Local polynomial method for ensemble forecast of time series

We present a nonparametric approach based on local polynomial regression for ensemble forecast of time series. The state space is first reconstructed by embedding the univariate time series of the response variable in a space of dimension (<i>D</i>) with a delay time (&tau;). To obtain a forecast from a given time point <i>t</i>, three steps are involved: (i) the current state of the system is mapped on to the state space, known as the feature vector, (ii) a small number (<i>K</i>=&alpha;*<i>n</i>, &alpha;=fraction (0,1] of the data, <i>n</i>=data length) of neighbors (and their future evolution) to the feature vector are identified in the state space, and (iii) a polynomial of order <i>p</i> is fitted to the identified neighbors, which is then used for prediction. A suite of parameter combinations (<i>D</i>, &tau;, &alpha;, <i>p</i>) is selected based on an objective criterion, called the Generalized Cross Validation (GCV). All of the selected parameter combinations are then used to issue a T-step iterated forecast starting from the current time <i>t</i>, thus generating an ensemble forecast which can be used to obtain the forecast probability density function (PDF). The ensemble approach improves upon the traditional method of providing a single mean forecast by providing the forecast uncertainty. Further, for short noisy data it can provide better forecasts. We demonstrate the utility of this approach on two synthetic (Henon and Lorenz attractors) and two real data sets (Great Salt Lake bi-weekly volume and NINO3 index). This framework can also be used to forecast a vector of response variables based on a vector of predictors

Local polynomial method for ensemble forecast of time series

International audienceWe present a nonparametric approach based on local polynomial regression for ensemble forecast of time series. The state space is first reconstructed by embedding the univariate time series of the response variable in a space of dimension (D) with a delay time (?). To obtain a forecast from a given time point t, three steps are involved: (i) the current state of the system is mapped on to the state space, known as the feature vector, (ii) a small number (K=?*n, ?=fraction (0,1] of the data, n=data length) of neighbors (and their future evolution) to the feature vector are identified in the state space, and (iii) a polynomial of order p is fitted to the identified neighbors, which is then used for prediction. A suite of parameter combinations (D, ?, ?, p) is selected based on an objective criterion, called the Generalized Cross Validation (GCV). All of the selected parameter combinations are then used to issue a T-step iterated forecast starting from the current time t, thus generating an ensemble forecast which can be used to obtain the forecast probability density function (PDF). The ensemble approach improves upon the traditional method of providing a single mean forecast by providing the forecast uncertainty. Further, for short noisy data it can provide better forecasts. We demonstrate the utility of this approach on two synthetic (Henon and Lorenz attractors) and two real data sets (Great Salt Lake bi-weekly volume and NINO3 index). This framework can also be used to forecast a vector of response variables based on a vector of predictors

Changes in the Seasonality of Precipitation over the Contiguous USA

Consequences of possible changes in annual total precipitation are dictated, in part, by the timing of precipitation events and changes therein. Herein, we investigated historical changes in precipitation seasonality over the US using observed station precipitation records to compute a standard seasonality index (SI) and the day of year on which certain percentiles of the annual total precipitation were achieved (percentile day of year). The mean SI from the majority of stations exhibited no difference in 1971–2000 relative to 30-year periods earlier in the century. However, analysis of the day of year on which certain percentiles of annual total precipitation were achieved indicated spatially coherent patterns of change. In some regions, the mean day of the year on which the 50th percentile of annual precipitation was achieved differed by 20–30 days between 1971–2000 and both 1911–1940 and 1941–1970. Output from the 10-Atmosphere-Ocean General Circulation Models (AOGCM) simulations of 1971–2000, 2046–2065, and 2081–2100 was used to determine whether AOGCMs are capable of representing the seasonal distribution of precipitation and to examine possible future changes. Many of the AOGCMs qualitatively captured spatial patterns of seasonality during 1971–2000, but there was considerable divergence between AOGCMs in terms of future changes. In both the west and southeast, 7 of 10 AOGCMs indicated later attainment of the 50th percentile accumulation in 2047–2065, implying a possible reversal of the twentieth-century tendency toward relative increases in precipitation receipt during winter and early spring over the southeast. However, this is also a region characterized by considerable interannual variability in the percentile day of year during the historical period

Seasonal flows of international British Columbia-Alaska rivers: The nonlinear influence of ocean-atmosphere circulation patterns

The northern portion of the Pacific coastal temperate rainforest (PCTR) is one of the least anthropogenically modified regions on earth and remains in many respects a frontier area to science. Rivers crossing the northern PCTR, which is also an international boundary region between British Columbia, Canada and Alaska, USA, deliver large freshwater and biogeochemical fluxes to the Gulf of Alaska and establish linkages between coastal and continental ecosystems. We evaluate interannual flow variability in three transboundary PCTR watersheds in response to El Niño-Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO), Arctic Oscillation (AO), and North Pacific Gyre Oscillation (NPGO). Historical hydroclimatic datasets from both Canada and the USA are analyzed using an up-to-date methodological suite accommodating both seasonally transient and highly nonlinear teleconnections. We find that streamflow teleconnections occur over particular seasonal windows reflecting the intersection of specific atmospheric and terrestrial hydrologic processes. The strongest signal is a snowmelt-driven flow timing shift resulting from ENSO- and PDO-associated temperature anomalies. Autumn rainfall runoff is also modulated by these climate modes, and a glacier-mediated teleconnection contributes to a late-summer ENSO-flow association. Teleconnections between AO and freshet flows reflect corresponding temperature and precipitation anomalies. A coherent NPGO signal is not clearly evident in streamflow. Linear and monotonically nonlinear teleconnections were widely identified, with less evidence for the parabolic effects that can play an important role elsewhere. The streamflow teleconnections did not vary greatly between hydrometric stations, presumably reflecting broad similarities in watershed characteristics. These results establish a regional foundation for both transboundary water management and studies of long-term hydroclimatic and environmental change

Secure Routing-Based Energy Optimization for IoT Application with Heterogeneous Wireless Sensor Networks

Wireless sensor networks (WSNs) and the Internet of Things (IoT) are increasingly making an impact in a wide range of domain-specific applications. In IoT-integrated WSNs, nodes generally function with limited battery units and, hence, energy efficiency is considered as the main design challenge. For homogeneous WSNs, several routing techniques based on clusters are available, but only a few of them are focused on energy-efficient heterogeneous WSNs (HWSNs). However, security provisioning in end-to-end communication is the main design challenge in HWSNs. This research work presents an energy optimizing secure routing scheme for IoT application in heterogeneous WSNs. In our proposed scheme, secure routing is established for confidential data of the IoT through sensor nodes with heterogeneous energy using the multipath link routing protocol (MLRP). After establishing the secure routing, the energy and network lifetime is improved using the hybrid-based TEEN (H-TEEN) protocol, which also has load balancing capacity. Furthermore, the data storage capacity is improved using the ubiquitous data storage protocol (U-DSP). This routing protocol has been implemented and compared with two other existing routing protocols, and it shows an improvement in performance parameters such as throughput, energy efficiency, end-to-end delay, network lifetime and data storage capacity