The existence of an upper limit for extremes of quantities in the earth sciences, e.g. for river discharge or wind speed, is sometimes suggested. Estimated parameters in extreme-value distributions can assist in interpreting the behaviour of the system. Using simulation, this study investigated how sample size influences the results of statistical tests and related interpretations. Commonly used estimation techniques (maximum likelihood and probability-weighted moments) were employed in a case study; the results were applied in judging time series of annual maximum river flow from two stations on the same river, but with different lengths of observation records. The results revealed that sample size is crucial for determining the existence of an upper bound.

With ongoing climate change, analysis of trends in maximum annual daily river flow is of interest. Flow magnitude and timing during the year were investigated in this study. Observations from 11 unregulated rivers in northern Sweden were analysed, using extreme-value distributions with time-dependent parameters. The Mann–Kendall test was used to investigate possible trends. The extreme-value statistics revealed no significant trends for the stations considered, but the Mann–Kendall test showed a significant upward trend for some stations. For timing of maximum flow (day of the year), the Mann–Kendall test revealed significant downward trends for two stations (with the longest records). This implies that the day of the maximum flow is occurring earlier in the year in northern Sweden.

In this work, we introduce a local linear nonparametric estimation of the regression function of a censored scalar response random variable, given a functional random covariate. Under standard conditions, we establish the pointwise and the uniform almost-complete convergences, with rates, of the proposed estimator. Then, we carry out a simulation study and a real data analysis in order to compare the performances of our methodology with those of the kernel method.

Microtopography can be a key driver of heterogeneity in the ground thermal and hydrological regime of permafrost landscapes. In turn, this heterogeneity can influence plant communities, methane fluxes, and the initiation of abrupt thaw processes. Here we have implemented a two-tile representation of microtopography in JULES (the Joint UK Land Environment Simulator), where tiles are representative of repeating patterns of elevation difference. Tiles are coupled by lateral flows of water, heat, and redistribution of snow, and a surface water store is added to represent ponding. Simulations are performed of two Siberian polygon sites, (Samoylov and Kytalyk) and two Scandinavian palsa sites (Stordalen and Iškoras).

The model represents the observed differences between greater snow depth in hollows vs. raised areas well. The model also improves soil moisture for hollows vs. the non-tiled configuration (“standard JULES”) though the raised tile remains drier than observed. The modelled differences in snow depths and soil moisture between tiles result in the lower tile soil temperatures being warmer for palsa sites, as in reality. However, when comparing the soil temperatures for July at 20 cm depth, the difference in temperature between tiles, or “temperature splitting”, is smaller than observed (3.2 vs. 5.5 ∘C). Polygons display small (0.2 ∘C) to zero temperature splitting, in agreement with observations. Consequently, methane fluxes are near identical (+0 % to 9 %) to those for standard JULES for polygons, although they can be greater than standard JULES for palsa sites (+10 % to 49 %).

Through a sensitivity analysis we quantify the relative importance of model processes with respect to soil moisture and temperatures, identifying which parameters result in the greatest uncertainty in modelled temperature. Varying the palsa elevation between 0.5 and 3 m has little effect on modelled soil temperatures, showing that using only two tiles can still be a valid representation of sites with a range of palsa elevations. Mire saturation is heavily dependent on landscape-scale drainage. Lateral conductive fluxes, while small, reduce the temperature splitting by ∼ 1 ∘C and correspond to the order of observed lateral degradation rates in peat plateau regions, indicating possible application in an area-based thaw model.