PMP and Climate Variability and Change: A Review

[EN] A state-of-the-art review on the probable maximum precipitation (PMP) as it relates to climate variability and change is presented. The review consists of an examination of the current practice and the various developments published in the literature. The focus is on relevant research where the effect of climate dynamics on the PMP are discussed, as well as statistical methods developed for estimating very large extreme precipitation including the PMP. The review includes interpretation of extreme events arising from the climate system, their physical mechanisms, and statistical properties, together with the effect of the uncertainty of several factors determining them, such as atmospheric moisture, its transport into storms and wind, and their future changes. These issues are examined as well as the underlying historical and proxy data. In addition, the procedures and guidelines established by some countries, states, and organizations for estimating the PMP are summarized. In doing so, attention was paid to whether the current guidelines and research published literature take into consideration the effects of the variability and change of climatic processes and the underlying uncertainties.The authors would like to acknowledge the support of the Global Water Futures Program and the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery Grant RGPIN-2019-06894). The fourth author acknowledges the support of the Spanish Ministry of Science and Innovation, Project TETISCHANGE (RTI2018-093717-B-100). The first author appreciates the continuous support from the Scott College of Engineering of Colorado State University.Salas, JD.; Anderson, ML.; Papalexiou, SM.; Francés, F. (2020). PMP and Climate Variability and Change: A Review. Journal of Hydrologic Engineering. 25(12):1-16. https://doi.org/10.1061/(ASCE)HE.1943-5584.0002003S1162512Abbs, D. J. (1999). 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The Perils of Regridding: Examples Using a Global Precipitation Dataset

Canada First Research Excellence Fund’s Global Water Futures program, the Natural Sciences and Engineering Research Council of Canada, the Canada Research Chairs program, and the Pacific Institute for Mathematical StudiesPeer ReviewedGridded precipitation datasets are used in many applications such as the analysis of climate variability/change and hydrological modeling. Regridding precipitation datasets is common for model coupling (e.g., coupling atmospheric and hydrological models) or comparing different models and datasets. However, regridding can considerably alter precipitation statistics. In this global analysis, the effects of regridding a precipitation dataset are emphasized using three regridding methods (first-order conservative, bilinear, and distance-weighted averaging). The differences between the original and regridded dataset are substantial and greatest at high quantiles. Differences of 46 and 0.13 mm are noted in high (0.95) and low (0.05) quantiles, respectively. The impacts of regridding vary spatially for land and oceanic regions; there are substantial differences at high quantiles in tropical land regions, and at low quantiles in polar regions. These impacts are approximately the same for different regridding methods. The differences increase with the size of the grid at higher quantiles and vice versa for low quantiles. As the grid resolution increases, the difference between original and regridded data declines, yet the shift size dominates for high quantiles for which the differences are higher. While regridding is often necessary to use gridded precipitation datasets, it should be used with great caution for fine resolutions (e.g., daily and subdaily), because it can severely alter the statistical properties of precipitation, specifically at high and low quantiles

Probabilistic Evaluation of Drought in CMIP6 Simulations

As droughts have widespread social and ecological impacts, it is critical to develop long-term adaptation and mitigation strategies to reduce drought vulnerability. Climate models are important in quantifying drought changes. Here, we assess the ability of 285 CMIP6 historical simulations, from 17 models, to reproduce drought duration and severity in three observational data sets using the Standardized Precipitation Index (SPI). We used summary statistics beyond the mean and standard deviation, and devised a novel probabilistic framework, based on the Hellinger distance, to quantify the difference between observed and simulated drought characteristics. Results show that many simulations have less than error in reproducing the observed drought summary statistics. The hypothesis that simulations and observations are described by the same distribution cannot be rejected for more than of the grids based on our distance framework. No single model stood out as demonstrating consistently better performance over large regions of the globe. The variance in drought statistics among the simulations is higher in the tropics compared to other latitudinal zones. Though the models capture the characteristics of dry spells well, there is considerable bias in low precipitation values. Good model performance in terms of SPI does not imply good performance in simulating low precipitation. Our study emphasizes the need to probabilistically evaluate climate model simulations in order to both pinpoint model weaknesses and identify a subset of best-performing models that are useful for impact assessments

Final Report developed under Contract #3000704047 for Natural Resources Canada

Natural Resources CanadaNon-Peer ReviewedIn the recent decades, precipitation patterns and corresponding streamflow responses in many cold regions catchments have changed considerably due to warming. Understanding historical changes and predicting future responses are of great importance for planning and management of water resources systems. Regional climate simulations using convention- permitting models are helpful in representing the fine-scale cloud and mesoscale processes, which are critical for understanding the physical mechanisms that cause in convective precipitation. From a hydrological perspective, these fine resolution simulations are helpful in understanding the runoff generation mechanisms, particularly for mountainous watersheds, which have high spatial variation in precipitation due to large differences in elevation over small distances. The sister-study of this report, the Bow River Basin Study (BRBS), used a physically based hydrological land surface scheme along with a water management model, coupled with a high resolution convention- permitting atmospheric regional model (Weather Research and Forecasting, WRF) to understand the streamflow generating mechanisms and identify the changes in streamflow responses of the Bow and Elbow River Basins. The coupled model appears to provide a large improvement in predictability, with minimal calibration of parameters and without bias correction of forcing from the atmospheric model. The model4 was able to provide reliable estimates of streamflows, despite the complex topography in the catchment. Using the WRF Pseudo Global Warming (PGW) scenario, estimated future streamflows simulated were then used to develop projected flow exceedance curves. The uncertainty in the simulations is extremely helpful in the risk assessment for downstream flood inundations. However, the uncertainty in streamflows cannot be assessed as the WRF- PGW dataset was only available for a single realization, because of the high computational cost. The research presented in this report focusses instead on using the highly efficient hydrological model developed and verified in BRBS whilst assessing uncertainty using another regional climate model, the CanRCM4, where many realizations are available for different boundary conditions. Since the CanRCM4 simulations have a relatively low resolution, a novel methodology was developed to adjust regional climate model outputs using the WRF-PGW data. An ensemble of 15 CanRCM4 simulations was used to force the Bow River basin model to determine a measure of the uncertainty in the simulated streamflows, and the projected streamflow exceedance probability curves. These curves are extremely useful for risk assessment for downstream flood inundations. Given the importance of understanding how much extreme precipitation will change in urban areas of the basin, where short duration high intensity events cause flash flooding, frequency analysis of these events was carried out for Calgary and Intensity Duration Frequency (IDF) curves were developed. A ready-to-use empirical form of IDF curve has been proposed from this analysis for the City of Calgary. The results from the WRF-PGW modelling indicated that future high flow, low frequency (exceedances less than 10%) streamflow events will decrease compared to those under the current climate condition by 4, 9 and 1.6 m3/s for the Bow River at Banff and Calgary and Elbow River at Sarcee Bridge respectively. The average of the 15 new CanRCM4-WRF-PGW results supports the above result with some greater decreases in streamflow of 9, 16 and 4 m3/s for Bow River at Banff and Calgary and Elbow River at Sarcee Bridge respectively. However, there were some CanRCM4-WRF-PGW realisations that suggested substantial increases in future low frequency streamflow from those indicated by the average CanRCM4- WRF-PGW-drive MESH model. The below average, high frequency (exceedances greater than 30%) future streamflows will increase modestly in all gauging locations by from 1 to 12.5 m3/s. The results of the extreme precipitation analysis at Calgary indicated an increase in future extreme precipitation events of all duration and return periods. On an average an increase of 1.5 times is noted for short return periods (=2, 5), and an increase of 4 times for long return periods (=500, 1000)

Πιθανοτικές κατανομές μέγιστης εντροπίας και στατιστική-στοχαστική μοντελοποίηση της βροχόπτωσης

188 σ.Εξετάζονται τρία κυρίως θέματα: (α) η δυνατότητα να χρησιμοποιηθεί μια θεωρητική αρχή, συγκεκριμένα η αρχή της μέγιστης εντροπίας, ως βάση για τη διαμόρφωση και την επιλογή πιθανοτικών κατανομών κατάλληλων για γεωφυσικές μεταβλητές και ειδικότερα για τη βροχόπτωση, (β) η πιθανοτική-στατιστική ανάλυση σε παγκόσμια κλίμακα της ημερήσιας βροχόπτωσης καθώς και της ακραίας ημερήσιας βροχόπτωσης και (γ) η στοχαστική δομή της ημερήσιας βροχόπτωσης σε πολύ μικρή χρονική κλίμακα. Βασικός στόχος της έρευνας είναι να διατυπώσει απλά αλλά θεμελιώδη και ευρέως ενδιαφέροντος ερωτήματα σχετικά με τη στατιστική-στοχαστική φύση της βροχόπτωσης και να δώσει απαντήσεις όχι μόνο θεωρητικής αλλά κυρίως πρακτικής αξίας. Σχετικά με την αρχή της μέγιστης εντροπίας, η έμφαση δίνεται στη διαμόρφωση και στη λογική και θεωρητική τεκμηρίωση απλών περιορισμών που σε συνδυασμό με τον κλασικό ορισμό της εντροπίας, δηλαδή αυτού των Boltzmann-Gibbs-Shannon, θα οδηγούν σε ευέλικτες και απλές κατανομές κατάλληλες για την πιθανοτική περιγραφή της βροχόπτωσης αλλά και άλλων γεωφυσικών μεταβλητών. Για τη στατιστική ανάλυση της ημερήσιας βροχόπτωσης, εξετάστηκαν τρεις διαφορετικές πτυχές της. Πρώτον, η εποχιακή διακύμανση της με επίκεντρο στις ιδιότητες της περιθώριας κατανομή της. Συγκεκριμένα εκπονήθηκε μια μαζική εμπειρική ανάλυση περισσότερων από 170 000 μηνιαίων δειγμάτων βροχόπτωσης σε περισσότερους από 14 000 σταθμούς σε όλο τον κόσμο με στόχο να απαντηθούν δύο βασικά ερωτήματα: (α) ποια στατιστικά χαρακτηριστικά της ημερήσιας βροχόπτωσης παρουσιάζουν τη μεγαλύτερη εποχιακή διακύμανση, και (β) κατά πόσον υπάρχει ή όχι ένα σχετικά απλό πιθανοτικό μοντέλο ικανό να περιγράψει τη θετική ημερήσια βροχόπτωση για κάθε μήνα και σε κάθε περιοχή του κόσμου. Δεύτερον, εξετάζεται η ουρά της κατανομής της ημερήσιας βροχόπτωσης, δηλαδή, το μέρος της κατανομής που περιγράφει τα ακραία γεγονότα. Αναλύθηκαν ακραίες βροχοπτώσεις σε περισσότερους από 15 000 σταθμούς και συγκρίθηκε η απόδοση τεσσάρων κοινών πιθανοτικών μοντέλων ουράς που αντιστοιχούν στις κατανομές Pareto, Weibull, Λογαριθμοκανονικής και Γάμα. Σκοπός ήταν να αποκαλυφθεί ποιος τύπος ουράς περιγράφει καλύτερα τη συμπεριφορά των ακραίων γεγονότων. Τρίτον, αναλύονται οι χρονοσειρές της ετήσιας μέγιστης ημερήσιας βροχόπτωσης σε περισσότερους από 15 000 σταθμούς με στόχο να απαντηθεί ίσως το βασικότερο ερώτημα της στατιστικής υδρολογίας, δηλαδή, ποια εκ των τριών κατανομών ακραίων τιμών περιγράφει καλύτερα τα ετήσια μέγιστα της ημερήσιας βροχόπτωσης. Τέλος, εξετάζονται οι στοχαστικές ιδιότητες της βροχόπτωσης σε λεπτή χρονική κλίμακα, μελετώντας ένα μοναδικό σύνολο δεδομένων που περιλαμβάνει μετρήσεις επτά επεισοδίων βροχόπτωσης με χρονική διακριτότητα 5-10 δευτερόλεπτων. Το ερώτημα που τίθεται και επιχειρείται να απαντηθεί είναι αν είναι δυνατόν ένα μοναδικό και απλό στοχαστικό μοντέλο να αναπαράγει τη μεγάλη στατιστική διαφοροποίηση που παρατηρήθηκε στα επεισόδια αυτά.Three main issues are examined: (a) the potential to use a theoretical principle, namely the principle of maximum entropy, as a basis for formulating and selecting probabilistic distributions suitable for geophysical variables and more specifically for rainfall, (b) the probabilistic-statistical analysis of daily rainfall and of extreme daily rainfall on a global scale, and (c) the stochastic structure of daily rainfall at fine temporal scales. The main goal of this research is to formulate simple yet fundamental and of wide interest questions, mainly regarding the statistical-stochastic nature of rainfall, and try to provide answers not only of theoretical but mostly of practical value. Regarding the principle of maximum entropy the emphasis is given on formulating and logically justifying simple constraints to be used along with the maximization of the classical definition of entropy, i.e., the Boltzmann-Gibbs-Shannon entropy, that will lead suitable probability distributions for rainfall, or more generally, for geophysical processes. Regarding the statistical analysis of daily rainfall, three different aspects are examined. First, the seasonal variation of daily rainfall is investigated focusing on the properties of its marginal distribution. A massive empirical analysis is performed of more than 170 000 monthly daily rainfall records from more than 14 000 stations from all over the globe aiming to answer two major questions: (a) which statistical characteristics of daily rainfall vary the most over the months and how much, and (b) whether or not there is a relatively simple probability model that can describe the nonzero daily rainfall at every month and every area of the world. Second, the distribution tail of daily rainfall is studied, i.e., the distribution’s part that describes the extreme events. More than 15 000 daily rainfall records are analysed in order to test the performance of four common distribution tails that correspond to the Pareto, the Weibull, the Lognormal and the Gamma distributions aiming to find out which of them better describes the behaviour of extreme events. Third, the annual maximum daily rainfall is analysed. The annual maxima time series from more than 15 000 stations from all over the world are extracted and examined in order to answer one of the most basic questions in statistical hydrology, i.e., which one of the three Extreme Value distributions better describes the annual maximum daily rainfall. Finally, regarding the stochastic properties of rainfall at fine temporal scales, a unique dataset, comprising measurements of seven storm events at a temporal resolution of 5-10 seconds, is studied. The question raised and attempted to be answered is if it is possible for a single and simple stochastic model to generate a plethora of temporal rainfall patterns, as well as to detect the major characteristics of such a model.Σίμων-Μιχαήλ Δ. Παπαλεξίο

A Cautionary Note on the Reproduction of Dependencies through Linear Stochastic Models with Non-Gaussian White Noise

Since the prime days of stochastic hydrology back in 1960s, autoregressive (AR) and moving average (MA) models (as well as their extensions) have been widely used to simulate hydrometeorological processes. Initially, AR(1) or Markovian models with Gaussian noise prevailed due to their conceptual and mathematical simplicity. However, the ubiquitous skewed behavior of most hydrometeorological processes, particularly at fine time scales, necessitated the generation of synthetic time series to also reproduce higher-order moments. In this respect, the former schemes were enhanced to preserve skewness through the use of non-Gaussian white noise— a modification attributed to Thomas and Fiering (TF). Although preserving higher-order moments to approximate a distribution is a limited and potentially risky solution, the TF approach has become a common choice in operational practice. In this study, almost half a century after its introduction, we reveal an important flaw that spans over all popular linear stochastic models that employ non-Gaussian white noise. Focusing on the Markovian case, we prove mathematically that this generating scheme provides bounded dependence patterns, which are both unrealistic and inconsistent with the observed data. This so-called “envelope behavior” is amplified as the skewness and correlation increases, as demonstrated on the basis of real-world and hypothetical simulation examples