Upmanu LallColumbia University

How has water influenced the history of man and life on Earth?

How has man determined the history, distribution and pathways of water?

How have climate variations and change determined water and life at different scales, places and times?

How has water constrained and determined climate? When/how will the human induced hydrologic

change dominate that due to climate, and in turn determine aspects of regional and global climate change and variability?

How can we assess or predict a hydrologic future for the 21st century to address impending concerns of water stress for man and life given potentially dramatic hydrologic changes due to changes in seasonal and long term climate variability and to human factors?

How will we manage such changes?

Nonstationarity?

Hydrology

Society Goals

Curiosity

Manage Variability

Design: Long Term Risk Management

Operation: Manage Residual Risk

Processes

Structure

Dynamics

Planetary Context

(bio-geo-human-systems)

Evolution

KnowledgeFluid MechanicsStochastic Processes

Challenges:

1. Spatial Heterogeneity, Scales & Continuum, Structure of Turbulence/Transport

2. Long Term Evolution (not much literature, except for climate)

Open or Closed System? Strong Feedbacks with other earth systems

A Semi-classical View

Do we have satisfactory models for long term evolution?

Climate Dynamics

Weather

Social Dynamics

Ocean-Atmosphere

Dynamics

Land Use Dynamics

Ecological Dynamics

Geomorphology

Demographics

Think about actual processes involved time and space scales, thresholds, intermittent or continuous

Other processes*

* e.g., Tectonic activity, uplift

A Restricted View of the Earth System

Hydrology

Climate Dynamics

Weather

Social Dynamics

Ocean-Atmosphere

Dynamics

Land Use Dynamics

Ecological Dynamics

Geomorphology

Demographics

Think about actual processes involved time and space scales, thresholds, intermittent or continuous

Other processes*

A Restricted View of the Earth System

Hydromorphology

Climate Dynamics

Weather

Social Dynamics

Ocean-Atmosphere

Dynamics

Land Use Dynamics

Ecological Dynamics

Geomorphology

Demographics

Orgaqnization time and space scales, thresholds, intermittent or continuous dynamics, system/state boundaries

Other processes*

Hydrology

A Restricted View of the Earth System

Non-Autonomous Forced Dynamical System

));((,( θyxx

tgfdt

d

A number of inter-acting stores state variablesForced by exogenous variables that are time varying (continuous or intermittent)Spatially averaged, discrete or continuous time

Focus (often): Fluxes, Patterns, Mean Residence TimesDoes this system have interesting dynamics?

Suppose we think of this system as a RLC network

Are the internal dynamics of x dominated by y? dynamics of y?

Analogies -- Role of R? C? L?

Are there strong +ve and –ve feedbacks across x

Nonstationarity in x Nonstationarity in x changes in y, changes in changes in y, changes in θθ, changes in , changes in f(.,.,.) or allf(.,.,.) or all

Dominant interest in Mean value – statistics of state variables Stimulus response modeling (spatial emphasis, short term)

▪ Event Models▪ Continuous Simulation Models

▪ Components can often be decomposed into separate models Slow components (e.g. groundwater) modeled separately (forced by fast

component model) and provide initial conditions for stimulus-response of faster component

Cumulative effects modeling is unidirectional and naïve – model formulation does not explicitly consider full dynamics or interactions across interfaces

Long term Dynamics – either in terms of statistical properties of state variables or parametrically determined by statistical properties of exogenous variables No good paradigm available for modeling long term dynamics

including feedbacks across key exogenous variables at appropriate space and time scales (we are in a discovery phase)

Hydrology “open terrestrial system” hillslope/basin scales response function to

forcing forecasts from initial and

boundary value problems Prescribed topography,

soils, vegetation, use, climate (rain, etc)

=> Stationary* probability distributions whether the problem is treated deterministically or statistically

Hydromorphology Interacting planetary “stores”

hierarchy “closed system?”

Regimes in space-time, predictability, transition, stability

Parametric evaluation of boundary value problems

Boundary conditions/interfaces evolve -- coupled

=> “holistic?” view of global and local hydrologic cycle and its dependence on changing conditions non-stationary, unless conditional probability

Weather Climate

Non-Autonomous Forced Dynamical System

))((,( tgfdt

dyx

x

But ….

Now x includes human population state variables, technology, infrastructure and income state variables as endogenous to the system

Human, infrastructure and river networks interact to prescribe both the evolution of the water state variables and the networks themselves

Prediction examples:

Long term evolution of population patterns in the river basin

Long term evolution of water and other infrastructure

Changing biota and landscape

Non-Autonomous Forced Dynamical System?

))((,( tgfdt

dyx

x

Now – as far as the water cycle is concerned, we could have closure

but many, many other “cycles” have to be accounted for

interactions across all planetary stores

human dynamics accounted for as endogenous

External forcing is solar radiation

Example prediction problems:

Gaia – Symbiosis across vegetation, atmosphere and humans through water?

Population density – spatial and temporal variations

The Greenhouse, the Thermohaline Conveyer, Abrupt Climate Change

Local Changes in Flood Frequency due to Urbanization/Land Use Change etc

Climate induced Changes in Floods

Nature, 2002

Nature, 2003

IWV(cm)

Atmospheric Rivergenerates flooding

CZD

Russian River flooding in Monte Rio, California

18 February 2004

photo courtesy of David Kingsmill

Russian River, CA Flood Eventof 18-Feb-04

GPS IWV data from near CZD: 14-20 Feb 2004

Bodega Bay

Cloverdale

Atmospheric river

10” rain at CZD

in ~48 hours

IWV

(c

m)

IWV

(i

nch

es)

Slide from Paul Neiman’s talk

SST Composites for Extreme Floods

Coast of Western US

Look for what happens by latitude

60 years per station, 50 stations

10 largest Floods

Washington

Oregon

N. California

C. California

S. California

10 smallest Floods

Wavelet Analysis of 1000 year sample of annual maximum NINO3 from a 110,000 year integration of the Cane-Zebiak Model with stationary forcing ( Clement and Cane, 1999)

2005 Headline

1 2 3 4 5 6 7 8 10 12 14 17 20 23 28 33 39 47 56 66 79 94 111 132 157 187 222 264 314 374 445 529

0

2

4

6

8

10

12

14

16

18

x 107

PO

WE

R

Frequency

Colorado River Compact Failure in the Absence of Lake Powell

1 2 3 4 5 6 7 8 10 12 14 17 20 23 28 33 39 47 56 66 79 94 111 132 157 187 222 264

0

0.5

1

1.5

2

x 1013

PO

WE

R

BOOTSTRAP SEVERITY WAVELET

Frequency

Colorado River Compact Failure WITH Lake Powell

RelativeVariance

Recurrence Period

1 5 10 20 30 80 100 200

Development Utilization Allocation

Hypothesis: In a given climate and technology, position on the river network has been a determinant of human population and its infrastructure development

Role of mean supply vs role of variability in space and time

Scale and Direction of Human Feedbacks

Global Population Growth

0

2

4

6

8

10

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

YEAR (AD)

Po

pula

tion

in B

illio

ns

Most ecological species (w/o predators) have population growth dynamics that are not too different from logistic, with carrying capacity determined by local resources. Is water a likely resource constraint?

If yes, is it a local or global constraint?

How is it manifest?

Scoping the feedback, as a function of scale……….

Urban Forest Management(evapotranspiration rates)

Ring Porous Wood OnlyRing Porous Wood Only• assume 15 sq mi forest SLC assume 15 sq mi forest SLC • ~3 MG per day~3 MG per day• SLC indoor ~44 MG per daySLC indoor ~44 MG per day

Average Daily Vapor Pressure Deficit (kPa)

From: S. Bush & D. Pataki

Diffuse Porous

Ring Porous

Source: Craig Forster

Marshall et al, 2001

S. Florida – draining the swamps changes regional moisture recycling -- desertification

Rivers have undergone significant degradation in flow and quality as well

Width of Ganges at the confluence with Yamuna is now typically 3 to 4 km smaller

With all these benefits, it is not surprising that farmers and entrepreneurs have invested around US$12 billion in groundwater pump structures. This sum is huge, especially when compared with the US$20 billion of public money spent on surface-water irrigation schemes over the last 50 years

Water Table Decline >400 ft

Large Scale Irrigation changes the Monsoon?

Irrigation changed water vapor flux

A Proposal to Link Major Indian River Systems:$160 Billion Capital Cost

33 Dams (9 Major)

30 Major Canals covering 12,500km

34 million hectares to be irrigated (12x Area of Bangladesh) =30% of current

34GW of hydropower

Flood Control

Navigation

VIRTUAL WATER FLOWS (1995)measured in crop ET, cereals

EU (15) excluding intra-trade

Primary Challenge:What is important, when, where and how?

How to develop and test a suitable low order dynamical modeling system to understand the currency of water in global evolution

How can data sets be developed to support hypothesis development for long term evolution of the Gaia system

How can we learn and build from integrated hydrology structure-evolution modeling and data sets

Decomposition of Climate and Human Factors: Low frequency climate oscillations translate into systematically changing

frequency and intensity of precipitation and aquifer recharge/discharge. How are these manifest in natural and modified hydrology in different

climate zones? What are the dominant frequencies of response of different hydrologic

components? How do they depend on spatial scale and the spatial distribution of

development in the system? What are key climatic or development thresholds that lead to abrupt

hydrologic change?

Water and the Development of Societies – Agent/Environment Interaction: Does human “control” and development of surface and subsurface

water fluxes superposed on the pattern of climatic exigencies lead to emergent and predictable patterns or cycles of infrastructure development, hydrologic modification and climate impact?

Is the observed scaling of population density with area related to position on the drainage network, and the seasonal and interannual variation of hydrologic fluxes over the drainage network?

What is the role played by agriculture and ecosystems in determining water use and human population density?

How does the population distribution and scaling with area change as storage infrastructure and other technological innovations change the variability and scaling of hydrologic fluxes with area?

From Human to Water to Climate: How have regional hydrologic changes induced by human activity

modified regional climate? How does changing planetary temperature, terrestrial biota and

land use translate into changes in atmospheric water composition and the hydrologic cycle?

How do these changes determine a future planetary climate?