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Challenges in Predictability Science and Limits-to-Prediction for Hydrologic Systems

In this report, we derive challenges for predictability science examining knowledge gaps and operational needs. For each challenge we identify milestones to mark progress. Finally, we limit discussion to the subfield of hydrometeorology out of a practical necessity, with an implied relevance to the broader discipline of hydrology.

The coupled hydrometeorological predictability problem is chosen to show how a focused set of challenges in predictability science and “limits-to-prediction” research may be derived from current gaps in understanding and from the current operational needs. More importantly, milestones need to be defined for these challenges in order to guide progress in purposeful directions and establish two-way communications between the research and applications communities. Predictability and understanding the limits-to-prediction are, however, core issues in many specializations in hydrology such as ecohydrology, subsurface chemical fate and transport, etc. Advances in understanding predictability and using that knowledge to improve predictions benefits the nation in a wide range of applications (Box 3-1). The purpose of this section, however, is to focus on one of the predictability problems in hydrologic science—hydrometeorology—and in the process identify those structural issues that are common to diverse hydrologic science applications.

During the past century, many anomalous climate events



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Report of a Workshop on Predictability & Limits-to-Prediction in Hydrologic Systems 3 Challenges in Predictability Science and Limits-to-Prediction for Hydrologic Systems In this report, we derive challenges for predictability science examining knowledge gaps and operational needs. For each challenge we identify milestones to mark progress. Finally, we limit discussion to the subfield of hydrometeorology out of a practical necessity, with an implied relevance to the broader discipline of hydrology. The coupled hydrometeorological predictability problem is chosen to show how a focused set of challenges in predictability science and “limits-to-prediction” research may be derived from current gaps in understanding and from the current operational needs. More importantly, milestones need to be defined for these challenges in order to guide progress in purposeful directions and establish two-way communications between the research and applications communities. Predictability and understanding the limits-to-prediction are, however, core issues in many specializations in hydrology such as ecohydrology, subsurface chemical fate and transport, etc. Advances in understanding predictability and using that knowledge to improve predictions benefits the nation in a wide range of applications (Box 3-1). The purpose of this section, however, is to focus on one of the predictability problems in hydrologic science—hydrometeorology—and in the process identify those structural issues that are common to diverse hydrologic science applications. During the past century, many anomalous climate events

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Report of a Workshop on Predictability & Limits-to-Prediction in Hydrologic Systems Box 3-1 From Research to Operations Considerable operational and regulatory hydrology is based on predictive model output. Hydrologic models are essential tools used to characterize the benefits and costs of proposed private and public actions. Simulation models used in hydrology attempt to predict the movement of water, chemicals, and sediment across the landscape. In this respect there are a number of problems related to the setting—i.e., the natural and built landscape—that are common to all hydrologic models. These include underresolved processes (subgrid scale effects associated with discretization of processes that vary on a wide range of scales), incomplete chemical and biological parameterizations (shortcomings in characterizing and monitoring heterogeneous chemical, surface chemistry, and microbial processes in the environment), and lack of adequate sampling for model specification and initialization (failure of sparse monitoring networks to capture the true variations across the landscape). Each type of hydrologic model, nonetheless, has additional problems that are specific to its construct and application context. It is not feasible to perform a complete survey of research needs for all predictive hydrologic models and prediction applications in the various agencies engaged in these activities. Here we present three examples of application areas outside of hydrometeorology where research in predictability and limits-to-prediction may have practical impacts and may serve the nation by enhancing the capability of predicting environmental processes linked to the movement of water across the landscape. Erosion and Sediment Transport (USDA) Problem: We cannot currently predict, to even within orders of magnitude, how many tons of sediment leave a watershed in a year. Critical Issues: The critical issues include development of mechanistic models of erosion to replace empirical predictive models such as those based on the widely used “Universal Soil Loss Equa-

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Report of a Workshop on Predictability & Limits-to-Prediction in Hydrologic Systems tion” and development of models for sediment storage on the floodplain and resuspension and transport processes in the river. Watershed Rainfall–Runoff Transformation (NWS, USGS) Problem: We cannot currently predict the spatial pattern of watershed response to precipitation and cannot quantitatively describe the surface and subsurface contributions to streamflow with enough accuracy and consistency to be operationally useful. Critical Issues: Initial and boundary conditions are the critical issues. Watershed runoff and streamflow are affected by heterogeneity in soil hydraulic properties, landscape structural properties (e.g., hydrogeological layering, compaction of soil horizons, and soil organic content, roots, and pores), soil moisture profile, surface–subsurface interaction, interception by plants, snowpack, and storm properties. Although our understanding of individual processes is improving, the integration of that body of knowledge in spatially distributed predictive models has not been approached systematically. Groundwater Management in Irrigated Agriculture (USDA, USGS, BLM) Problem: We need to provide sufficient water for the crop plants and to minimize movement of harmful chemicals to the aquifer below. Critical Issues: We do not have reliable means to go from core or plot scale measurements of hydraulic properties to estimated field scale hydraulic pathways in predictive models. We need to replace empirical parameterizations of chemical and biological fate and transport in the environment with models based on the results of fundamental understanding in heterogeneous chemistry, surface chemistry, and microbiology.

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Report of a Workshop on Predictability & Limits-to-Prediction in Hydrologic Systems have disrupted American lives. Persistent droughts like those associated with the dust bowls of the 1930s and the recent drought of 1988 ruined Midwest crops and farmland. The Mississippi floods of 1927 and 1993 were equally devastating. Even larger regional climate variations may occur in the future, especially if the global climate is seriously influenced by the rise in concentrations of greenhouse gases, as some models and observations indicate. Increasing the extent to which such events can be predicted is an integral component of the World Climate Research Programme's (WCRP) Global Energy and Water Cycle Experiment (GEWEX) as well as the U.S. Gloabal Change Research Program (USGCRP) Water Cycle Plan, National Aeronautics and Space Administration’s Global Water and Energy Cycle (GWEC), and Natiohnal Oceanic and Atmospheric Administration’s Office of Global Program GEWEX Americas Prediction Project (GAPP) programs. CONCEPTUAL MODEL FOR MAKING PREDICTIONS The conceptual framework for hydrometeorological predictability is that of a coupled land–atmosphere–ocean system. At the largest time and space scales, the cycling of water over continental regions can be viewed as net inflow of water vapor to a particular basin, net transfer of water from the atmosphere to the surface by excess of precipitation over local evapotranspiration, and net river discharge from the basin, which over the long run must balance the net inflow of water vapor. On a continental scale, the rivers discharge into the oceans, and the oceans are net sources of atmospheric water, which is transported to the land regions. The fluxes and stored amounts of water vary greatly in space and time. Parts of these variations are regular, following the annual cycle of solar forcing in time and the physical controls of geography (topography, soil, and vegetation cover) in space. Superimposed upon these regular variations are the irregular fluctuations or changes caused by the chaotic dynamics of the land–atmosphere– ocean system. Such chaotic behavior is generated both internally in the basin and externally (e.g., by the general circulation of the atmosphere). Storage processes within soil and vegetation modu-

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Report of a Workshop on Predictability & Limits-to-Prediction in Hydrologic Systems late both the regular and the irregular variations in water and energy fluxes. During the workshop, Huug van den Dool reported on empirical studies that indicate the tendency toward persistence of summer droughts and that suggest early-season soil moisture anomalies as a contributing causal agent. Recent extreme hydroclimate events have provided a focal point for studies of land– atmosphere interactions, illustrating the complexity of the atmospheric response to surface anomalies. The heavy precipitation that caused record-breaking flooding within the Mississippi River basin in 1993 has been associated alternatively with high and low soil water anomalies in different areas. Physical processes invoked in the alternative explanations include (1) surface-heating effects on the boundary-layer capping inversion and associated suppression of deep convection, (2) influences of surface conditions on the low-level jet in the southern Great Plains. At the other hydroclimatic extreme, initially dry soil conditions in the Mississippi basin have been put forward as a possible cause of the 1988 summer drought. It appears that potential atmospheric predictability associated with land-surface anomalies could be especially significant during the warmer part of the year. During the workshop, Randy Koster summarized studies (using climate models) that indicate that land factors are contributors to seasonal precipitation variability under a set of conditions that favor strong land–atmosphere coupling. Outside of these circumstances, the variations in seasonal precipitation do not appear to be related to antecedent or concurrent conditions at the land surface. Remote influences, such as seasonal to interannual ocean temperature anomalies (e.g., El Niño-Southern Oscillation), probably outweigh any land influences during winter and could also be important in setting up the initial springtime land surface soil moisture anomalies. Similarly, Hong and Kalnay (2000) showed that the drought of 1998 over Oklahoma and Texas, once established in early spring by sea surface temperature (SST) anomalies and by favorable initial conditions, was maintained by local soil moisture positive feedback. However, the influence of all hydrologic anomalies (soil moisture,

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Report of a Workshop on Predictability & Limits-to-Prediction in Hydrologic Systems snow extent, soil freezing and thawing) on subsequent weather patterns and short-term climate predictions is still largely unknown. Observing, understanding, and modeling these coupled hydrometeorological processes through the full range of spatial and temporal scales are essential not only for developing long-range predictive capability, but also for developing basic understanding of the water cycle. During the workshop, Kevin Trenberth emphasized the synergy between models and observations and the water and energy cycles in addressing one of the key issues in global change research today: Is the hydrologic cycle changing? Three important unresolved issues are (1) whether the coupling between the land surface and the climate system is sufficiently strong so that knowledge of the land surface states will enhance prediction, (2) whether the accuracy and resolution of current and future remote sensing observations are sufficient to provide information useful for enhanced predictions, (3) and whether current coupled models are capable of simulating critical processes. In other words, if we can accurately observe initial land surface conditions, does this result in increased hydro-meteorological predictability? When and where is this predictability likely to be most important? Are present global and regional climate models capable of simulating and hence predicting coupled features, and where are the current limitations? The talks by Adam Schlosser and Dag Lohmann at the workshop illustrated the range of activities in the hydrometeorological research community that focus on these questions with a variety of approaches and atmospheric and land surface models. KEY UNRESOLVED ISSUES AND RESEARCH CHALLENGES Using predictability in the hydrometeorological system example as the context to introduce some key unresolved issues, five challenges are identified in predictability science and limits-to-prediction for hydrologic systems. Each is discussed below along with associated research milestones identified at the workshop.

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Report of a Workshop on Predictability & Limits-to-Prediction in Hydrologic Systems Separating the Predictable and the Unpredictable Although weather is not predictable beyond a few weeks because of its inherently nonlinear and chaotic nature, aspects of climate may be predictable for much longer because of the presence of low-frequency interannual variations such as El Niño, the Madden Julian Oscillation, and the Quasi-Biennial Oscillation. The term “potential predictability” is often used to define that part of the climate variations that exceeds weather noise. The idea is that the variance of seasonal precipitation is made up of a component reflecting daily weather (high-frequency random) variations, which are unpredictable beyond the deterministic predictability limits of about 2 weeks. The second component is any additional or multiplicative variance that is, at least, potentially predictable because of it links to physical systems with longer-range memory (e.g., oceans, continental soil moisture). The first component is considered noise and is estimated from a statistical model that is fitted from daily, within-season precipitation. Estimates of the climate noise are compared with the total variance, and where the total variance exceeds the estimated noise, one can conclude that there is a potential for long-range prediction. The separation of weather noise and climate signal should not be interpreted as simply the separation of the effects of initial and boundary conditions for the land–ocean–atmosphere system. During the workshop, Roger Pielke, Sr., presented a case example where the coupled hydrology/ecosystem and climate model evolves into different equilibria depending on the initial conditions. Thus, the slowly varying component of the system (the eco-system in this case) affects the system through both boundary and initial state effects. Similar signal and noise separation techniques are required for other applications in hydrology where predictability associated with persistence, local factors, and remote influences needs to be separated. The research milestones related to separating the predictable and the unpredictable include estimation of the time scales over which hydrologic variables can be predicted in the real world

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Report of a Workshop on Predictability & Limits-to-Prediction in Hydrologic Systems and determination of how well these time scales are simulated in modeling systems. Characterization of Subgrid Scale (SGS) Processes The massive development of computational resources has led to important advances in prediction methods and to a basic understanding of complex environmental phenomena. Nevertheless, the scale disparity intrinsic to linked hydrologic systems (e.g., land–atmosphere, surface–subsurface, water–ecosystems–biogeochemical, etc.) makes direct numerical simulation impossible. The systems contain variabilities on ranges of scales that are impossible to resolve on a common computational grid. As a result there remain fundamental issues in the formulation of computational models, especially in terms of the representation of subgrid scale (SGS) processes. In the workshop, Joe Tribbia introduced an example that demonstrated the effects of SGS parameterizations on error propagation in models and demonstrated how model-based estimates of limits-to-prediction are affected by the approach to representing SGS processes. The example of the sensitivity of atmospheric forecasts to the SGS representation of moist convection and the formation of precipitating clouds showed that model results are highly dependent on subtle and buried assumptions. Looking at model results using two different SGS parameterizations provides a useful diagnostic tool for identifying discrepancies owing to SGS processes. Very high-quality observations are needed to choose the better of the two methods or to improve them, as Dr. Tribbia showed in the case of a forecasted Gulf Coast storm event. SGS processes remain the Achilles heel of many prediction systems. They represent a limit to predictability (as defined in this report) brought about by the influence of processes with disparate scales. There are a number of other examples where SGS processes affect the behavior and skill of the parent model. These include the representation of atmospheric boundary layer and of its effects on the exchanges of moisture, heat, and biogeochemical substances between the surface and the atmosphere. The representation of pore scale to plot scale variability in soil characteristics

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Report of a Workshop on Predictability & Limits-to-Prediction in Hydrologic Systems has a large impact on the prediction of water movement near the surface. At even smaller scales, the molecular diffusion scale to pore scale characterization of soils significantly affects the prediction of large-scale contaminant plume migration in the subsurface. As demonstrated by Dr. Tribbia at the workshop, it is the availability of high-resolution and reliable observation data sets resulting from operational networks or field experiments that can identify discrepancies in predictions due to SGS processes. Research milestones related to the characterization of SGS processes include the following: development of systematic ways of defining the relevant scales for a problem and how to pose models of the right complexity designing experiments that explicitly help formulate models for unresolved scales use of a hierarchy of models with differing levels of complexity, and use of ensembles of model simulations that include uncertainty to explore predictability systematic investigation, quantification, and cross-comparison of model sensitivities in well-posed and well-directed intercomparison projects estimation of the degree to which the atmosphere, the land-surface processes, and the subsurface are coupled together in the real world, including determination of how the degree of coupling differs among modeling systems. Benefiting from the Synergy of Models and Measurements Data assimilation or the merging of models and data is the application of the set of mathematical techniques that provides physically consistent estimates of spatially distributed environmental variables. Inverse problems are closely related to data assimilation and share many features. Estimates from data assimilation are often based on merging scattered and/or indirect measurements of states and parameters with dynamic models that impose

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Report of a Workshop on Predictability & Limits-to-Prediction in Hydrologic Systems physical consistency constraints. In this respect data assimilation is an effective strategy for extracting value (or information) from measurements that may be incomplete or noisy by themselves but form effective constraints on models that can provide the connectivity in space and time in between measurements. Because of its joint use of observations and models, data assimilation can also provide efficient tools to capture the multiscale variations of spatial fields in hydrologic systems. A key consideration in data assimilation is that the models that provide the so-called background predictions and the systems that provide the same measurements are both uncertain. The role of data assimilation is to merge these two estimates based on their degree of uncertainty and produce a combined estimate that has desirable statistical properties (e.g., unbiased, minimum variance, etc.). Model calibration, which has a rich history in hydrology, is distinct from data assimilation in that the former is focused on the model and the latter on measurements and inference of the system state. More importantly, data assimilation is directed toward finding the errors of estimation given all the sources of uncertainty, whereas model calibration does not typically consider these uncertainties directly. The development of a data assimilation framework for hydrologic systems remains a major challenge (1) because of strong nonlinearities in the dynamic behavior of hydrologic systems, (2) because of involvement of diverse spatial scales in the determination of hydrologic events, and (3) because of a lack of reliable knowledge about the uncertainties of measurements and models. During the workshop, Baxter Vieux presented case examples of predictability research (basin runoff prediction) that show the need for developing the synergy provided by advanced models and intensive measurements. In order to benefit from the synergy of models and measurements both in the context of data assimilation and in general, it is necessary that models be physically based and well tested. Classic hydrologic models that have been optimized for use with point observations (such as precipitation and streamflow) are inadequate for extension to data assimilation which is distributed in space. What is needed are models and model components for hydrologic processes need to be developed that can work well with point as well as with mapped observations.

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Report of a Workshop on Predictability & Limits-to-Prediction in Hydrologic Systems Models must also follow predefined criteria for parameter parsimony and overall observability. Observability is a property of a system that is defined as the degree to which an increasing number of observations leads to diminishing uncertainty about the state of the system. Finally, it should be recognized that models for prediction and for assimilation applications may have significantly different requirements/characteristics. The requirements for models used in prediction and these for models used in assimilation need to be defined. Research milestones related to synergy between models and measurements include the following: improve the initial conditions (and thus take better advantage of predictability associated with information present in the initial conditions); allow efficient improvement of the models by comparison of short forecasts with the observations provide community data sets on regional hydrologic systems extend data assimilation systems to take advantage of emerging satellite data. Making the Observations that Accelerate Model Improvements Accurate, appropriate ground-based measurements of both the state of hydrologic reservoirs and fluxes between reservoirs are the single most critical factor that will drive advances in predictability and predictions. These critical areas illustrate compelling needs. First, distributed, well-designed networks that measure temperature, precipitation (rainfall and snowfall), snowpack, soil moisture, vegetation properties, radiation, wind, evaporative flux, and humidity will provide the foundation for improved predictions of water fluxes at or near the land surface. Precipitation is one of the key forcing factors of regional hydrologic systems. During the workshop, Witek Krajewski provided an overview of the current

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Report of a Workshop on Predictability & Limits-to-Prediction in Hydrologic Systems state of precipitation- monitoring systems and the prospects for the future enhancement of the networks. Though some capability is currently available in the United States and worldwide, to address each of these measurements, significant improvements will be required both nationally and internationally if we are to achieve advances in predictability of the water cycle at the land surface. Similarly, new measurement technology and network design are critically needed to improve the predictability and prediction of chemical fluxes, of transportation, and of impacts on terrestrial ecosystems and aquatic ecosystems in both inland and coastal waters. Finally, new measurements to characterize properties of the earth’s “critical zone” are sorely needed for both hydrologic science and integrative studies linking hydrology with other earth and environmental sciences. The critical zone is “the heterogeneous, near-surface environment in which complex interactions involving rock, soil, water, air and living organisms regulate the natural habitat and determine the availability of life-sustaining resources” (NRC, 2001a). Measurement networks must be well designed for emerging research and applications; they cannot simply be extensions of existing networks. Designs that served the predictive tools of past decades may not be the most appropriate for integrating ground-based and remotely sensed measurements for the predictive tools we will have available in the coming decades. Better process understanding is the key benefit of intensive field campaigns and sustained research at long-term experimental sites. Although the hydrologic community can point to a number of successful field campaigns lasting from days to months, the availability of long-term experimental sites has been limited. Both the U.S. Geological Survey and the U.S. Agricultural Research Service have well-established small-scale research catchments and have a long-term commitment to maintaining them as research sites. However, these only address hydrologic and biogeochemical issues at scales of a few meters to a few kilometers. The National Science Foundation’s Long-Term Ecological Research (LTER) program is also a resource for understanding processes in the critical zone at scales of a few kilometers to tens of kilometers. Efforts such as NASA’s and NOAA’s Continental-Scale International Experiment (GCIP) and GEWEX America Prediction Project (GAPP)

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Report of a Workshop on Predictability & Limits-to-Prediction in Hydrologic Systems efforts have addressed important hydrologic issues at the regional to continental scale. However, there is currently a critical need for sustained investigations at these larger scales as well as at smaller scales. During the workshop, Vijay Gupta stressed that sustained, long-term regionally representative ground-based measurements in research basins can serve as a test bed for the testing of new scientific hypotheses and instruments. As hydrologic science develops further applications of remote sensing, requirements for ground-based network design are changing. For example, the current network of index sites for snow water equivalent may not be ideally located to provide ground data combined with snow-cover area from satellite remote sensing, to estimate basinwide snow water equivalence. Rather, a network of sites with greater topographic variability in siting may be more appropriate. Simulation and design studies with dense measurements from research basins can be used to evaluate tradeoffs and demonstrate data value. Research milestones related to making observations that accelerate modeling progress include the following: development of benchmarks for monitoring systems, and implementation of special initiatives in algorithm development and assessment of new technologies estimates of uncertainty associated with observations made at different scales and using different measurement technologies improvement of access to existing data development of a multiagency definition of hydrologic data requirements, development of strategies for coordinated observations, and development of effective mechanisms for data sharing and dissemination estimation of evaporation and recharge on scales that allow linking the subsurface, surface, and atmospheric hydrologic systems use and promotion of paleo/proxy data for insights on long-term variations.

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Report of a Workshop on Predictability & Limits-to-Prediction in Hydrologic Systems Measuring Predictability Designing metrics for quantifying limits-to-prediction is a major challenge. During the workshop, Upmanu Lall provided a lecture on the state of the art in quantifying predictability and pointed out some of the more promising future pathways. He showed that past efforts aimed at quantitatively determining predictability in hydrologic systems have been based either on idealized systems of dynamic equations or on mechanistically and/or numerically refined model studies believed to be representative of the “true” system. In both cases, the approach has been to quantify predictability intrinsic to the system by employing analogs that enable the use of methods such as those of nonlinear dynamics (e.g., Lyapunov exponents and information theoretic/entropy) and/or statistical comparison of model forecasts with observations (e.g., threat scores and root mean squared errors). However, we are still unable to adequately deal with many predictability measure issues critical to hydrology. In the workshop, Efi Foufoula-Georgiou used the example of Quantitative Precipitation Forecast (QPF) to demonstrate the difficulties in defining robust and reliable measures for limits-to-prediction. These difficulties mostly have to do with the range of scales over which hydrologic processes vary and with the intermittency in some of the variables. Traditional metrics such as root mean squared error or threat scores to often fail to adequately capture the accuracy of predictions. Metrics that increase the understanding of the various kinds of predictability and that help to characterize memories, pathways, and feedback in hydrologic systems are needed. Further, persistence effects need to be distinguished from other factors that lead to predictability (e.g., remote influences and feedback mechanisms). One approach that can address the above issues is to define a probabilistic framework that includes the concept of a combined stochastic-deterministic error and allows for its quantification. Such a framework would permit the development of numerical optimization strategies such as adaptive mesh refinement and data assimilation that are consistent with the level of accuracy justified by the available data.

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Report of a Workshop on Predictability & Limits-to-Prediction in Hydrologic Systems During the workshop, Roger Ghanem presented one such framework. The framework maintains that a predicted variable has multiple sources of error. There are computation-related errors that can be controlled by refining the numerical approximations. There are parameter uncertainty errors that can be controlled through refining a probabilistic approach to model parameters. There are also initialization and boundary specification errors that can be controlled through refining the measurements used in prediction models. Finally, there are model structure errors that can be refined through improvements in understanding the modeled processes. The challenge is to develop techniques for separating these errors and controlling them individually. As yet, the hydrologic science community has no commonly agreed-upon or widely used techniques for evaluating forecast skill that are robust with respect to other factors such as persistence and intermittency. For hydrologists, a great remaining research challenge is to properly design tools and techniques so that the predictability and limits of prediction in hydrologic systems can be better quantified. These measures need to be defined in the context of specific forecast quantities and spatial and temporal scales. Research milestones related to measuring predictability include the following: definition of robust measures of limits-to-prediction that account for scale and inter-mittency issues and that are capable of distinguishing persistence effects introduction of methods to infer predictability and limits-to-prediction from observa-tional data sets.