David E. Rupp

Time scale and intensity dependency in multiplicative cascades for temporal rainfall disaggregation

[1] Multiplicative random cascades (MRCs) can parsimoniously generate highly intermittent patterns similar to those in rainfall. The elemental MRC model parameter is the cascade weight, which determines how rainfall at one scale is partitioned at the next smallest scale in the cascade. While it is known that the probability density of these weights may vary with both time scale and rainfall intensity, nearly all previous studies have considered either time scale or intensity separately. We examined the simultaneous dependency of the weights on both factors and assessed the impacts of explicitly including these dependencies in the MRC model. On the basis of the observed relationships between cascade weights and time scale and intensity, four progressively more “dependent” models were constructed to disaggregate a long time series of daily rainfall to hourly intervals. We found that inclusion of the intensity dependency on the model parameters that generate dry intervals greatly improved performance. For the relatively small range of time scales over which the rainfall was disaggregated, varying model parameters with time scale resulted in minor improvement.

A unified approach for process-based hydrologic modeling: 1. Modeling concept

This work advances a unified approach to process-based hydrologic modeling to enable controlled and systematic evaluation of multiple model representations (hypotheses) of hydrologic processes and scaling behavior. Our approach, which we term the Structure for Unifying Multiple Modeling Alternatives (SUMMA), formulates a general set of conservation equations, providing the flexibility to experiment with different spatial representations, different flux parameterizations, different model parameter values, and different time stepping schemes. In this paper, we introduce the general approach used in SUMMA, detailing the spatial organization and model simplifications, and how different representations of multiple physical processes can be combined within a single modeling framework. We discuss how SUMMA can be used to systematically pursue the method of multiple working hypotheses in hydrology. In particular, we discuss how SUMMA can help tackle major hydrologic modeling challenges, including defining the appropriate complexity of a model, selecting among competing flux parameterizations, representing spatial variability across a hierarchy of scales, identifying potential improvements in computational efficiency and numerical accuracy as part of the numerical solver, and improving understanding of the various sources of model uncertainty.

Seasonal Climate Variability and Change in the Pacific Northwest of the United States

Observed changes in climate of the U.S. Pacific Northwest since the early twentieth century were examined using four different datasets. Annual mean temperature increased by approximately 0.68‐0.88C from 1901 to 2012, with corroborating indicators including a lengthened freeze-free season, increased temperature of the coldest night of the year, and increased growing-season potential evapotranspiration. Seasonal temperature trends over shorter time scales (,50yr) were variable. Despite increased warming rates in most seasons over the last half century, nonsignificant cooling was observed during spring from 1980 to 2012. Observations show a long-term increase in spring precipitation; however, decreased summer and autumn precipitation and increased potential evapotranspiration have resultedin larger climatic water deficits over the past four decades. A bootstrapped multiple linear regression model was used to better resolve the temporal heterogeneity of seasonal temperature and precipitation trends and to apportion trends to internal climate variability, solar variability, volcanic aerosols, and anthropogenic forcing. The El Ni~ Oscillation and the Pacific‐ North American pattern were the primary modulators of seasonal temperature trends on multidecadal time scales: solar and volcanic forcing were nonsignificant predictors and contributed weakly to observed trends. Anthropogenic forcing was a significant predictor of, and the leading contributor to, long-term warming; natural factors alone fail to explain the observed warming. Conversely, poor model skill for seasonal precipitationsuggeststhatotherfactorsneedtobeconsideredtounderstandthesourcesofseasonalprecipitation trends.

A unified approach for process-based hydrologic modeling: 2. Model implementation and case studies

This work advances a unified approach to process-based hydrologic modeling, which we term the “Structure for Unifying Multiple Modeling Alternatives (SUMMA).” The modeling framework, introduced in the companion paper, uses a general set of conservation equations with flexibility in the choice of process parameterizations (closure relationships) and spatial architecture. This second paper specifies the model equations and their spatial approximations, describes the hydrologic and biophysical process parameterizations currently supported within the framework, and illustrates how the framework can be used in conjunction with multivariate observations to identify model improvements and future research and data needs. The case studies illustrate the use of SUMMA to select among competing modeling approaches based on both observed data and theoretical considerations. Specific examples of preferable modeling approaches include the use of physiological methods to estimate stomatal resistance, careful specification of the shape of the within-canopy and below-canopy wind profile, explicitly accounting for dust concentrations within the snowpack, and explicitly representing distributed lateral flow processes. Results also demonstrate that changes in parameter values can make as much or more difference to the model predictions than changes in the process representation. This emphasizes that improvements in model fidelity require a sagacious choice of both process parameterizations and model parameters. In conclusion, we envisage that SUMMA can facilitate ongoing model development efforts, the diagnosis and correction of model structural errors, and improved characterization of model uncertainty.

Drainage of a horizontal Boussinesq aquifer with a power law hydraulic conductivity profile

[1] Solutions to the Boussinesq equation describing drainage into a fully penetrating channel have been used for aquifer characterization. Two analytical solutions exist for early- and late-time drainage from a saturated,homogeneous, and horizontal aquifer following instantaneous drawdown. The solutions for discharge Q can be expressed as dQ/dt = -aQ b , where a is constant and b takes on the value 3 and 3/2 for early and late time, respectively. Though many factors can contribute to departures from the two predictions, we explore the effect of having permeability decrease with depth, as it is known that many natural soils exhibit this characteristic. We derive a new set of analytical solutions to the Boussinesq equation for k oc z n , where k is the saturated hydraulic conductivity, z is the height above an impermeable base, and n is a constant. The solutions reveal that in early time, b retains the value of 3 regardless of the value of n, while in late time, b ranges from 3/2 to 2 as n varies from 0 to oo. Similar to discharge, water table height h in late time can be expressed as dh/dt = -ch d , where d = 2 for constant k and d → oo as n → ∞. In theory, inclusion of a power law k profile does not complicate aquifer parameter estimation because n can be solved for when fitting b to the late-time data, whereas previously b was assumed to be 3/2. However, if either early- or late-time data are missing, there is an additional unknown. Under appropriate conditions, water table height measurements can be used to solve for an unknown parameter.

Detection and Attribution of Observed Changes in Northern Hemisphere Spring Snow Cover

Significant declines in spring Northern Hemisphere (NH) snow cover extent (SCE) have been observed over the last five decades. As one step toward understanding the causes of this decline, an optimal fingerprinting technique is used to look for consistency in the temporal pattern of spring NH SCE between observations and simulations from 15 global climate models (GCMs) that form part of phase 5 of the Coupled Model Intercomparison Project.The authors examinedsimulationsfrom 15 GCMsthat includedboth natural and anthropogenic forcing and simulations from 7 GCMs that included only natural forcing. The decline in observed NH SCE could be largely explained by the combined natural and anthropogenic forcing but not by natural forcing alone. However, the 15 GCMs, taken as a whole, underpredicted the combined forcing response by a factor of 2. How much of this underprediction was due to underrepresentation of the sensitivity to external forcing of the GCMs or to their underrepresentation of internal variability has yet to be determined.

Perspectives on the causes of exceptionally low 2015 snowpack in the western United States

Augmenting previous papers about the exceptional 2011-15 California drought, we offer new perspectives on the ‘snow drought’ that extended into Oregon in 2014 and Washington in 2015. Over 80% of measurement sites west of 115°W experienced record low snowpack in 2015, and we estimate a return period of 400-1000 years for Californias snowpack under the questionable assumption of stationarity. Hydrologic modeling supports the conclusion that 2015 was the most severe on record by a wide margin. Using a crowd-sourced superensemble of regional climate model simulations, we show that both human influence and sea surface temperature anomalies contributed strongly to the risk of snow drought in Oregon and Washington: the contribution of SST anomalies was about twice that of human influence. By contrast, SSTs and humans appear to have played a smaller role in creating Californias snow drought. In all three states, the anthropogenic effect on temperature exacerbated the snow drought.

Selecting climate change scenarios using impact‐relevant sensitivities

Climate impact studies often require the selection of a small number of climate scenarios. Ideally, a subset would have simulations that both (1) appropriately represent the range of possible futures for the variable/s most important to the impact under investigation and (2) come from global climate models (GCMs) that provide plausible results for future climate in the region of interest. We demonstrate an approach to select a subset of GCMs that incorporates both concepts and provides insights into the range of climate impacts. To represent how an ecosystem process responds to projected future changes, we methodically sample, using a simple sensitivity analysis, how an ecosystem variable responds locally to projected regional temperature and precipitation changes. We illustrate our approach in the Pacific Northwest, focusing on (a) changes in streamflow magnitudes in critical seasons for water management and (b) changes in annual vegetation carbon.

Superensemble Regional Climate Modeling for the Western United States

AbstractComputing resources donated by volunteers have generated the first superensemble of regional climate model results, in which the Hadley Centre Regional Model, version 3P (HadRM3P), and Hadley Centre Atmosphere Model, version 3P (HadAM3P), were implemented for the western United States at 25-km resolution. Over 136,000 valid and complete 1-yr runs have been generated to date: about 126,000 for 1960–2009 using observed sea surface temperatures (SSTs) and 10,000 for 2030–49 using projected SSTs from a global model simulation. Ensemble members differ in initial conditions, model physics, and (potentially, for future runs) SSTs. This unprecedented confluence of high spatial resolution and large ensemble size allows high signal-to-noise ratio and more robust estimates of uncertainty. This paper describes the experiment, compares model output with observations, shows select results for climate change simulations, and gives examples of the strength of the large ensemble size.

Late‐time drainage from a sloping Boussinesq aquifer

Numerical solutions to the nonlinear Boussinesq equation, applied to a steeply sloping aquifer and assuming uniform hydraulic conductivity, indicate that late-time recession discharge decreases nearly linearly in time. When recession discharge is characterized by −dQ/dt = aQb, this is equivalent to constant dQ/dt or b = 0. This result suggests that a previously reported exponential decrease with time (b = 1) of modeled recession discharge from a similar sloping aquifer represented by the same equation appears to be an artifact of the numerical solution scheme and its interpretation. Because the linearly decreasing recession discharge (b = 0) is not known from field studies, these findings challenge the application of a nonlinear Boussinesq framework assuming uniform conductivity and geometric similarity to infer hydraulic properties of sloping aquifers from observations of streamflow. This finding also questions the validity of the physical interpretation of the exponential decline in late time resulting from the commonly used linearized form of the Boussinesq equation, opposed to the full nonlinear equation, when applied under these conditions. For this reason, application of the linearized equation to infer hydraulic properties of sloping aquifers is also challenged, even if the observed recession is consistent with that of the linearized Boussinesq equation.