ALBERT

Description: This paper studies a 3-D generalization of Budyko's framework designed to capture the mutual interdependence among long-term mean actual evapotranspiration (E), potential evapotranspiration (Ep) and precipitation (P). For this purpose we use three dimensionless and dependent quantities: Ψ = E/P, Φ = Ep/P and Ω = E/Ep. This 3-D space and its 2-D projections provide an interesting setting to test the physical soundness of Budyko's hypothesis. We demonstrate analytically that Budyko-type equations are unable to capture the physical limit of the relation between Ω and Φ in humid environments, owing to the unfeasibility of Ep/P → 0 at E/Ep = 1. Using data from 146 sub-catchments in the Amazon River basin we overcome this inconsistency by proposing a physically consistent power law: Ψ = k Φe, with k = 0.66, and e = 0.83 (R2 = 0.93). This power law is compared with two other Budyko-type equations. Taking into account the goodness of fits and the ability to comply with the physical limits of the 3-D space, our results show that the power law is better suited to model the coupled water and energy balances within the Amazon River basin. Moreover, k is found to be related to the partitioning of energy via evapotranspiration in terms of Ω. This suggests that our power law implicitly incorporates the complementary relationship of evapotranspiration into the Budyko curve, which is a consequence of the dependent nature of the studied variables within our 3-D space. This scaling approach is also consistent with the asymmetrical nature of the complementary relationship of evapotranspiration. Looking for a physical explanation for the parameters k and e, the inter-annual variability of individual catchments is studied. Evidence of space–time symmetry in Amazonia emerges, since both between-catchment and between-year variability follow the same Budyko curves. Finally, signs of co-evolution of catchments are explored by linking spatial patterns of the power law parameters with fundamental characteristics of the Amazon River basin. In general, k and e are found to be related to vegetation, topography and water in soils.

Description: This paper studies a 3-D state space representation of Budyko's framework designed to capture the mutual interdependence among long-term mean actual evapotranspiration (E), potential evapotranspiration (Ep) and precipitation (P). For this purpose we use three dimensionless and dependent quantities: Ψ  =  E ⁄ P, Φ  =  Ep ⁄ P and Ω  =  E ⁄ Ep. This 3-D space and its 2-D projections provide an interesting setting to test the physical soundness of Budyko's hypothesis. We demonstrate analytically that Budyko-type equations are unable to capture the physical limit of the relation between Ω and Φ in humid environments, owing to the unfeasibility of Ep ⁄ P  =  0 when E ⁄ Ep  →  1. Using data from 146 sub-catchments in the Amazon River basin we overcome this inconsistency by proposing a physically consistent power law: Ψ  =  kΦe, with k  =  0.66, and e  =  0.83 (R2  =  0.93). This power law is compared with two other Budyko-type equations. Taking into account the goodness of fits and the ability to comply with the physical limits of the 3-D space, our results show that the power law is better suited to model the coupled water and energy balances within the Amazon River basin. Moreover, k is found to be related to the partitioning of energy via evapotranspiration in terms of Ω. This suggests that our power law implicitly incorporates the complementary relationship of evapotranspiration into the Budyko curve, which is a consequence of the dependent nature of the studied variables within our 3-D space. This scaling approach is also consistent with the asymmetrical nature of the complementary relationship of evapotranspiration. Looking for a physical explanation for the parameters k and e, the inter-annual variability of individual catchments is studied. Evidence of space–time symmetry in Amazonia emerges, since both between-catchment and between-year variability follow the same Budyko curves. Finally, signs of co-evolution of catchments are explored by linking spatial patterns of the power law parameters with fundamental characteristics of the Amazon River basin. In general, k and e are found to be related to vegetation, topography and water in soils.

Description: We derive and solve a linear stochastic model for the evolution of discharge and runoff in an order-one watershed. The system is forced by a statistically stationary compound Poisson process of instantaneous rainfall events. The relevant time scales are hourly or larger, and for large times, we show that the discharge approaches a limiting invariant distribution. Hence any of its properties are with regard to a rainfall-runoff system in hydrological equilibrium. We give an explicit formula for the Laplace transform of the invariant density of discharge in terms of the catchment area, the residence times of water in the channel and the hillslopes, and the mean frequency and the probability distribution of rainfall inputs. As a study case, we consider a watershed under a stationary rainfall regime in the tropical Andes of Colombia and test the probability distribution predicted by the model against the corresponding seasonal statistics. A mathematical analysis of the invariant distribution is performed yielding formulas for the invariant moments of discharge in terms of those of the rainfall. The asymptotic behavior of the probabilities of extreme discharge events is explicitly derived for heavy-tailed and light-tailed families of distributions of rainfall inputs. The scaling structure of discharge is asymptotically characterized in terms of the parameters of the model and under the assumption of wide sense scaling for the precipitation amounts and the inverse of the residence time in the channel. Our results give insights into the conversion of uncertainty inherent to the rainfall-runoff dynamics and the roles played by different geophysical variables, with the ratio between the mean frequency of rainfall events to the residence time along the hillslopes largely determining the qualitative properties of the distribution of discharge.

Description: Atmospheric rivers (ARs) are filaments of extensive water vapor transport in the lower troposphere that play a crucial role in the distribution of freshwater but can also cause natural and economic damage by facilitating heavy precipitation. Here, we investigate the large-scale spatiotemporal synchronization patterns of heavy precipitation events (HPEs) over the western coast and the continental regions of North America (NA), during the period from 1979 to 2018. In particular, we use event synchronization and a complex network approach incorporating varying delays to examine the temporal evolution of spatial patterns of HPEs in the aftermath of land-falling ARs. For that, we employ the SIO-R1 catalog of ARs that landfall on the western coast of NA, ranked in terms of intensity and persistence on an AR-strength scale which varies from level AR1 to AR5, along with daily precipitation estimates from ERA5 with a 0.25∘ spatial resolution. Our analysis reveals a cascade of synchronized HPEs, triggered by ARs of level AR3 or higher. On the first 3 d after an AR makes landfall, HPEs mostly occur and synchronize along the western coast of NA. In the subsequent days, moisture can be transported to central and eastern Canada and cause synchronized but delayed HPEs there. Furthermore, we confirm the robustness of our findings with an additional AR catalog based on a different AR detection method. Finally, analyzing the anomalies of integrated water vapor transport, geopotential height, upper-level meridional wind, and precipitation, we find atmospheric circulation patterns that are consistent with the spatiotemporal evolution of the synchronized HPEs. Revealing the role of ARs in the precipitation patterns over NA will lead to a better understanding of inland HPEs and the effects that changing climate dynamics will have on precipitation occurrence and consequent impacts in the context of a warming atmosphere.

Description: Characterized by their specific geometry, atmospheric rivers (ARs) are narrow, long, and transient channels of intensive water vapor transport in the lower troposphere. They play an essential role in the water supply for precipitation in the mid-latitudes but can also trigger natural hazards such as floods and landslides by facilitating heavy precipitation events. In this study, we link the occurrence of landslides in western North America (NA) during the past decades to the precipitation triggered by land-falling ARs hitting the western coastline of the region. For this, we use a landslide inventory, rainfall estimates with a daily temporal resolution, and a catalog of land-falling ARs characterized in terms of strength and persistence based on the AR scale by Ralph et al., 2019. We employ two attribution models to relate rainfall to ARs and then landslides to AR-induced rainfall. Our results show that ARs precede between 60% and 100% of the landslides reported along the western coast of North America. Intense and persistent ARs are the most common precursors. As a further analysis, we study the synchronization pattern of landslides and ARs to determine if their association is unique and significant. In the coastal regions, the precedence relation of ARs leading to landslides is statistically significant. Further inland, landslides are less likely, but those that do occur are significantly correlated with very intense and persistent ARs. Understanding and revealing the impacts of ARs on landslides in western North America will lead to better forecasts and risk assessments of these natural hazards.