Gerard H. Roe

Controls on the channel width of rivers: Implications for modeling fluvial incision of bedrock

On the basis of the Manning equation and basic mass conser- vation principles, we derive an expression for scaling the steady- state width (W) of river channels as a function of discharge (Q), channel slope (S), roughness (n), and width-to-depth ratio (a): W 5 (a( a1 2) 2/3 ) 3/8 Q 3/8 S 23/16 n 3/8 . We propose that channel width-to- depth ratio, in addition to roughness, is a function of the material in which the channel is developed, and that where a river is con- fined to a given material, width-to-depth ratio and roughness can be assumed constant. Given these simplifications, the expression emulates traditional width-discharge relationships for rivers incis- ing bedrock with uniformly concave fluvial long profiles. More sig- nificantly, this relationship describes river width trends in terrain with spatially nonuniform rock uplift rates, where conventional discharge-based width scaling laws are inadequate. We suggest that much of observed channel width variability in river channels confined by bedrock is a simple consequence of the tendency for water to flow faster in steeper reaches and therefore occupy smaller channel cross sections. We demonstrate that using conventional scaling relationships for channel width can result in underestima- tion of stream-power variability in channels incising bedrock and that our model improves estimates of spatial patterns of bedrock incision rates.

Effects of orographic precipitation variations on the concavity of steady-state river profiles

The concavity, or curvature, of river profiles has long been taken to be a fundamental indicator of the underlying processes governing fluvial erosion, and thereby of landscape evolution. However, erosion laws have generally been derived without accounting for the strong orographically driven gradients in precipitation typically found in mountainous regions. In addition, field measurements have found discrepancies between the form of measured stream profiles and theoretically derived values. Introducing a simple physically based feedback, we find that orographically induced variations in precipitation strongly affect the curvature of steady-state river profiles. This feedback complicates efforts to infer the form of erosion laws from observed profile concavities, but could help explain discrepancies between observations and theory. Our results demonstrate a strong feedback through which climate influences the form of river profiles and show how such climatic effects act to limit the relief of unglaciated mountain ranges.

Time-Varying Climate Sensitivity from Regional Feedbacks

AbstractThe sensitivity of global climate with respect to forcing is generally described in terms of the global climate feedback—the global radiative response per degree of global annual mean surface temperature change. While the global climate feedback is often assumed to be constant, its value—diagnosed from global climate models—shows substantial time variation under transient warming. Here a reformulation of the global climate feedback in terms of its contributions from regional climate feedbacks is proposed, providing a clear physical insight into this behavior. Using (i) a state-of-the-art global climate model and (ii) a low-order energy balance model, it is shown that the global climate feedback is fundamentally linked to the geographic pattern of regional climate feedbacks and the geographic pattern of surface warming at any given time. Time variation of the global climate feedback arises naturally when the pattern of surface warming evolves, actuating feedbacks of different strengths in different...

A Mechanism for the High Rate of Sea Ice Thinning in the Arctic Ocean

Submarine measurements of sea ice draft show that the ice has thinned in some parts of the Arctic Ocean at a remarkably high rate over the past few decades. The spatial pattern indicates that the thinning was a strong function of ice thickness, with the greatest thinning occurring where the ice was initially thickest. A similar relationship between sea ice thinning and the initial thickness is reproduced individually by three global climate models in response to increased levels of carbon dioxide in the models’ atmosphere. All three models have weak trends in their surface winds and one model lacks ice dynamics altogether, implying that trends in the atmosphere or ice circulation are not necessary to produce a relatively high rate of thinning over the central Arctic or a thickness change that increases with the initial thickness. A general theory is developed to describe the thinning of sea ice subjected to climate perturbations, and it is found that the leading component of the thickness dependence of the thinning is due to the basic thermodynamics of sea ice. When perturbed, sea ice returns to its equilibrium thickness by adjusting its growth rate. The growth‐thickness relationship is stabilizing and hence can be reckoned as a negative feedback. The feedback is stronger for thinner ice, which is known to adjust more quickly to perturbations than thicker ice. In addition, thinner ice need not thin much to increase its growth rate a great deal, thereby establishing a new equilibrium with relatively little change in thickness. In contrast, thicker ice must thin much more. An analysis of a series of models, with physics ranging from very simple to highly complex, indicates that this growth‐thickness feedback is the key to explaining the models’ relatively high rate of thinning in the central Arctic compared to thinner ice in the subpolar seas.

Glacier Changes and Regional Climate: A Mass and Energy Balance Approach*

The mass balance of a glacier is a complex consequence of the combination of atmospheric variables that control it. However, the understanding of past, present, and future glacier states is often predicated on very simplified representations of the mass balance–climate relationship. Here, a full surface energy and mass balance (SEMB) model is developed to explore the relationship between glacier equilibrium-line altitudes (ELAs) and climate at a regional scale. This model is applied to central Asia because of the diverse climate regimes and glacier history. The model captures the pattern in ELAs well; the seasonal cycle in energy balance terms are comparable to studies on individual glaciers in central Asia, and the proportionality factor relating melt to temperature is within the range of those reported for individual glaciers within the area. In regions where precipitation is low, ablation at the ELA is dominated by sublimation. Conversely, where precipitation is high, ablation at the ELA is dominated by melt and surface runoff. In turn, the sensitivity of the ELA to changes in climate is strongly tied to the dominant ablation process. In particular, ELAs in melt-dominated regions are most sensitive to interannual variability in air temperature, while ELAs in sublimation-dominated regions are most sensitive to interannual variability in precipitation. Glaciers in sublimation-dominated regions are acutely sensitive to even small changes in atmospheric variables. Finally, changes in clouds are shown to be important in all regions through their influence on the shortwave and longwave radiative fluxes, which dominate the surface energy balance at the ELA.

Soil Thermal and Ecological Impacts of Rain on Snow Events in the Circumpolar Arctic

Rain on snow (ROS) events are rare in most parts of the circumpolar Arctic, but have been shown to have great impact on soil surface temperatures and serve as triggers for avalanches in the midlatitudes, and they have been implicated in catastrophic die-offs of ungulates. The study of ROS is inherently challenging due to the difficulty of both measuring rain and snow in the Arctic and representing ROS events in numerical weather predictions and climate models. In this paper these challenges are addressed, and the occurrence of these events is characterized across the Arctic. Incidents of ROS in Canadian meteorological station data and in the 40-yr ECMWF Re-Analysis (ERA-40) are compared to evaluate the suitability of these datasets for characterizing ROS. The ERA-40 adequately represents the large-scale synoptic fields of ROS, but too often has a tendency toward drizzle. Using the ERA-40, a climatology of ROS events is created for thresholds that impact ungulate populations and permafrost. It is found that ROS events with the potential to harm ungulate mammals are widespread, but the large events required to impact permafrost are limited to the coastal margins of Beringia and the island of Svalbard. The synoptic conditions that led to ROS events on Banks Island in October of 2003, which killed an estimated 20 000 musk oxen, and on Svalbard, which led to significant permafrost warming in December of 1995, are examined. Compositing analyses are used to show the prevailing synoptic conditions that lead to ROS in four disparate parts of the Arctic. Analysis of ROS in the daily output of a fully coupled GCM under a future climate change scenario finds an increase in the frequency and areal extent of these events for many parts of the Arctic over the next 50 yr and that expanded regions of permafrost become vulnerable to ROS.

The response of glaciers to intrinsic climate variability: observations and models of late-Holocene variations in the Pacific Northwest

Discriminating between glacier variations due to natural climate variability and those due to true climate change is crucial for the interpretation and attribution of past glacier changes, and for the expectations of future changes. We explore this issue for the well-documented glaciers of Mount Baker in the Cascades Mountains of Washington State, USA, using glacier histories, glacier modeling, weather data and numerical weather model output. We find that natural variability alone is capable of producing kilometer-scale excursions in glacier length on multi-decadal and centennial timescales. Such changes are similar in magnitude to those attributed to a global Little Ice Age. The null hypothesis, that no climate change is required to explain the glacier fluctuations in this setting, cannot be rejected. These results for Mount Baker glaciers are also consistent with an earlier study analyzing individual glaciers in Scandinavia and the Alps. The principle that long-timescale fluctuations of glacier length can be driven by short-timescale fluctuations in climate reflects a robust and fundamental property of stochastically forced physical systems with memory. It is very likely that this principle also applies to other Alpine glaciers and that it therefore complicates interpretations of the relationship between glacier and climate history. However, the amplitude and timescale of the length fluctuations depends on the details of the particular glacier geometry and climatic setting, and this remains largely unevaluated for most glaciers.

The Mutual Interaction between Continental-Scale Ice Sheets and Atmospheric Stationary Waves

The great continental ice sheets of the Pleistocene represented significant obstacles to the Northern Hemisphere midlatitude westerlies. They must therefore have forced large changes in the atmospheric circulation, and consequently also in the patterns of accumulation and melting over the ice sheets themselves. A simplified threedimensional coupled ice sheet‐stationary wave model is developed in order to understand the ice sheet’s response to the circulation changes that it induces. Consistent with ice age climate simulations, the ice sheet topography induces an anticyclonic circulation over the ice sheet, causing a slight warming over the western slopes and a stronger cooling over the remainder. The modeled feedbacks significantly affect the ice sheet configuration, with the most important influences being the patterns of summer temperature, and the topographically induced precipitation field. The time evolution of the ice sheet is also changed by the atmospheric feedbacks and the results suggest the possibility of multiple equilibrium solutions.

The Shape of Things to Come: Why Is Climate Change So Predictable?

The framework of feedback analysis is used to explore the controls on the shape of the probability distribution of global mean surface temperature response to climate forcing. It is shown that ocean heat uptake, which delays and damps the temperature rise, can be represented as a transient negative feedback. This transient negative feedback causes the transient climate change to have a narrower probability distribution than that of the equilibrium climate response (the climate sensitivity). In this sense, climate change is much more predictable than climate sensitivity. The width of the distribution grows gradually over time, a consequence of which is that the larger the climate change being contemplated, the greater the uncertainty is about when that change will be realized. Another consequenceof this slow growthis that furtherefforts to constrain climate sensitivity will be of very limited value for climate projections on societally relevant time scales. Finally, it is demonstrated that the effect on climate predictability of reducing uncertainty in the atmospheric feedbacks is greater than the effect of reducing uncertainty in ocean feedbacks by the same proportion. However, at least at the global scale, the total impact of uncertainty in climate feedbacks is dwarfed by the impact of uncertainty in climate forcing, which in turn is contingent on choices made about future anthropogenic emissions.

Assimilation of Time-Averaged Pseudoproxies for Climate Reconstruction

The efficacy of a novel ensemble data assimilation (DA) technique is examined in the climate field reconstruction (CFR) of surface temperature. A minimalistic, computationally inexpensive DA technique is employed that requires only a static ensemble of climatologically plausible states. Pseudoproxy experiments are performed with both general circulation model (GCM) and Twentieth Century Reanalysis (20CR) data byreconstructingsurfacetemperaturefieldsfromasparsenetworkofnoisypseudoproxies.TheDAapproach is compared to a conventional CFR approach based on principal component analysis (PCA) for experiments on global domains. DA outperforms PCA in reconstructing global-mean temperature in all experiments and is more consistent across experiments, with a range of time series correlations of 0.69‐0.94 compared to 0.19‐ 0.87 for the PCA method. DA improvements are even more evident in spatial reconstruction skill, especially in sparsely sampled pseudoproxy regions and for 20CR experiments. It is hypothesized that DA improves spatialreconstructionsbecauseitreliesoncoherent,spatiallylocaltemperaturepatterns,whichremainrobust even when glacial states are used to reconstruct nonglacial states and vice versa. These local relationships, as utilized by DA, appear to be more robust than the orthogonal patterns of variability utilized by PCA. Comparing results for GCM and 20CR data indicates that pseudoproxy experiments that rely solely on GCM data may give a false impression of reconstruction skill.