. Although targeted at the scientific community, contributions with application perspectives were of crucial importance and both an overview of the current state of the art as well as operational opportunities were presented. Hosted at the Robert-Schuman Haus in Trier, the conference gained widespread attention and attracted an international audience from all parts of the world, which underlines the global dimension of land degradation and desertification processes. Based on a rigorous review of submitted abstracts, more than 100 contributions were accepted for oral and poster presentation, which are found in these proceedings edition in full paper form. Please note: This document is optimised for screen resolution, to receive a high-resolution version please contact the editors.

It has been the overall aim of this research work to assess the potential of hyperspectral remote sensing data for the determination of forest attributes relevant to forest ecosystem simulation modeling and forest inventory purposes. A number of approaches for the determination of structural and chemical attributes from hyperspectral remote sensing have been applied to the collected data sets. Many of the methods to be found in the literature were up to now just applied to broadband multispectral data, applied to vegetation canopies other than forests, reported to work on the leaf level or with modelled data, not validated with ground truth data, or not systematically compared to other methods. Attributes that describe the properties of the forest canopy and that are potentially open to remote sensing were identified, appropriate methods for their retrieval were implemented and field, laboratory and image data (HyMap sensor) were acquired over a number of forest plots. The study on structural attributes compared statistical and physical approaches. In the statistical section, linear predictive models between vegetation indices derived from HyMap data and field measurements of structural forest stand attributes were systematically evaluated. The study demonstrates that for hyperspectral image data, linear regression models can be applied to quantify leaf area index and crown volume with good accuracy. For broadband multispectral data, the accuracy was generally lower. The physically-based approach used the invertible forest reflectance model (INFORM), a combination of well established sub-models FLIM, SAIL and LIBERTY. The model was inverted with HyMap data using a neural network approach. In comparison to the statistical approach, it could be shown that the reflectance model inversion works equally well. In opposition to empirically derived prediction functions that are generally limited to the local conditions at a certain point in time and to a specified sensor type, the calibrated reflectance model can be applied more easily to different optical remote sensing data acquired over central European forests. The study on chemical forest attributes evaluated the information content of HyMap data for the estimation of nitrogen, chlorophyll and water concentration. A number of needle samples of Norway spruce were analysed for their total chlorophyll, nitrogen and water concentrations. The chemical data was linked to needle spectra measured in the laboratory and canopy spectra measured by the HyMap sensor. Wavebands selected in statistical models were often located in spectral regions that are known to be important for chlorophyll detection (red edge, green peak). Predictive models were applied on the HyMap image to compute maps of chlorophyll concentration and nitrogen concentration. Results of map overlay operations revealed coherence between total chlorophyll and zones of stand development stage and between total chlorophyll and zones of soil type. Finally, it can be stated that the hyperspectral remote sensing data generally contains more information relevant to the estimation of the forest attributes compared to multispectral data. Structural forest attributes, except biomass, can be determined with good accuracy from a hyperspectral sensor type like HyMap. Among the chemical attributes, chlorophyll concentration can be determined with good accuracy and nitrogen concentration with moderate accuracy. For future research, additional dimensions have to be taken into account, for instance through exploitation of multi-view angle data. Additionally, existing forest canopy reflectance models should be further improved.

Two areas were selected to represent major process regimes of Mediterranean rangelands. In the County of Lagads (Greece), situated east of the city of Thessaloniki, livestock grazing with sheep and goats is a major factor of the rural economy. In suitable areas, it is complemented by agricultural use. The region of Ayora (Spain) is located west of the city of Valencia. It is one of regions most affected by fires in Spain. First of all, long time series of satellite data were compiled for both regions on the basis of Landsat sensors, which cover the time until 1976 (Ayora) and 1984 (Lagadas) with one image per year. Using a rigorous processing scheme, the data were geometrically and radiometrically corrected Specific attention was given to an exact sensor calibration, the radiometric intercalibration of Landsat-TM and "MSS. Proportional cover of photosynthetically active vegetation was identified as a suitable quantitative indicator for assessing the state of rangelands. Using Spectral Mixture Analysis (SMA) it was inferred for all data sets. The extensive data base procured this way enabled to map fire events in the Ayora area based on sequential diachronic sets and provide fire dates, perimeter as well as fire recurrence for each pixel. The increasing fire frequency in the past decades is in large parts attributed to the accelerated abandonment of the area that leads to an encroachment of shrublands and the accumulation of combustible biomass. On the basis of the fire mapping results, a spatial and temporal stratification of the data set allowed to asses plant recovery dynamics on the landscape level through linear trend analysis. The long history of fire events in the Mediterranean frequently leads to processes of auto-succession. Following an initial dominance of herbaceous vegetation this commonly leads to similar plant communities as the ones present before the fire. On a temporal axis, this results in typical exponential post-fire trajectories which could also be shown in this study. The analysis of driving factors for post-fire dynamics confirmed the importance of aspect and slope. Locations with lower amounts of solar irradiation and favourable water supply yielded faster recovery rates and higher post-fire vegetation cover levels. In most cases, the vegetation cover levels observed before the fire were not reached within the post-fire observation period. In the area of Lagadas, linear trend analysis and additional statistical parameters were used to infer a degradation index. This could be used to illustrate a complex pattern of stability, regeneration and degradation of vegetation cover. These different processes and states are found in close proximity and are clearly determined by topography and elevation. Following a sequence of analyses, it was found that in particular steep, narrow valleys show positive trends, while negative trends are more abundant on plain or gently undulating areas. Considering the local grazing regime, this spatial differentiation was related to the accessibility of specific locations. Subsequently, animal numbers on community level were used to calculate efficient stocking rates and assess the temporal development of their relation with vegetation cover. This calculation of temporal trajectories illustrated that only some communities show the expected negative relation. To the contrary, a positive relation or even changing relation patterns are observed. This signifies recent concentration and intensification processes in the grazing scheme, as a result of which animals are kept in sheds, where additional feedstuffs are provided. In these cases, free roaming of livestock animals is often confined to some hours every day, which explains the spatial preference of easily accessible areas by the shepherds. Beyond these temporal trends, it was analysed whether the grazing pattern is equally reflected in a spatial trend. Making use of available geospatial information layers, the efforts required to reach each location was expressed as a cost. Then, cost zones could be defined and woody vegetation cover as a grazing indicator could be inferred for the different zones. Animal sheds were employed as starting features for this piospheric analysis, which could be mapped from very high spatial resolution Quickbird image data. The result was a clearly structured gradient showing increasing woody vegetation cover with increasing cost distance. On the basis of these two pilot studies, the elements of a monitoring and interpretation framework identified at the beginning of the work were evaluated and a formal interpretation scheme was presented.