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A model-based temperature adjustment scheme for wintertime sea-ice production retrievals from MODIS
(2022)

Knowledge of the wintertime sea-ice production in Arctic polynyas is an important requirement for estimations of the dense water formation, which drives vertical mixing in the upper ocean. Satellite-based techniques incorporating relatively high resolution thermal-infrared data from MODIS in combination with atmospheric reanalysis data have proven to be a strong tool to monitor large and regularly forming polynyas and to resolve narrow thin-ice areas (i.e., leads) along the shelf-breaks and across the entire Arctic Ocean. However, the selection of the atmospheric data sets has a large influence on derived polynya characteristics due to their impact on the calculation of the heat loss to the atmosphere, which is determined by the local thin-ice thickness. In order to overcome this methodical ambiguity, we present a MODIS-assisted temperature adjustment (MATA) algorithm that yields corrections of the 2 m air temperature and hence decreases differences between the atmospheric input data sets. The adjustment algorithm is based on atmospheric model simulations. We focus on the Laptev Sea region for detailed case studies on the developed algorithm and present time series of polynya characteristics in the winter season 2019/2020. It shows that the application of the empirically derived correction decreases the difference between different utilized atmospheric products significantly from 49% to 23%. Additional filter strategies are applied that aim at increasing the capability to include leads in the quasi-daily and persistence-filtered thin-ice thickness composites. More generally, the winter of 2019/2020 features high polynya activity in the eastern Arctic and less activity in the Canadian Arctic Archipelago, presumably as a result of the particularly strong polar vortex in early 2020.

The parameterization of ocean/sea-ice/atmosphere interaction processes is a challenge for regional climate models (RCMs) of the Arctic, particularly for wintertime conditions, when small fractions of thin ice or open water cause strong modifications of the boundary layer. Thus, the treatment of sea ice and sub-grid flux parameterizations in RCMs is of crucial importance. However, verification data sets over sea ice for wintertime conditions are rare. In the present paper, data of the ship-based experiment Transarktika 2019 during the end of the Arctic winter for thick one-year ice conditions are presented. The data are used for the verification of the regional climate model COSMO-CLM (CCLM). In addition, Moderate Resolution Imaging Spectroradiometer (MODIS) data are used for the comparison of ice surface temperature (IST) simulations of the CCLM sea ice model. CCLM is used in a forecast mode (nested in ERA5) for the Norwegian and Barents Seas with 5 km resolution and is run with different configurations of the sea ice model and sub-grid flux parameterizations. The use of a new set of parameterizations yields improved results for the comparisons with in-situ data. Comparisons with MODIS IST allow for a verification over large areas and show also a good performance of CCLM. The comparison with twice-daily radiosonde ascents during Transarktika 2019, hourly microwave water vapor measurements of first 5 km in the atmosphere and hourly temperature profiler data show a very good representation of the temperature, humidity and wind structure of the whole troposphere for CCLM.

Low-level jets (LLJs) are climatological features in polar regions. It is well known that katabatic winds over the slopes of the Antarctic ice sheet are associated with strong LLJs. Barrier winds occurring, e.g., along the Antarctic Peninsula may also show LLJ structures. A few observational studies show that LLJs occur over sea ice regions. We present a model-based climatology of the wind field, of low-level inversions and of LLJs in the Weddell Sea region of the Antarctic for the period 2002–2016. The sensitivity of the LLJ detection on the selection of the wind speed maximum is investigated. The common criterion of an anomaly of at least 2 m/s is extended to a relative criterion of wind speed decrease above and below the LLJ. The frequencies of LLJs are sensitive to the choice of the relative criterion, i.e., if the value for the relative decrease exceeds 15%. The LLJs are evaluated with respect to the frequency distributions of height, speed, directional shear and stability for different regions. LLJs are most frequent in the katabatic wind regime over the ice sheet and in barrier wind regions. During winter, katabatic LLJs occur with frequencies of more than 70% in many areas. Katabatic LLJs show a narrow range of heights (mostly below 200 m) and speeds (typically 10–20 m/s), while LLJs over the sea ice cover a broad range of speeds and heights. LLJs are associated with surface inversions or low-level lifted inversions. LLJs in the katabatic wind and barrier wind regions can last several days during winter. The duration of LLJs is sensitive to the LLJ definition criteria. We propose to use only the absolute criterion for model studies.

Intense, southward low-level winds are common in Nares Strait, between Ellesmere Island and northern Greenland. The steep topography along Nares Strait leads to channelling effects, resulting in an along-strait flow. This research study presents a 30-year climatology of the flow regime from simulations of the COSMO-CLM climate model. The simulations are available for the winter periods (November–April) 1987/88 to 2016/17, and thus, cover a period long enough to give robust long-term characteristics of Nares Strait. The horizontal resolution of 15 km is high enough to represent the complex terrain and the meteorological conditions realistically. The 30-year climatology shows that LLJs associated with gap flows are a climatological feature of Nares Strait. The maximum of the mean 10-m wind speed is around 12 m s-1 and is located at the southern exit of Smith Sound. The wind speed is strongly related to the pressure gradient. Single events reach wind speeds of 40 m s-1 in the daily mean. The LLJs are associated with gap flows within the narrowest parts of the strait under stably stratified conditions, with the main LLJ occurring at 100–250 m height. With increasing mountain Froude number, the LLJ wind speed and height increase. The frequency of strong wind events (>20 m s-1 in the daily mean) for the 10 m wind shows a strong interannual variability with an average of 15 events per winter. Channelled winds have a strong impact on the formation of the North Water polynya.

The state-of-the-art finite element software Plaxis 3D was applied in a real-world study site of the Turaida castle mound to investigate the slope stability of the mound and understand the mechanisms triggering landslides there. During the simulation, the stability of the castle mound was analysed and the most landslide-susceptible zones of hillslopes were determined. The 3D finite-element stability analysis has significant advantages over conventional 2D limit-equilibrium methods where locations of 2D stability sections are arbitrarily selected. Two modelling scenarios of the slope stability were elaborated considering deep-seated slides in bedrock and shallow landslides in the colluvial material of slopes. The model shows that shallow slides in colluvium are more probable. In the finite-element model, slope failure occurs along the weakest zone in colluvium, similarly to the situation observed in previous landslides in the study site. The physical basis of the model allows results to be obtained very close to natural conditions and delivers valuable insight in triggering mechanisms of landslides.

Climate change is expected to cause mountain species to shift their ranges to higher elevations. Due to the decreasing amounts of habitats with increasing elevation, such shifts are likely to increase their extinction risk. Heterogeneous mountain topography, however, may reduce this risk by providing microclimatic conditions that can buffer macroclimatic warming or provide nearby refugia. As aspect strongly influences the local microclimate, we here assess whether shifts from warm south-exposed aspects to cool north-exposed aspects in response to climate change can compensate for an upward shift into cooler elevations.

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.