An emerging theme related to the use of statistical methods in hydrology is the development of nonparametric methods for frequency analysis, spatial curve fitting, trend analysis, hypothesis testing, regression, time-series analysis, simulation, and other problems [ Helsel and Hirsch, 1992; Lall, this issue]. Nonparametric procedures afford significant advantages over their parametric counterparts. Nonparametric procedures generally reproduce the empirical structure of multivariate data sets yet they do not require assumptions about data or model structure, nor do they require parameter estimation. Therefore, nonparametric procedures do not suffer from the usual attendant losses associated with having chosen an incorrect model and used an inefficient parameter estimation algorithm. As a result, simple data resampling schemes such as the bootstrap and jackknife are beginning to become accepted by hydrologists [ Kitanidis, this issue; Lall, this issue] as conceptually simple (yet computationally intensive) alternatives to more complex parametric alternatives. On the one hand, Lall [this issue] argues that the literature on nonparametric function estimation has historically been very mathematical, yet in the simplest case, a moving-average, long accepted by practitioners, provides an illustrative example of how palatable nonparametric methods really are to practitioners. Together, Helsel and Hirsch [1992] and Lall [this issue] provide a comprehensive review, introduction, and comparison of nonparametric and parametric statistical procedures applied to a wide class of water and environmental applications. Maidment [1993, Chapters 17-19] also provides a comprehensive review of statistical methods useful in water resource investigations.
The challenges posed by extreme hydrological events continue to vex hydrologists. The introduction of the theory of L-moments [ Hosking, 1990] is probably the single most significant recent advance relating to our understanding of extreme events. Generally, L-moments are linear combinations of ordered observations, which are unbiased regardless of the parent population, hence L-moments allow us to discriminate the behavior of skewed hydrologic data which was difficult or impossible only a few years ago. Bobee and Rasmussen [this issue] and Maidment [1993, Chapter 18] review the theory and application of L-moments. It is no longer adequate to base our understanding of extreme events on a single sample of streamflow. Bobee and Rasmussen [this issue] document advances in the use of regional information to improve our ability to understand and predict extreme events. Naturally, improvements in our ability to predict extreme events will ultimately come from improvements in our understanding of the physical processes along with improvements in regional statistical methods.
Recent statistical research has greatly improved methods for estimating sediment and nutrient transport in rivers. Cohn [this issue] argues that the bias of rating curve estimators can now be eliminated and a new unbiased and efficient approach based on stratified random sampling has emerged making it possible to design relatively low-cost sampling programs for measuring sediment and nutrient transport.
Innovations in statistical methodologies in hydrology are probably exemplified by the role of geostatistical methods in hydrogeology. Geostatistical methods continue to be developed for a wide range of new and old hydrogeological problems. Kitanidis [this issue] warns us that there is no scarcity of sophisticated techniques, yet their use is not always tempered with a basic understanding of statistical methods and common sense. Many successful methods that appear under different names in different fields are basically the same [ Kitanidis, this issue; McLaughlin, this issue]. There is a trend to develop Bayesian, data assimilation and other regional methods which can integrate many sources of information.