Upmanu Lall

A Nearest Neighbor Bootstrap For Resampling Hydrologic Time Series

A nonparametric method for resampling scalar or vector-valued time series is introduced. Multivariate nearest neighbor probability density estimation provides the basis for the resampling scheme developed. The motivation for this work comes from a desire to preserve the dependence structure of the time series while bootstrapping (resampling it with replacement). The method is data driven and is preferred where the investigator is uncomfortable with prior assumptions as to the form (e.g., linear or nonlinear) of dependence and the form of the probability density function (e.g., Gaussian). Such prior assumptions are often made in an ad hoc manner for analyzing hydrologic data. Connections of the nearest neighbor bootstrap to Markov processes as well as its utility in a general Monte Carlo setting are discussed. Applications to resampling monthly streamflow and some synthetic data are presented. The method is shown to be effective with time series generated by linear and nonlinear autoregressive models. The utility of the method for resampling monthly streamflow sequences with asymmetric and bimodal marginal probability densities is also demonstrated.

Streamflow simulation: A nonparametric approach

In this paper kernel estimates of the joint and conditional probability density functions are used to generate synthetic streamflow sequences. Streamflow is assumed to be a Markov process with time dependence characterized by a multivariate probability density function. Kernel methods are used to estimate this multivariate density function. Simulation proceeds by sequentially resampling from the conditional density function derived from the kernel estimate of the underlying multivariate probability density function. This is a nonparametric method for the synthesis of streamflow that is data-driven and avoids prior assumptions as to the form of dependence (e.g., linear or nonlinear) and the form of the probability density functions (e.g., Gaussian). We show, using synthetic examples with known underlying models, that the nonparametric method presented is more flexible than the conventional models used in stochastic hydrology and is capable of reproducing both linear and nonlinear dependence. The effectiveness of this model is illustrated through its application to simulation of monthly streamflow from the Beaver River in Utah.

Floods in a changing climate: Does the past represent the future?

Hydrologists have traditionally assumed that the annual maximum flood process at a location is independent and identically distributed. While nonstationarities in the flood process due to land use changes have long been recognized, it is only recently becoming clear that structured interannual, interdecadal, and longer time variations in planetary climate impart the temporal structure to the flood frequency process at flood control system design and operation timescales. The influence of anthropogenic climate change on the nature of floods is also an issue of societal concern. Here we focus on (1) a diagnosis of variations in the frequency of floods that are synchronous with low-frequency climate state and (2) an exploration of limiting flood probability distributions implied by a long simulation of a model of the El Nino/Southern Oscillation. Implications for flood risk analysis are discussed.

Categorical Climate Forecasts through Regularization and Optimal Combination of Multiple GCM Ensembles

Abstract A Bayesian methodology is used to assess the information content of categorical, probabilistic forecasts of specific variables derived from a general circulation model (GCM) forecast ensemble, and to combine a “prior” forecast (climatological probabilities of each category) with a categorical probabilistic forecast derived from a GCM ensemble to develop posterior, or “regularized” categorical probabilities. The combination algorithm assigns a weight to a particular model forecast and to climatology. The ratio of the sample likelihood of the model based on the posterior categorical probabilities, to that based on climatological probabilities, computed over the period of record of historical forecasts, provides a measure of the skill or information content of a candidate model. The weight given to a GCM forecast serves as a secondary indicator of its information content. Model weights are determined by maximizing the likelihood ratio. Results using the so-called ranked probability skill score as an...

Spatiotemporal variability of ENSO and SST teleconnections to summer drought over the United States during the twentieth century

Presented are investigations into the spatial structure of teleconnections between both the winter El Nino- Southern Oscillation (ENSO) and global sea surface temperatures (SSTs), and a measure of continental U.S. summer drought during the twentieth century. Potential nonlinearities and nonstationarities in the relationships are noted. During the first three decades of this century, summer drought teleconnections in response to SST patterns linked to ENSO are found to be strongest in the southern regions of Texas, with extensions into regions of the Midwest. From the 1930s through the 1950s, the drought teleconnection pattern is found to extend into southern Arizona. The most recent three decades show weak teleconnections between summer drought over southern Texas and Arizona, and winter SSTs, which is consistent with previous findings. Instead, the response to Pacific SSTs shows a clear shift to the western United States and southern regions of California. These epochal variations are consistent with epochal variations observed in ENSO and other low-frequency climate indicators. This changing teleconnection response complicates statistical forecasting of drought.

Improved combination of multiple atmospheric GCM ensembles for seasonal prediction

Abstract An improved Bayesian optimal weighting scheme is developed and used to combine six atmospheric general circulation model (GCM) seasonal hindcast ensembles. The approach is based on the prior belief that the forecast probabilities of tercile-category precipitation and near-surface temperature are equal to the climatological ones. The six GCMs are integrated over the 1950–97 period with observed monthly SST prescribed at the lower boundary, with 9–24 ensemble members. The weights of the individual models are determined by maximizing the log likelihood of the combination by season over the integration period. A key ingredient of the scheme is the climatological equal-odds forecast, which is included as one of the “models” in the multimodel combination. Simulation skill is quantified in terms of the cross-validated ranked probability skill score (RPSS) for the three-category probabilistic hindcasts. The individual GCM ensembles, simple poolings of three and six models, and the optimally combined mult...

Disaggregation procedures for stochastic hydrology based on nonparametric density estimation

Synthetic simulation of streamflow sequences is important for the analysis of water supply reliability. Disaggregation models are an important component of the stochastic streamflow generation methodology. They provide the ability to simulate multiseason and multisite streamflow sequences that preserve statistical properties at multiple timescales or space scales. In recent papers we have suggested the use of nonparametric methods for streamflow simulation. These methods provide the capability to model time series dependence without a priori assumptions as to the probability distribution of streamflow. They remain faithful to the data and can approximate linear or nonlinear dependence. In this paper we extend the use of nonparametric methods to disaggregation models. We show how a kernel density estimate of the joint distribution of disaggregate flow variables can form the basis for conditional simulation based on an input aggregate flow variable. This methodology preserves summability of the disaggregate flows to the input aggregate flow. We show through applications to synthetic data and streamflow from the San Juan River in New Mexico how this conditional simulation procedure preserves a variety of statistical attributes.

Probabilistic Multimodel Regional Temperature Change Projections

Abstract Regional temperature change projections for the twenty-first century are generated using a multimodel ensemble of atmosphere–ocean general circulation models. The models are assigned coefficients jointly, using a Bayesian linear model fitted to regional observations and simulations of the climate of the twentieth century. Probability models with varying degrees of complexity are explored, and a selection is made based on Bayesian deviance statistics, coefficient properties, and a classical cross-validation measure utilizing temporally averaged data. The model selected is shown to be superior in predictive skill to a naive model consisting of the unweighted mean of the underlying atmosphere–ocean GCM (AOGCM) simulations, although the skill differential varies regionally. Temperature projections for the A2 and B1 scenarios from the Intergovernmental Panel on Climate Change (IPCC) Special Report on Emissions Scenarios are presented.

A Nonparametric Wet/Dry Spell Model for Resampling Daily Precipitation

A nonparametric wet/dry spell model is developed for resampling daily precipitation at a site. The model considers alternating sequences of wet and dry days in a given season of the year. All marginal, joint, and conditional probability densities of interest (e.g., dry spell length, wet spell length, precipitation amount, and wet spell length given prior to dry spell length) are estimated nonparametrically using at-site data and kernel probability density estimators. Procedures for the disaggregation of wet spell precipitation into daily precipitation and for the generation of synthetic sequences are proffered. An application of the model for generating synthetic precipitation traces at a site in Utah is presented.

Anomalous ENSO Occurrences: An Alternate View*

There has been an apparent increase in the frequency and duration of El Nino-Southern Oscillation events in the last two decades relative to the prior period of record. Furthermore, 1990-95 was the longest period of sustained high Darwin sea level pressure in the instrumental record. Variations in the frequency and duration of such events are of considerable interest because of their implications for understanding global climatic variability and also the possibility that the climate system may be changing due to external factors such as the increased concentration of greenhouse gases in the atmosphere. Nonparametric statistical methods for time series analysis are applied to a 1882 to 1995 seasonal Darwin sea level pressure (DSLP) anomaly time series to explore the variations in El Nino-like anomaly occurrence and persistence over the period of record. Return periods for the duration of the 1990-95 event are estimated to be considerably smaller than those recently obtained by Trenberth and Hoar using a linear ARMA model with the same time series. The likelihood of a positive anomaly of the DSLP, as well as its persistence, is found to exhibit decadal- to centennial-scale variability and was nearly as high at the end of the last century as it has been recently. The 1990-95 event has a much lower return period if the analysis is based on the 1882-1921 DSLP data. The authors suggest that conclusions that the 1990-95 event may be an effect of greenhouse gas-induced warming be tempered by a recognition of the natural variability in the system.