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Predictability Science: Definitions

During the workshop, three types of predictability and limits to prediction were identified. The first two follow from classical definitions and the third one introduced in this workshop is a particularly relevant addition for hydrologic systems.

Predictability of the first kind is associated with information present in the initial conditions. Its importance can be assessed by the extent to which the predictions are sensitive to the initial conditions. For example quantitative precipitation forecasts (QPF) remain major challenges for the community. Various approaches to QPF are each characterized by varying performances at different lead times and aggregation levels. A complete QPF system will re-quire not only a systematic framework for the merging forecasts from various approaches but also deeper insight into precipitation, severe weather, and runoff processes that ultimately produce floods, which are the most costly (in terms of human life and property) realization of weather hazard in many places including the U.S. Sensitivity to initial conditions is also charac-teristic of many other hydrologic systems (e.g., surface-subsurface processes, integrated eco-logical-hydrologic systems) that involve coupled processes where two-way linkages result in feedbacks that can amplify errors in initialization.

Predictability of the second kind is associated with information present in the boundary conditions. Its importance can be assessed by the extent to which predictions are sensitive to these boundary conditions. For example there are known local



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Report of a Workshop on Predictability & Limits-to-Prediction in Hydrologic Systems 2 Predictability Science: Definitions During the workshop, three types of predictability and limits to prediction were identified. The first two follow from classical definitions and the third one introduced in this workshop is a particularly relevant addition for hydrologic systems. Predictability of the first kind is associated with information present in the initial conditions. Its importance can be assessed by the extent to which the predictions are sensitive to the initial conditions. For example quantitative precipitation forecasts (QPF) remain major challenges for the community. Various approaches to QPF are each characterized by varying performances at different lead times and aggregation levels. A complete QPF system will re-quire not only a systematic framework for the merging forecasts from various approaches but also deeper insight into precipitation, severe weather, and runoff processes that ultimately produce floods, which are the most costly (in terms of human life and property) realization of weather hazard in many places including the U.S. Sensitivity to initial conditions is also charac-teristic of many other hydrologic systems (e.g., surface-subsurface processes, integrated eco-logical-hydrologic systems) that involve coupled processes where two-way linkages result in feedbacks that can amplify errors in initialization. Predictability of the second kind is associated with information present in the boundary conditions. Its importance can be assessed by the extent to which predictions are sensitive to these boundary conditions. For example there are known local

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Report of a Workshop on Predictability & Limits-to-Prediction in Hydrologic Systems and remote factors (such as ocean surface temperatures) that affect variability in regional precipitation on intraseasonal to interannual time scales. Conditioning long-lead predictions on slower evolving states of the climate system has been shown to only partially reduce the uncertainty of forecasts. There is growing demand for long-lead predictions that reduce the risk associated with climate-sensitive activities. Robust operational prediction systems that may meet this demand are built on the basic understanding of how local and remote factors contribute to the total hydrologic variability. Increasingly ensembles forecasts are used to identify the bound on the uncertainty associated with error-prone parameters and inputs. Examples of needed basic research in this area include 1) increasing the reproducibility of ensemble models, 2) developing statistically representative ensemble members based on randomized inputs, and 3) developing ensembles of cases from each in an ensemble of models. Hydrologic systems contain heterogeneous geological, topographic, and ecological fea-tures that vary on multiple scales. The pervasive nature of nonlinear scale interactions in hydrological systems was introduced in the Workshop as a third source of predictability (or, in most cases, loss of predictability). Predictability of the third kind asserts that the effective response of systems at larger scales is not completely determined by scaling local processes (e.g., scaling up from small scales to larger scales is not a linear process). In hydrologic science heterogeneity is a rule and it cannot necessarily be fully captured by randomization of parameters. Interactions among microscale features often lead to effects that are not completely represented in macroscale predictions based on effective parameters for microscale models. Examples include enhanced surface flux due to land-breeze circulations over heterogeneous patches, on regional recharge and discharge patterns over complex terrain. There are processes and conditions when the effective parameter approach to scaling may be feasible. In the remaining circumstances the macroscale and microscale predictive relations for hydrologic processes may have different functional forms and dependencies. Furthermore, there may be organizing principles at work that result in simple procedures for statistically relating variables across a wide range of scales in the hydrologic

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Report of a Workshop on Predictability & Limits-to-Prediction in Hydrologic Systems system. These scale considerations affect limits to prediction in hydrologic systems and they place in question traditional ideas in hydrologic predictions. For example, spatial and temporal averages are not necessarily more predictable as traditionally believed if the averaging covers a scale that contains a strong transition or change in behavior (analogous to a bifurcation in dynamic systems).