Review of Statistical Analysis of Hydrologic Variables: Methods and Applications edited by Ramesh S. V. Teegavarapu, Jose D. Salas, and Jery R. Stedinger

A search with the term “statistical hydrology” on Google Books or Amazon Books fetches hundreds of titles written by a number of academics and engineers. Any book on hydrology has at least one chapter devoted to the statistical treatment of hydrological data. With such a breadth of resources already available, it may be easy to dismiss Statistical Analysis of Hydrologic Variables: Methods and Applications as just another book in this category.

Hydrology, just like a number of other fields, is undergoing a rapid transformation with terms like big data, machine learning, and more recently, deep learning, finding their way into its vernacular (Shen 2018). These novel tools, along with the wealth of data being generated through satellite observations and models, are going to revolutionize different areas in hydrologic science (Ganguly et al. 2014). While these are still at the exploratory stage, students, researchers, and practitioners alike have to understand the fundamentals and evolution of the field. This book is a comprehensive treatment of a wide range of statistical methods in the analysis of hydrological variables.

Aside from the introductory chapter, the book comprises 11 chapters, the first five of which relate to the main components of the hydrological cycle: precipitation, evaporation, infiltration, groundwater, and streamflow. The remaining six chapters discuss a wide range of applications, including analysis of extreme events, urban water management, water quality, multivariate data analysis, and record events.

Chapter 2 presents an in-depth description of statistical methods in the analysis of precipitation data. The authors give an overview of how precipitation data is collected both directly and indirectly. Statistical analysis of precipitation data often requires fitting of a probability distribution. A suite of probability distributions exists, several of which have been employed in hydrology. After explaining the different plotting position formulae and providing the mathematical form of the most commonly used distributions, they give, in Table 2-2, an extensive list of recent studies that use different probability distributions to characterize precipitation at different time scales followed by various parameter estimation methods and goodness-of-fit measures. The authors then present a discussion on extreme value analysis along with challenges such as missing data, stationarity, etc. The chapter concludes with a brief discussion on assessing the influence of climate teleconnection patterns and climate change on historical data.

Chapter 3 is a detailed description of evapotranspiration and evaporative demand. At the outset, the authors explain how, despite it being a critical component of the hydrological cycle—and hence any water balance exercise—evapotranspiration is challenging to measure directly. Practitioners have to resort to alternative estimation techniques. The authors contend that statistical analysis is peripheral to the estimation of fluxes. However, with a growing interest in temporal changes of evapotranspiration due to a changing climate, trend analysis and their significance are often analyzed. Therefore, the chapter focuses primarily on the physical processes involved and the different approaches for estimating evapotranspiration, namely energy and water balance models, eddy covariance techniques, and remote sensing. A discussion on reference evapotranspiration including the Penman-Monteith and ASCE standardized reference evapotranspiration equations along with sources of uncertainty and sensitivity are presented. However, no discussion is provided on the extremal principle presented by Wang et al. (2004), which employs the argument that under thermodynamic equilibrium the thermal and hydrologic states of the land surface resulting from interaction between land and atmospheric processes tend to maximize evaporation. The chapter concludes with a trend analysis of global evapotranspiration and atmospheric evaporative demand.

Infiltration and soil moisture are other variables that rely more on a physics-based analysis than on a statistical treatment of data. Chapter 4 discusses the role of infiltration in the hydrological cycle and the processes that affects infiltration. The main infiltration models and methods for measuring soil water content are presented, but there is no discussion of the generalized infiltration model or systems approach from which several popular infiltration models can be derived (Singh and Yu 1990). The challenge practitioners face is to scale up laboratory or point scale measurements. Various methods, including pedotransfer functions and geostatistical scaling methods, along with sources of uncertainty and treatments are presented and discussed. Entropy theory of infiltration as well as of soil moisture has been developed but has found no place in the book (Singh 2010a, b). The next chapter discusses the application of probability distributions in groundwater hydrology. Basic statistics and procedure for fitting common probability distributions to hydraulic conductivity data, with examples, are described. Finally, the application of the gamma distribution to residence time and age, and water quality is presented.

Streamflow plays a major role in hydrology and water resources management. Understanding the nature, patterns, trends, and timing (Khedun et al. 2019; Khedun et al. 2020; Milhous 2020) of streamflow records is critical for planning, management, and hazard mitigation. Chapters 6–8 focus on the analysis of streamflow time series, and more importantly, its evil twins: floods and droughts. In Chapter 6, the focus is on the analysis of streamflow data at different spatial and temporal timescales. The autoregressive moving average (ARMA) model is introduced followed by more complex ones: periodic ARMA (PARMA) and seasonal ARMA (SARMA), which account for periodicity or seasonality; fractional ARMA (FARMA) and others to model long-memory processes; and contemporaneous ARMA (CARMA) and contemporaneous PARMA (CPARMA) for modeling complex river systems.

Bulletin 17-B (US Interagency Advisory Committee on Water Data 1982) is the recommended methodology for flood frequency analysis in the United States. However, with a changing climate, questions about stationarity of flow time series and the procedures therein have evolved over time. In Chapter 7, a detailed explanation of the procedure, more particularly the characteristics of the log-Pearson type III (LP3), the recommended probability distribution for flood series, and treatment of outliers are provided along with a description of changes in the new Bulletin 17C (England et al. 2019). This chapter also includes a discussion, with examples, on how climate change and climate variability can be incorporated in flood frequency analysis—something that is particularly important given that clients (municipalities, land developers, etc.) are now asking consultants to consider the effect of future climate when designing hydraulic infrastructures.

Droughts, unlike floods, do not occur abruptly and have a definite beginning or end; they are complex phenomenon, and their impacts can be wide-ranging. There are several definitions for drought (Mishra and Singh 2010); the hydrological definition pertains to water availability in streams and other water bodies that farmers and municipalities rely on. Dwindling flow or supply is a cause for concern. Understanding the hydrometeorological causes behind droughts—both the onset and end—is critical in managing and mitigating the impacts of this critical natural hazard. In Chapter 8, the authors start by providing definitions for both low flows and drought. Methodically characterizing drought events (initiation, duration, magnitude, intensity, termination, and spatial extent) is essential because no two droughts are similar. Low flows and drought parameters, just like high flows or floods, can be modeled by fitting probability distribution functions. Similarly, ARMA and related models can be also used. The chapter provides a detailed description for fitting probability distributions, especially when drought events span multiple years, and briefly discusses regional analysis of droughts.

Chapter 9 focusses on probabilistic models for urban stormwater management, a crucial topic, given that extensive urbanization is often the prime cause of flooding [e.g., Hurricane Harvey in Houston in 2017 (Zhang et al. 2018)]. While flood frequency and return period analysis are discussed in Chapters 6 and 7, Chapter 9 focusses on two relatively novel statistical approaches: analytical probabilistic stormwater models (APSWM) and performance modeling and uncertainty analysis of best management practices (BMPs). APSWM complements conventional urban stormwater management approaches. It uses the probabilistic characteristics of local rainfall events and the properties of the catchment to estimate the frequency distributions of flood peak and volume. Extensions and new developments in this approach are discussed. One notable application is the study of flood attenuation potential of low impact developments, e.g., rainwater harvesting, bioretention systems, etc. In the second part of the chapter, the authors present, along with an example, a suite of techniques for the assessment of the performance of BMPs employed in pollution control. Both methods presented are topical given the massive investments expected in the near future in infrastructure renewal and upgrade in the United States and elsewhere to mitigate the dreadful effects of a changing climate and to safeguard the quality and health of waterbodies.

Chapter 10 is devoted to statistical methods employed in water quality analysis. Careful analysis of water quality data is critical as often only a limited sample is available from which the state of the population is to be inferred. Errors can easily crop up at various stages in the process—sampling, transport, or in the laboratory—and therefore practitioners have to be acquainted with the proper ways to handle and interpret the data. At the outset, the author remarks that “data users often waste a great deal of time arguing whether or not the data are normally distributed, when the far more important question is whether or not the data adequately represent the real population of interest.” Commonly employed statistical tests, probability distributions, sampling, time series analysis, and seasonality are presented.

Interest, and the number of papers published in the last decade, on multivariate hydrological data analysis has exploded with the introduction of copula to this field (Singh and Strupczewski 2007). This chapter touches on conventional multivariate distributions in hydrology before segueing into the copula method. The copula method is a formidable tool (Zhang and Singh 2019); it allows the construction of bivariate and multivariate probability distributions without the constraints and assumption imposed by conventional methods. The main advantage being that the methods allow the marginal distributions of individual variables to be of any form and can be correlated. In this chapter, a careful guide on the successful selection of the most appropriate copula, from the wide family that exists, is presented and illustrated through multiple vivid examples.

Chapter 12 is perhaps the most interesting one in this volume. It is an exposition on hydrologic record events. Gumbel (1958) famously said, “Il est impossible que l’improbable n’arrive jamais” (“The improbable is bound to happen one day”), or as the authors put it “the probability that the largest observed flood discharge on a river will be exceeded is 1.” The devastation caused by Hurricane Harvey has cemented this notion—that of the “big one”—in every hydrologist’s mind. This chapter introduces the theory of records, which goes beyond the theory of extremes that hydrologists are familiar with. The chapter first discusses parametric and nonparametric properties of hydrologic records and then explores the application of this theory to the development of flood envelope curves. Envelope curves are the upper bound of flood events and are loosely associated with the probable maximum flood. The authors present the historical background of envelope curves, their probabilistic interpretation including exceedance probability, which is essential in the design of large hydraulic structures. Applications, through case studies in Europe and the US, are also presented.

In 12 carefully curated chapters, the authors of the various chapters and editors of this book have captured in one place the most important concepts in statistical hydrology. Every chapter is well illustrated and includes, where necessary, examples and case studies that highlight applications. The authors also include an extensive list of references, which will be extremely useful to researchers in the field. The only problem that we find with this book is the repetition of statistical concepts and probability distributions, sometimes with confusing and inconsistent notations across the chapters. The reason being that each chapter was written by a different set of authors and they found it important to start with the basics in their respective area of focus, and then extrapolate to its applications. In some sense, it may not necessarily be bad thing; it may even comfort practitioners to see the topics discussed in the language that they are most familiar with.

In conclusion, we believe that this book is an incomparable addition to the library of graduate students and engineers alike. We forsee it to be on the recommended reading for every statistical hydrology class. Both the authors and editors are to be commended for the exceptional effort that was required to put this together.