Understanding the link between the Sun and climate is vital in the current incidence of global climate change, and 10Be in natural archives constitutes an excellent tracer for this purpose. As cosmic rays enter the atmosphere, cosmogenic isotopes like 10Be and 14C are formed. Variations in solar activity modulate the amount of incoming cosmic rays, and thereby cosmogenic isotope production. Atmospherically produced 10Be enters natural archives such as sediments and glaciers by wet and dry deposition within about a year of production. 10Be from natural archives therefore provides information on past solar activity, and because these archives also contain climate information, solar activity and climate can be linked. One remaining question is to what degree 10Be in natural archives reflects production, and to what extent the local and regional environment overprints the production signal. To explore this, 10Be was measured at annual resolution over the last 600 years in a Greenland ice core. Measurement potentials for these samples benefited from the development of a new laboratory method of co-precipitating 10Be with niobium. To diversify geographic location and archive media type, a pioneer study of measuring 10Be with annual resolution in varved lake sediments from Finland was conducted, with samples from the entire 20th century. Pathways of 10Be into lake sediments are more complex than into glacial ice, inferring that contemporary atmospheric conditions may not be recorded. Here, it is shown for the first time that tracing the 11-year solar cycle through lake sediment 10Be variations is possible. Results also show that on an annual basis, 10Be deposition in ice and sediment archives is affected by local environmental conditions. On a slightly longer timescale, however, diverse 10Be records exhibit similar trends and a negative correlation with solar activity. Cyclic variability of 10Be deposition persisted throughout past grand solar minima, when little or no sunspot activity was recorded. 10Be levels indicate that although solar activity has been high during the 20th century, levels are not unprecedented in the investigated 600 years. Aerosol 10Be/7Be values indicate possible influence of stratosphere-troposphere exchange on isotope abundance and the production signal.

This thesis consists of two parts.The first part considers further development of a model used for marital fertility, the Coale-Trussell's fertility model, which is based on age-specific fertility rates. A new model is suggested using individual fertility data and a waiting time after pregnancies. The model is named the waiting model and can be understood as an alternating renewal process with age-specific intensities. Due to the complicated form of the waiting model and the way data is presented, as given in the United Nation Demographic Year Book 1965, a normal approximation is suggested together with a normal approximation of the mean and variance of the number of births per summarized interval. A further refinement of the model was then introduced to allow for left truncated and censored individual data, summarized as table data. The waiting model suggested gives better understanding of marital fertility and by a simulation study it is shown that the waiting model outperforms the Coale-Trussell model when it comes to estimating the fertility intensity and to predict the mean and variance of the number of births for a population. The second part of the thesis focus on developing functional clustering methods.The methods are motivated by and applied to varved (annually laminated) sediment data from lake Kassj\"on in northern Sweden. The rich but complex information (with respect to climate) in the varves, including the shapes of the seasonal patterns, the varying varve thickness, and the non-linear sediment accumulation rates makes it non-trivial to cluster the varves. Functional representations, smoothing and alignment are functional data tools used to make the seasonal patterns comparable.Functional clustering is used to group the seasonal patterns into different types, which can be associated with different weather conditions. A new non-parametric functional clustering method is suggested, the Bagging Voronoi K-mediod Alignment algorithm, (BVKMA), which simultaneously clusters and aligns spatially dependent curves. BVKMA is used on the varved lake sediment, to infer on climate, defined as frequencies of different weather types, over longer time periods. Furthermore, a functional model-based clustering method is proposed that clusters subjects for which both functional data and covariates are observed, allowing different covariance structures in the different clusters. The model extends a model-based functional clustering method proposed by James and Suger (2003). An EM algorithm is derived to estimate the parameters of the model.

Paleoclimatic archives, such as lake sediments, extend our understanding of terrestrial and aquatic ecosystem dynamics in relation to climate variability beyond the period covered by instrumental data. In this context, annually laminated (i.e. varved) lake sediments are particularly valuable, as they offer high temporal resolution and undisturbed sediment. However, in order to extract reliable climate information from lake sediments, a careful calibration with the processes controlling the sediment formation is essential. This thesis combines limnological and paleolimnological data from a varved, boreal lake in northern Sweden (Nylandssjön, Nordingrå) collected over different time scales. The main aim of the thesis is to gain a more refined insight into which processes are reflected in the sedimentary diatom assemblage. More specifically, sequential sediment trap records were coupled with physical, chemical and biological lake monitoring and environmental data for comparison and validation with the varved sediment record. The main result of the thesis is that timing, succession and inter-annual variability of key limnological and environmental processes (e.g. ice-cover duration, lake over-turn or catchment run-off) are of major importance for the sedimentary diatom assemblage formation. Continuous monitoring of physico-chemical parameters over three consecutive years identified varying winter air temperature as a major factor influencing in-lake processes and hence the diatom record. Timing of lake over-turn and catchment run-off seemed to be the driver for monospecific diatom blooms, which are reflected in the annual sediment signal. The integrated annual diatom signal in the sediment was dominated by spring or autumn blooms, resulting either from a Cyclotella glomerata dominated spring bloom after relatively warm winter conditions, or a Asterionella formosa dominated autumn bloom after relatively cold winter conditions. The analysis of the diatom stratigraphy in the varved sediment over several decades corroborated the importance of climatic variables (late winter air temperature and NAO), even though the variables with the most predictive power for variance in the diatom data were associated with sediment composition (C, N and sedimentation rate) and pollution (Pb and Cu). Overall, the analysis of the drivers of inter-annual and decadal diatom assemblage fluctuations emphasizes the importance of winter air temperature, indicating that weather extremes may be disproportionately represented in annual sediment records in contrast to nutrient concentrations or sedimentation rate.