Streamflow forecasting using functional regression

Streamflow, as a natural phenomenon, is continuous in time and so are the meteorological variables which influence its variability. In practice, it can be of interest to forecast the whole flow curve instead of points (daily or hourly). To this end, this paper introduces the functional linear models and adapts it to hydrological forecasting. More precisely, functional linear models are regression models based on curves instead of single values. They allow to consider the whole process instead of a limited number of time points or features. We apply these models to analyse the flow volume and the whole streamflow curve during a given period by using precipitations curves. The functional model is shown to lead to encouraging results. The potential of functional linear models to detect special features that would have been hard to see otherwise is pointed out. The functional model is also compared to the artificial neural network approach and the advantages and disadvantages of both models are discussed. Finally, future research directions involving the functional model in hydrology are presented

Flood frequency analysis at ungauged catchments with the GAM and MARS approaches in the Montreal region, Canada

Regional frequency analysis (RFA) aims to estimate quantiles of extreme hydrological variables (e.g. floods or low-flows) at sites where little or no hydrological data is available. This information is of interest for the optimal planning and management of water resources. A number of regional estimation models are evaluated and compared in this study and then used for regional estimation of flood quantiles at ungauged catchments located in the Montreal region in southern Quebec, Canada. In this study, two neighborhood approaches using canonical correlation analysis (CCA) and the region of influence (ROI) method are applied to delineate homogenous regions. Three regression methods namely log-linear regression model (LLRM), generalized additive models (GAM), and multivariate adaptive regression splines (MARS), recently introduced in the RFA context, are considered for regional estimation. These models are also applied considering all stations (ALL). The considered models, especially MARS, have never been used previously in a concrete application. Results indicate that MARS and GAM have comparable predictive performances, especially when applied with the whole dataset. Results also show that MARS used in combination with the CCA approach provide improved performances compared to all considered regional approaches. This may reflect the flexibility of the combination of these two approaches, their robustness, and their ability to better reproduce the hydrological phenomena, especially in real-world conditions when limited data are available

Historical and Projected Surface Temperature over India during the 20th and 21st century.

Surface Temperature (ST) over India has increased by ~0.055 K/decade during 1860-2005 and follows the global warming trend. Here, the natural and external forcings (e.g., natural and anthropogenic) responsible for ST variability are studied from Coupled Model Inter-comparison phase 5 (CMIP5) models during the 20th century and projections during the 21st century along with seasonal variability. Greenhouse Gases (GHG) and Land Use (LU) are the major factors that gave rise to warming during the 20th century. Anthropogenic Aerosols (AA) have slowed down the warming rate. The CMIP5 projection over India shows a sharp increase in ST under Representative Concentration Pathways (RCP) 8.5 where it reaches a maximum of 5 K by the end of the 21st century. Under RCP2.6 emission scenarios, ST increases up to the year 2050 and decreases afterwards. The seasonal variability of ST during the 21st century shows significant increase during summer. Analysis of rare heat and cold events for 2080-2099 relative to a base period of 1986-2006 under RCP8.5 scenarios reveals that both are likely to increase substantially. However, by controlling the regional AA and LU change in India, a reduction in further warming over India region might be achieved

A new look at weather-related health impacts through functional regression.

A major challenge of climate change adaptation is to assess the effect of changing weather on human health. In spite of an increasing literature on the weather-related health subject, many aspect of the relationship are not known, limiting the predictive power of epidemiologic models. The present paper proposes new models to improve the performances of the currently used ones. The proposed models are based on functional data analysis (FDA), a statistical framework dealing with continuous curves instead of scalar time series. The models are applied to the temperature-related cardiovascular mortality issue in Montreal. By making use of the whole information available, the proposed models improve the prediction of cardiovascular mortality according to temperature. In addition, results shed new lights on the relationship by quantifying physiological adaptation effects. These results, not found with classical model, illustrate the potential of FDA approaches

Data-Enhancement Strategies in Weather-Related Health Studies.

Although the relationship between weather and health is widely studied, there are still gaps in this knowledge. The present paper proposes data transformation as a way to address these gaps and discusses four different strategies designed to study particular aspects of a weather-health relationship, including (i) temporally aggregating the series, (ii) decomposing the different time scales of the data by empirical model decomposition, (iii) disaggregating the exposure series by considering the whole daily temperature curve as a single function, and (iv) considering the whole year of data as a single, continuous function. These four strategies allow studying non-conventional aspects of the mortality-temperature relationship by retrieving non-dominant time scale from data and allow to study the impact of the time of occurrence of particular event. A real-world case study of temperature-related cardiovascular mortality in the city of Montreal, Canada illustrates that these strategies can shed new lights on the relationship and outlines their strengths and weaknesses. A cross-validation comparison shows that the flexibility of functional regression used in strategies (iii) and (iv) allows a good fit of temperature-related mortality. These strategies can help understanding more accurately climate-related health

Aggregating the response in time series regression models, applied to weather-related cardiovascular mortality.

In environmental epidemiology studies, health response data (e.g. hospitalization or mortality) are often noisy because of hospital organization and other social factors. The noise in the data can hide the true signal related to the exposure. The signal can be unveiled by performing a temporal aggregation on health data and then using it as the response in regression analysis. From aggregated series, a general methodology is introduced to account for the particularities of an aggregated response in a regression setting. This methodology can be used with usually applied regression models in weather-related health studies, such as generalized additive models (GAM) and distributed lag nonlinear models (DLNM). In particular, the residuals are modelled using an autoregressive-moving average (ARMA) model to account for the temporal dependence. The proposed methodology is illustrated by modelling the influence of temperature on cardiovascular mortality in Canada. A comparison with classical DLNMs is provided and several aggregation methods are compared. Results show that there is an increase in the fit quality when the response is aggregated, and that the estimated relationship focuses more on the outcome over several days than the classical DLNM. More precisely, among various investigated aggregation schemes, it was found that an aggregation with an asymmetric Epanechnikov kernel is more suited for studying the temperature-mortality relationship

EMD-regression for modelling multi-scale relationships, and application to weather-related cardiovascular mortality.

In a number of environmental studies, relationships between nat4ural processes are often assessed through regression analyses, using time series data. Such data are often multi-scale and non-stationary, leading to a poor accuracy of the resulting regression models and therefore to results with moderate reliability. To deal with this issue, the present paper introduces the EMD-regression methodology consisting in applying the empirical mode decomposition (EMD) algorithm on data series and then using the resulting components in regression models. The proposed methodology presents a number of advantages. First, it accounts of the issues of non-stationarity associated to the data series. Second, this approach acts as a scan for the relationship between a response variable and the predictors at different time scales, providing new insights about this relationship. To illustrate the proposed methodology it is applied to study the relationship between weather and cardiovascular mortality in Montreal, Canada. The results shed new knowledge concerning the studied relationship. For instance, they show that the humidity can cause excess mortality at the monthly time scale, which is a scale not visible in classical models. A comparison is also conducted with state of the art methods which are the generalized additive models and distributed lag models, both widely used in weather-related health studies. The comparison shows that EMD-regression achieves better prediction performances and provides more details than classical models concerning the relationship

A cold-health watch and warning system, applied to the province of Quebec (Canada).

CONTEXT: A number of studies have shown that cold has an important impact on human health. However, almost no studies focused on cold warning systems to prevent those health effects. For Nordic regions, like the province of Quebec in Canada, winter is long and usually very cold with an observed increase in mortality and hospitalizations throughout the season. However, there is no existing system specifically designed to follow in real-time this mortality increase throughout the season and to alert public health authorities prior to cold waves. OBJECTIVE: The aim is to establish a watch and warning system specifically for health impacts of cold, applied to different climatic regions of the province of Quebec. METHODOLOGY: A methodology previously used to establish the health-heat warning system in Quebec is adapted to cold. The approach identifies cold weather indicators and establishes thresholds related to extreme over-mortality or over-hospitalization events in the province of Quebec, Canada. RESULTS AND CONCLUSION: The final health-related thresholds proposed are between (-15 °C, -23 °C) and (-20 °C, -29 °C) according to the climatic region for excesses of mortality, and between (-13 °C, -23 °C) and (-17 °C, -30 °C) for excesses of hospitalization. These results suggest that the system model has a high sensitivity and an acceptable number of false alarms. This could lead to the establishment of a cold-health watch and warning system with valid indicators and thresholds for each climatic region of Quebec. It can be seen as a complementary system to the existing one for heat warnings, in order to help the public health authorities to be well prepared during an extreme cold event

A heat-health watch and warning system with extended season and evolving thresholds.

BACKGROUND: Many countries have developed heat-health watch and warning systems (HHWWS) or early-warning systems to mitigate the health consequences of extreme heat events. HHWWS usually focuses on the four hottest months of the year and imposes the same threshold over these months. However, according to climate projections, the warm season is expected to extend and/or shift. Some studies demonstrated that health impacts of heat waves are more severe when the human body is not acclimatized to the heat. In order to adapt those systems to potential heat waves occurring outside the hottest months of the season, this study proposes specific health-based monthly heat indicators and thresholds over an extended season from April to October in the northern hemisphere. METHODS: The proposed approach, an adoption and extension of the HHWWS methodology currently implemented in Quebec (Canada). The latter is developed and applied to the Greater Montreal area (current population 4.3 million) based on historical health and meteorological data over the years. This approach consists of determining excess mortality episodes and then choosing monthly indicators and thresholds that may involve excess mortality. RESULTS: We obtain thresholds for the maximum and minimum temperature couple (in °C) that range from (respectively, 23 and 12) in April, to (32 and 21) in July and back to (25 and 13) in October. The resulting HHWWS is flexible, with health-related thresholds taking into account the seasonality and the monthly variability of temperatures over an extended summer season. CONCLUSIONS: This adaptive and more realistic system has the potential to prevent, by data-driven health alerts, heat-related mortality outside the typical July-August months of heat waves. The proposed methodology is general and can be applied to other regions and situations based on their characteristics

Heat-related mortality prediction using low-frequency climate oscillation indices: Case studies of the cities of Montréal and Québec, Canada

Background: Heat-related mortality is an increasingly important public health burden that is expected to worsen with climate change. In addition to long-term trends, there are also interannual variations in heat-related mortality that are of interest for efficient planning of health services. Large-scale climate patterns have an important influence on summer weather and therefore constitute important tools to understand and predict the variations in heat-related mortality. Methods: In this article, we propose to model summer heat-related mortality using seven climate indices through a two-stage analysis using data covering the period 1981–2018 in two metropolitan areas of the province of Québec (Canada): Montréal and Québec. In the first stage, heat attributable fractions are estimated through a time series regression design and distributed lag nonlinear specification. We consider different definitions of heat. In the second stage, estimated attributable fractions are predicted using climate index curves through a functional linear regression model. Results: Results indicate that the Atlantic Multidecadal Oscillation is the best predictor of heat-related mortality in both Montréal and Québec and that it can predict up to 20% of the interannual variability. Conclusion: We found evidence that one climate index is predictive of summer heat-related mortality. More research is needed with longer time series and in different spatial contexts. The proposed analysis and the results may nonetheless help public health authorities plan for future mortality related to summer heat