Statistics in WR: Lecture 1 Key Themes – Knowledge discovery in hydrology – Introduction to probability and statistics – Definition of random variables Reading: Helsel and Hirsch, Chapter 1

How is new knowledge discovered? By deduction from existing knowledge By experiment in a laboratory By observation of the natural environment After completing the Handbook of Hydrology in 1993, I asked myself the question: how is new knowledge discovered in hydrology? I concluded:

Deduction – Isaac Newton Deduction is the classical path of mathematical physics – Given a set of axioms – Then by a logical process – Derive a new principle or equation In hydrology, the St Venant equations for open channel flow and Richard’s equation for unsaturated flow in soils were derived in this way. (1687) Three laws of motion and law of gravitation

Experiment – Louis Pasteur Experiment is the classical path of laboratory science – a simplified view of the natural world is replicated under controlled conditions In hydrology, Darcy’s law for flow in a porous medium was found this way. Pasteur showed that microorganisms cause disease & discovered vaccination Foundations of scientific medicine

Observation – Charles Darwin Observation – direct viewing and characterization of patterns and phenomena in the natural environment In hydrology, Horton discovered stream scaling laws by interpretation of stream maps Published Nov 24, 1859 Most accessible book of great scientific imagination ever written

Conclusion for Hydrology Deduction and experiment are important, but hydrology is primarily an observational science discharge, water quality, groundwater, measurement data collected to support this.

Great Eras of Synthesis Scientific progress occurs continuously, but there are great eras of synthesis – many developments happening at once that fuse into knowledge and fundamentally change the science Physics (relativity, structure of the atom, quantum mechanics) Geology (observations of seafloor magnetism lead to plate tectonics) Hydrology (synthesis of water observations leads to knowledge synthesis) 2020

Hydrologic Science Hydrologic conditions (Fluxes, flows, concentrations) Hydrologic Process Science (Equations, simulation models, prediction) Hydrologic Information Science (Observations, data models, visualization Hydrologic environment (Physical earth) Physical laws and principles (Mass, momentum, energy, chemistry) It is as important to represent hydrologic environments precisely with data as it is to represent hydrologic processes with equations

A sea change in computing Massive Data Sets Federation, Integration, Collaboration There will be more scientific data generated in the next five years than in the history of humankind Evolution of Many-core and Multicore Parallelism everywhere What will you do with 100 times more computing power? The power of the Client + Cloud Access Anywhere, Any Time Distributed, loosely-coupled, applications at scale across all devices will be the norm Slide from Jeff Dozier, UCSB

1.Thousand years ago – Experimental Science – Description of natural phenomena 2.Last few hundred years – Theoretical Science – Newton’s Laws, Maxwell’s Equations… 3.Last few decades – Computational Science – Simulation of complex phenomena 4.Today – Data-Intensive Science – Scientists overwhelmed with data sets from many different sources Data captured by instruments Data generated by simulations Data generated by sensor networks – eScience is the set of tools and technologies to support data federation and collaboration For analysis and data mining For data visualization and exploration For scholarly communication and dissemination (With thanks to Jim Gray) Emergence of a fourth research paradigm Slide from Jeff Dozier, UCSB

Space, L Time, T Variable, V D Data Cube – What, Where, When “What” “Where” “When” A data value

Continuous Space-Time Data Model -- NetCDF Space, L Time, T Variables, V D Coordinate dimensions {X} Variable dimensions {Y}

Space, FeatureID Time, TSDateTime Variables, TSTypeID TSValue Discrete Space-Time Data Model

Geostatistics Time Series Analysis Multivariate analysis Hydrologic Statistics How do we understand space-time correlation fields of many variables?

288 USGS sites with flow and Nitrogen data These sites are ones that were used for the Sparrow model that continue to be operational to

Colorado River at Austin, Tx ( )

Mean Annual Flow

Is there a relation between flow and water quality? Total Nitrogen in water

Are Annual Flows Correlated?