The Cauchy-Schlomilch transformation

The Cauchy-Schl\"omilch transformation states that for a function $f$ and $a, \, b > 0$, the integral of $f(x^{2})$ and $af((ax-bx^{-1})^{2}$ over the interval $[0, \infty)$ are the same. This elementary result is used to evaluate many non-elementary definite integrals, most of which cannot be obtained by symbolic packages. Applications to probability distributions is also given

Revisión de los eventos de afloramiento en Galicia: eventos fuera de temporada en las rías (1967–2009)

Over the last decades several studies have been conducted on upwelling along the Galician coast that have significantly improved the knowledge of this process. These investigations showed that upwelling along this coast is a frequent phenomenon during the spring and summer months, pumping colder Eastern North Atlantic Central Water into the rias. Nevertheless, several upwelling events in autumn and winter have been characterized in the Galician rias, indicating that the upwelling process along the Galician coast is not a phenomenon restricted to spring and summer. In this study the recurrence of these upwelling events has been reviewed from published articles and analyzed from 1967 to 2009 along the western and northern Galician coasts in terms of an upwelling index. The highest mean number of days under favorable upwelling conditions per month was observed during spring and summer on the western (18–26 days) and northern (12–14 days) coasts. During autumn and winter the number of days was lower (11–18 days, western coast; 8–10 days, northern coast) although not negligible, showing the possibility of observing upwelling events during this period. In fact, during these months a significant probability of observing favorable upwelling conditions along both coasts (26%) was found, though the most probable situation corresponded to unfavorable upwelling conditions (44%). The results thus revealed that these events cannot be considered isolated episodes. Upwelling processes in the rias should be observed under favorable conditions, such as prevalence of northerly wind at the adjacent western Galician shelf, independently of the season.Durante las últimas décadas se han llevado a cabo varios estudios relacionados con el fenómeno de afloramiento a lo largo de la costa de Galicia que han mejorado significativamente el conocimiento de este proceso. De los resultados de estos trabajos se ha encontrado que el afloramiento a lo largo de esta costa es un fenómeno frecuente durante los meses de primavera y verano, introduciendo Agua Central del Atlántico Norte en el interior de las rías. Sin embargo, en las rías gallegas se han caracterizado varios eventos de afloramiento durante otoño e invierno que indican que este proceso no es un fenómeno exclusivo de las estaciones de primavera y verano. En este estudio se hace una revisión de estos eventos teniendo en cuenta artículos ya publicados y también se analiza su recurrencia a lo largo de las costas oeste y norte de Galicia a partir de datos de índice de afloramiento de 1967 a 2009. El número medio de días por mes con condiciones favorables de afloramiento más elevado se observó durante los meses de primavera y verano en la costa oeste (18–26 días) y costa norte (12–14 días). Durante otoño e invierno este número de días fue menor (11–18 días, costa oeste; 8–10 días, costa norte) aunque no despreciable, indicando la posibilidad de observar eventos de afloramiento durante este periodo. De hecho, durante estos meses se observó una cierta probabilidad de obtener condiciones favorables de afloramiento a lo largo de ambas costas (26%), aunque la situación más probable correspondió a condiciones desfavorables (44%). Estos resultados revelaron que estos eventos no se pueden considerar como episodios aislados. De esto se deduce que los procesos de afloramiento en las rías deberían ser observados bajo condiciones favorables, tales como vientos predominantes del norte en la plataforma adyacente, independientemente de la estación.publishe

Hydrological and erosion response at micro-plot to -catchment scale following forest wildfire, north-central Portugal

Wildfires can have important impacts on hydrological and soil erosion processes, due to the destruction of vegetation cover and changes to soil properties. According to Shakesby and Doerr (2006), these wildfire effects are: i) much better known at small spatial scales (especially erosion plots) than at the scale of catchments; ii) much better studied with respect to overland flow and streamflow (and, then, especially peak discharges) than to soil erosion. Following up on a precursor project studying runoff generation and the associated soil losses from micro-plot to slope-scale in Portuguese eucalypt forests, the EROSFIRE-II project addresses the connectivity of these processes across hillslopes as well as within the channel network. This is done in the Colmeal study area in central Portugal, where the outlet of an entirely burnt catchment of roughly 10 ha was instrumented with a gauging station continuously recording water level and tubidity, and five slopes were each equipped with 4 runoff plots of < 0,5 m2 (“micro-plot”) and 4 slope-scale plots as well as 1 slope-scale sediment fence. Starting one month after the August 2008 wildfire, the plots were monitored at 1- to 2-weekly intervals, depending on the occurrence of rainfall. The gauging station became operational at the end of November 2008, since the in-situ construction of an H-flume required several weeks. A preliminary analysis of the data collected till the end of 2008, focusing on two slopes with contrasting slope lengths as well as the gauging station: revealed clear differences in runoff and erosion between: (i) the micro-plot and slope-scale plots on the same hillslope; (ii) the two slopes; (iii) an initial dry period and a subsequent much wetter period; (iv) the slopes and the catchment-scale, also depending on the sampling period. These results suggest that the different processes govern the hydrological and erosion response at different spatial scales as well as for different periods, with soil water repellency playing a role during the initial post-fire period. The current presentation will review these preliminary results based on the data collected during the first year after the wildfire

Runoff at the micro-plot and slope scale following wildfire, central Portugal

Through their effects on soil properties and vegetation/litter cover, wildfires can strongly enhance overland flow generation and accelerate soil erosion [1] and, thereby, negatively affect land-use sustainability as well as downstream aquatic and flood zones. Wildfires are a common phenomenon in present-day Portugal, devastating in an average year some 100.000 ha of forest and woodlands and in an exceptional year like 2003 over 400.000 ha. There therefore exists a clear need in Portugal for a tool that can provide guidance to post-fire land management by predicting soil erosion risk, on the one hand, and, on the other, the mitigation effectiveness of soil conservation measures. Such a tool has recently been developed for the Western U.S.A. [3: ERMiT] but its suitability for Portuguese forests will need to be corroborated by field observations. Testing the suitability of existing erosion models in recently burned forest areas in Portugal is, in a nutshell, the aim of the EROSFIRE projects. In the first EROSFIRE project the emphasis was on the prediction of erosion at the scale of individual hill slopes. In the ongoing EROSFIRE-II project the spatial scope is extended to include the catchment scale, so that also the connectivity between hill slopes as well as channel and road processes are being addressed. Besides ERMiT, the principal models under evaluation for slope-scale erosion prediction are: (i) the variant of USLE [4] applied by the Portuguese Water Institute after the wildfires of 2003; (ii) the Morgan–Morgan–Finney model (MMF) [5]; (iii) MEFIDIS [6]. From these models, MEFIDIS and perhaps MMF will, after successful calibration at the slope scale, also be applied for predicting catchment-scale sediment yields of extreme events

Runoff and erosion at the micro-plot and slope scale in a small burnt catchment, central Portugal

Wildfires can have important impacts on hydrological processes and soil erosion in forest catchments, due to the destruction of vegetation cover and changes to soil properties. However, the processes involved are non-linear and not fully understood. This has severely limited the understanding on the impacts of wildfires, especially in the up-scaling from hillslopes to catchments; in consequence, current models are poorly adapted for burnt forest conditions. The objective of this presentation is to give an overview of the hydrological response and sediment yield from the micro-plot to slope scale, in the first year following a wildfire (2008/2009) that burnt an entire catchment nearby the Colmeal village, central Portugal. The overview will focus on three slopes inside the catchment, with samples including: • Runoff at micro-plot scale (12 bounded plots) and slope scale (12 open plots); • Sediments and Organic Matter loss at micro-plot scale (12 bounded plots) and slope scale (12 open plots plus 3 Sediment fences); • Rainfall and Soil moisture data; • Soil Water Repellency and Ground Cover data. The analysis of the first year following the wildfire clearly shows the complexity of runoff generation and the associated sediment transport in recently burnt areas, with pronounced differences between hillslopes and across spatial scales as well as with marked variations through time. This work was performed in the framework of the EROSFIRE-II project (PTDC/AGR-CFL/70968/2006) which has as overall aim to predict soil erosion risk in recently burnt forest areas, including common post-fire forest management practices; the project focuses on the simultaneous measurement of runoff and soil erosion at multiple spatial scales.The results to be presented in this session are expected to show how sediment is generated, transported and exported in the Colmeal watershed; and contribute to understand and simulate erosion processes in burnt catchments, including for model development and evaluation

Coastal warming under climate change: global, faster and heterogeneous

The assessment of expected changes in coastal sea surface temperature (SST) on a global scale is becoming increasingly important due to the growing pressure on coastal ecosystems caused by climate change. To achieve this objective, 17 Global Climate Models from CMIP6 were used, with data from historical and hist-1950 experiments spanning 1982-2050. This analysis highlights significant warming of coastal areas worldwide, with higher and more variable rates of warming than observed in previous decades. All basins are projected to experience an increase in coastal SST near 1 °C by mid-century, with some regions exhibiting nearshore SST anomalies exceeding 2 °C for the period 2031-2050 relative to 1995-2014. Regarding the Eastern Upwelling Boundary Systems, only the Canary upwelling system and the southern part of the Humboldt upwelling system manage to show lower-than-average SST warming rates, maintaining, to a certain extent, their ability to buffer global warming.publishe