Abstract. 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 (E p ) and precipitation (P ). For this purpose we use three dimensionless and dependent quantities: = E/P , = E p /P and = E/E p . 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 and in humid environments, owing to the unfeasibility of E p /P = 0 when E/E p → 1. Using data from 146 sub-catchments in the Amazon River basin we overcome this inconsistency by proposing a physically consistent power law: = k e , with k = 0.66, and e = 0.83 (R 2 = 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 . 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 interannual 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.

In this study, we validate precipitation estimates remotely sensed by the Tropical Rainfall Measuring Mission (TRMM) at monthly and seasonal timescales, during the period 1998-2015, by calculating and analyzing diverse error metrics between the 3B43 V7 product and in situ measurements from 1,180 rain gauges over Colombia, of which at least 987 are fully independent of TRMM. We explore the existence of spatiotemporal patterns to assess the performance of 3B43 V7 over the five major natural regions of Colombia: Caribbean, Pacific, Andes, Orinoco and Amazon. The results show that 3B43 V7 product is able to capture the phase of the annual cycle of monthly mean precipitation, but the performance is not good for the amplitude, in particular over the Andes and Pacific regions owing to complex climatic and topographic conditions. In general, 3B43 V7 exhibits good performance in the low-lying and plain Amazon, Orinoco and Caribbean regions. Over the Andes region, characterized by complex topography, overestimation errors are identified [root mean squared error (RMSE) ≥83.59 mm•month −1 and relative bias (BIAS) ≥4.69%], whereas the extremely wet rainfall regime of the Pacific region is largely underestimated (RMSE ≥253.52 mm •month −1 and BIAS ≤−11.75%). These errors are greater during the wet seasons when the metrics reach worse scores than those reported in similar studies worldwide. Occurrence analyses showed that 3B43 V7 misses very frequent light rainfall events and less frequent but very heavy storms, which contribute to the overall underestimation (overestimation) observed over the Pacific (Andes) region. The error characteristics identified and quantified in this study confirm the well-documented limitations of remote precipitation sensing and constitute a warning about major challenges that complex climatic and physiographic features can impose on satellite rainfall missions.

Abstract. Atmospheric rivers (ARs) are filaments of extensive water vapor transport in the lower troposphere, that play a crucial role in the distribution of water, but can also cause natural and economical damage by facilitating heavy rainfall. Here, we investigate the large-scale spatio-temporal synchronization patterns of heavy rainfall over the western coast and the continental regions of North America (NA), during the period from 1979 to 2018. In particular, we utilize event synchronization and a complex network approach incorporating varying delays to examine the temporal evolution of spatial patterns of heavy rainfall events in the aftermath of land-falling ARs. For that, we employ the SIO-R1 catalog of ARs that land-fall over the western coast of NA, categorized in terms of strength and persistence on an AR-intensity scale which varies from category 1 to 5, along with daily rainfall estimates from the ERA5 reanalysis with 0.25° spatial resolution. Our analysis reveals a cascade of synchronized heavy rainfall events, triggered by ARs of category 3 or higher: in the first 3 days after the first day of an AR strike, rainfall events 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 heavy rainfall there. Furthermore, we assess the robustness of our findings by studying an additional AR detection method. Finally, analyzing the anomalies of integrated water vapor transport, geopotential height, upper-level meridional wind, and rainfall, we find atmospheric circulation patterns that are consistent with the spatio-temporal evolution of the synchronized heavy rainfall events. Understanding and revealing the effects of ARs in the rainfall patterns over NA will lead to better anticipating the evolution of the climate dynamics of the region in the context of a changing climate.

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<p>Atmospheric rivers (ARs) are filaments of extensive water vapor transport in the lower troposphere. They play a crucial role in the global water cycle and are a main source of fresh water for the mid-latitudes. However, very intense and persistent ARs are important triggers of heavy rainfall events and have been associated with natural and economical damage. Further motivated by their high impacts, in the last decade occurrences of ARs have been intensively studied, detection algorithms have been developed, and multiple AR catalogs have been produced. As a common approach, the detection of ARs is based on localizing anomalous atmospheric transport of moisture, usually by setting an absolute threshold on vertically integrated vapor transport (IVT) and/or vertically integrated water vapor (IWV) fields. Behind this methodology, there is the implicit assumption of stationary atmospheric moisture levels, which is not necessarily true for long periods under the context of a warming atmosphere. Also, these thresholds have proven to vary regionally which results in often excluded low-level ARs.</p> <p>Here, we introduce <em>AR-tracks</em>, a global, high-resolution catalog of atmospheric rivers that we have developed based on the Image-Processing-based Atmospheric River Tracking (IPART) algorithm, using IVT estimates of the ERA5 reanalysis data set. As opposed to conventional detection methods, IPART calculates anomalies of the IVT field at the synoptical spatiotemporal scale of ARs and is, therefore, free from magnitude thresholds and stationarity assumptions. The resulting catalog displays a list of AR events, with a spatial resolution of 0.75° x 0.75° and a temporal resolution of 6 hours, covering the period between 1979 and 2019. For each AR, we provide common parameters such as the time and location of the landfall, the respective IVT value, the area, the width, and the length of the AR. Moreover, we also track the contour and the axis of each AR, the position of the centroid, and the proportion of the AR that is located over ocean and land, and over the different continents.</p> <p>To show the potential of this new catalog, we study the spatiotemporal variability of European ARs between 1979-2019, analyzing the robustness of our results for distinct parameter choices in the definition of <em>AR-tracks.</em> We also use a novel power spectral measure to identify periodic cycles in the occurrence of European ARs, revealing spatially heterogeneous seasonal and multi-annual periodicities. Finally, we discuss the role of land-falling ARs as a trigger of heavy precipitation events in the regional domain.</p> <p>With the extensive data we provide in this new catalog, we aim at contributing to the further understanding of the role of ARs in global climate dynamics, as long-lived ARs having cross-continent tracks can be reliably traced through their tropical/subtropical origins to high-latitude landfall, and novel topics such as inland penetration of ARs can be studied.</p>

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.

Abstract. 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.

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