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Two independent random elements taking values in a separable Hilbert space are considered. The aim is to develop a test with bootstrap calibration to check whether they have the same distribution or not. A transformation of both random elements into a new separable Hilbert space is considered so that the equality of expectations of the transformed random elements is equivalent to the equality of distributions. Thus, a bootstrap test procedure to check the equality of means can be used in order to solve the original problem. It will be shown that both the asymptotic and bootstrap approaches proposed are asymptotically correct and consistent. The results can be applied, for example, in functional data analysis. In practice, the test can be solved with simple operations in the original space without applying the mentioned transformation, which is used only to guarantee the theoretical results. Empirical results and comparisons with related methods support and complement the theory.

Seismic data are typically employed to monitor earthquake activity, but they can also be exploited in order to investigate the existing links between the seismic signal and a broad range of physical processes occurring in the nearby rivers. For instance, the noise related to water turbulence during high discharges has a clear impact on the seismic signal. Concurrently, high-flows in gravel-bed rivers involve the displacement of large volumes of coarse sediment particles, travelling as bedload, which in turn should be the source of an additional and non-negligible amount of seismic noise. Data derived from the 3-years seismic monitoring of a gravel-bed river located in NW of Spain are considered. First, we have accomplished spectral analysis over the seismic noise generated by more than 10 river flow events with high discharge. Then, we have applied several statistical analysis not only for calibrating the functions describing the links between seismic noise and fluvial discharge but also in order to identify the thresholds for detection of incipient bedload transport and geomorphic change in the seismic signal.

Wildfires release substantial quantities of carbon (C) into the atmosphere but they also convert part of the burnt biomass into pyrogenic organic matter (PyOM). This is richer in C and, overall, more resistant to environmental degradation than the original biomass, and, therefore, PyOM production is an efficient mechanism for C sequestration. The magnitude of this C sink, however, remains poorly quantified, and current production estimates, which suggest that ~1-5% of the C affected by fire is converted to PyOM, are based on incomplete inventories. Here, we quantify, for the first time, the complete range of PyOM components found in-situ immediately after a typical boreal forest fire. We utilized an experimental high-intensity crown fire in a jack pine forest (Pinus banksiana) and carried out a detailed pre- and postfire inventory and quantification of all fuel components, and the PyOM (i.e., all visually charred, blackened materials) produced in each of them. Our results show that, overall, 27.6% of the C affected by fire was retained in PyOM (4.8 ± 0.8 t C ha(-1)), rather than emitted to the atmosphere (12.6 ± 4.5 t C ha(-1)). The conversion rates varied substantially between fuel components. For down wood and bark, over half of the C affected was converted to PyOM, whereas for forest floor it was only one quarter, and less than a tenth for needles. If the overall conversion rate found here were applicable to boreal wildfire in general, it would translate into a PyOM production of ~100 Tg C yr(-1) by wildfire in the global boreal regions, more than five times the amount estimated previously. Our findings suggest that PyOM production from boreal wildfires, and potentially also from other fire-prone ecosystems, may have been underestimated and that its quantitative importance as a C sink warrants its inclusion in the global C budget estimates.