dynamic modeling to inform environmental management

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Graduate College Dissertations and Theses Dissertations and Theses

2008

Dynamic Modeling to Inform Environmental Management: Dynamic Modeling to Inform Environmental Management:

Applications in Energy Resources and Ecosystem Services Applications in Energy Resources and Ecosystem Services

Mark Gately University of Vermont

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DYNAMIC MODELING TO INFORM ENVIRONMENTAL MANAGEMENT:

APPLICATIONS IN ENERGY RESOURCES AND ECOSYSTEM SERVICES

A Thesis Presented

by

Mark Gately

to

The Faculty of the Graduate College

of

The University of Vermont

In Partial Fulfillment of the Requirements

for the Degree of Master of Science

Specializing in Community Development and Applied Economics

October, 2008

Accepted by the Faculty of the Graduate College, The University of Vermont, in partial fulfillment of the requirements for the degree of Master of Science, specializing in Community Development and Applied Economics.

Thesis Examination Committee:

r

olodinsky, Ph.D.

Chairperson Robert Costanza, Ph.D.

Vice President for Research and Dean of Graduate Studies

Date: April 3, 2008

Abstract

Two original computer simulation models are presented in this thesis. Although these

models differ in their temporal, spatial, and structural dimensions, they are unified by a

common purpose: to build quantitative understanding of environmental resources and

better inform their future management.

According to the U.S. Department of the Interior’s Minerals Management Service, there

are significant undiscovered reserves of oil and natural gas located in the Gulf of Mexico

Outer Continental Shelf region. While the existence of these energy resources is critical

to the nation’s future economic well-being, of equal importance is the amount of already

extracted energy that will be required to deliver the new fuel to society in a useful form;

the difference between the two quantities is the net energy supply. “Energy return on

investment” (EROI) is an indicator of the net productivity of an energy supply process;

specifically, it is the ratio of gross energy production to total, direct plus indirect, energy

cost. Chapter 1 describes a dynamic model designed to calculate the EROI of offshore

energy extraction in the U.S. Gulf of Mexico from 1985 to 2004 under differing

assumptions regarding energy cost and technology. In 2004, the EROI of the process is

estimated to range from 10 to 25 depending on how comprehensively energy costs are

defined. In comparison, the EROI of U.S. onshore petroleum extraction in the 1930s was

at least 100.

Ecosystem services are those functions of ecosystems that support, directly or indirectly,

human welfare. Although interest in ecosystem services has surged in recent decades and

is currently still on the rise, these phenomena have yet to be universally quantified. The

current Multi-scale, Integrated Models of Ecosystem Services (MIMES) project is an

ambitious attempt to do so through dynamic, spatially explicit modeling. As a part of this

broad initiative, Chapter 2 details the development and testing of a model designed to

measure and map the ecosystem service “water regulation” at multiple scales. The model

is an extension of the well known and widely used “runoff curve number” method

originally developed by the U.S. Department of Agriculture; it is applied to the Winooski

watershed (Vermont, U.S.A.) and to the entire globe.

ii

Citation

Material from this thesis has been published in the following form:

Gately, M.. (2007). The EROI of U.S. offshore energy extraction: A net energy analysis

of the Gulf of Mexico. Ecological Economics, 63, 355-364.

Material from this thesis has been submitted for publication to Ecosystems on May 5,

2008 in the following form:

Gately, M.. On semantics and scale: Developing a dynamic multi-scale model of the

ecosystem service water regulation. Ecosystems.

iii

Table of Contents

Page

Citation ................................................................................................................................ ii

List of Tables ...................................................................................................................... v

List of Figures .................................................................................................................... vi

Introduction ......................................................................................................................... 1

Chapter 1. The EROI of U.S. offshore energy extraction: A net energy analysis of the

Gulf of Mexico .................................................................................................................... 6

1. Introduction ................................................................................................................ 7

2. EROI theory ............................................................................................................... 9

2.1. The stationary state ............................................................................................. 9

2.2. EROI dynamics ................................................................................................. 13

3. The offshore process ................................................................................................ 14

4. Model specification .................................................................................................. 17

4.1. Temporal and spatial articulation ...................................................................... 17

4.2. EROI calculation ............................................................................................... 18

4.3. Technology ....................................................................................................... 21

5. Results and conclusions ........................................................................................... 23

References ..................................................................................................................... 29

Appendix A ................................................................................................................... 31

Appendix B ................................................................................................................... 33

iv

Chapter 2. On semantics and scale: Developing a dynamic multi-scale model of the

ecosystem service water regulation .................................................................................. 35

1. Introduction .............................................................................................................. 35

2. Semantics ................................................................................................................. 39

3. Scale ......................................................................................................................... 41

4. A formal model of water regulation ........................................................................ 43

5. Results and discussion ............................................................................................. 50

5.1. Calibration and validation ................................................................................. 50

5.2. Scenario analysis ............................................................................................... 56

5.3. Scale effects ...................................................................................................... 59

5.4. The global application ....................................................................................... 61

6. Conclusion ............................................................................................................... 63

References ..................................................................................................................... 65

Literature Cited ................................................................................................................. 67

v

List of Tables

Page

Table 1.1 – Activity phases of the offshore process and their annual per unit costs by

water depth (Dismukes et al., 2003). ........................................................................ 19

Table 1.2 – Expenditure profile for platform abandonment and removal (Dismukes et al.,

2003). ........................................................................................................................ 21

Table 2.1 – A list of ecosystem services and their corresponding ecosystem functions

(Costanza et al., 1997). ............................................................................................. 36

Table 2.2 – Default CN parameterization for the 11-biome MIMES land cover scheme

and HSG. ................................................................................................................... 46

Table 2.3 – Results of model calibration (1992) and validation (2001). .......................... 54

Table 2.4 – Calibrated parameters. ................................................................................... 55

Table 2.5 – Scenario analysis............................................................................................ 57

Table 2.6 – Scale effects. .................................................................................................. 60

vi

List of Figures

Page

Fig. 1.1 – A generic energy supply process defined over the duration [0,T]...................... 9

Fig. 1.2 – The energy cost tier structure. .......................................................................... 12

Fig. 1.3 – A typical energy supply system, adapted from Cleveland and Costanza (1984).

................................................................................................................................... 12

Fig. 1.4 – Gross production of offshore oil and natural gas in the U.S., 1960 – 2004.

Source: Energy Information Administration. ........................................................... 15

Fig. 1.5 – Percentage of gross energy production in the U.S. GOM from depths greater

than 200 m, 1992 – 2005. Source: Energy Information Administration. ................ 16

Fig. 1.6 – Simplified model diagram. ............................................................................... 17

Fig. 1.7 – EROI of GOM offshore extraction using two alternative treatments of energy

cost (T1 and T3) and simulated technology, 1985 – 2004. ....................................... 23

Fig. 1.8 – EROI for various methods of electric power generation (Kubiszewski and

Cleveland et al., 2007). ............................................................................................. 24

Fig. 1.9 – EROI of GOM offshore extraction by water depth using two alternative

treatments of energy cost (T1 and T3) and constant 1985 technology, 1985 – 2004.

................................................................................................................................... 25

Fig. 1.10 – T3 EROI of extraction in the 0 – 60 m and 61 – 200 m regions using constant

1985 technology and simulated technology, 1985 – 2004. ....................................... 26

Fig. 1.11 – Historical GOM T3 EROI (1985 – 2004) and two alternate scenarios for the

near future (2005 – 2013).......................................................................................... 27

vii

Fig. 1.12 – Historical GOM energy production (1985 – 2004) and two alternate scenarios

for the near future (2005 – 2013). ............................................................................. 28

Fig. 2.1 – Two alternative methods of scaling: a) by “majority rule” and b) by

maintaining a percentage distribution. ...................................................................... 49

Fig. 2.2 – Simplified model diagram. ............................................................................... 49

Fig. 2.3 – 2001 land cover pattern (30 m) of the Winooski watershed. ............................ 52

Fig. 2.4 – HSG pattern (90 m) of the Winooski watershed. ............................................. 52

Fig. 2.5 – Modeled and observed runoff in the Winooski watershed, June 1 – October 31,

1992. .......................................................................................................................... 53

Fig. 2.6 – Modeled and observed runoff in the Winooski watershed, June 1 – October 31,

2001. .......................................................................................................................... 54

Fig. 2.7 – Total water regulation (thousand m3) in the Winooski watershed from June 1 –

October 31, 2001 at 330 m grain............................................................................... 56

Fig. 2.8 – Modeled runoff in the Winooski watershed June 1 – October 31, 2001 using

two alternate land cover scenarios: historical data and completely forested. ........... 58

Fig. 2. 9 Modeled runoff in the Winooski watershed June 1 – October 31, 2001 using

two alternate land cover scenarios: historical data and completely urbanized. ........ 58

Fig. 2.10 – Total water regulation (thousand m3) in the Winooski watershed, June 1 –

October 31, 2001 at 4 grain sizes: a) 450 m, b) 900 m, c) 2700 m, and d) 6000 m. . 60

Fig. 2.11 – Global land cover pattern (1 km). ................................................................... 62

Fig. 2.12 – Global HSG pattern (5 arcmin). ..................................................................... 62

viii

Fig. 2.13 – Global water regulation (1 deg) as the regulated percentage of a 2 in rainfall

event. ......................................................................................................................... 63

1

Introduction

As the scale of the human presence in the biosphere increases, Earth’s once

abundant stock of natural capital is becoming increasingly scarce. As Daly (1996) has

pointed out, “We have moved from a world relatively full of natural capital and empty of

man-made capital (and people) to a world relatively full of the latter and empty of the

former.” In the current “full world” era (that is, one full of humans and our various

artifacts), natural capital has replaced manufactured capital or human labor as the limiting

factor of economic development. Moreover, the vital life-support services that natural

capital stocks provide, such as climate and water regulation, have been degraded, and

continual degradation of these services may ultimately compromise the sustainability of

humans on Earth. Thus, there now exists an urgent and overarching need for improved

management of our environmental resources through proactive decision-making. To

inform decision-makers, an entirely new generation of computer models must be devised

and deployed; two such models are presented in this thesis.

A model is any abstract representation of reality. Based on the original insights of

Kenneth Craik (1943), recently developed “mental model” theories (Johnson-Laird,

1983; Gentner and Stevens, 1983) suggest that human reasoning and comprehension is

based on the construction and execution of “small scale models” within the human mind.

These psychological representations are derived using an understanding of the given

premises and some general knowledge and assumptions about how the world works.

Although commonly thought of as internal pictures or images, mental models are a more

2

general notion; they may also represent abstract concepts, such as happiness or value,

which cannot be arranged spatially.

Humans interact with their mental models via semantic, conceptual operations.

The inferences yielded are essential in decision situations for assessing the relative

utilities of the known alternatives. Often, a distinct mental model is conceived for each

explicit alternative scenario option, and a decision is reached based on interaction with

multiple models. Due to the limited capacity of the human working memory these

models are restricted in terms of complexity and resolution, and they are primarily based

on qualitative relationships. Nevertheless, mental models are usually sufficiently detailed

and accurate to provide reliable “ad hoc” decision support in everyday life.

In environmental management domains, however, complex systems prevail.

Economies and ecosystems are strongly linked and deviously complex systems (Costanza

et al., 1993). As such, they exhibit baffling dynamic behaviors characterized by non-

linearity, complex feedbacks, and spatial and temporal delays. Moreover, these

properties are often “emergent” and cannot be determined or explained by simply

aggregating the individual behaviors of the system’s component parts (von Bertalanffy,

1968). In order to reason about complex systems and properly anticipate their dynamic

behaviors, the modeling approach must not only be holistic and integrative (Levins,

1966), but also based on quantitative relationships between the constituent parts. Mental

models are thus only of limited insight in environmental management; informed and

dependable decision support in this domain requires an extension of our mental modeling

capabilities.

3

Mathematical models, for example, consist of mathematical expressions that

formally specify real systems. In particular, dynamic mathematical models are sets of

differential or difference equations that articulate a system’s behavior over time. These

models are potent, quantitative extensions to our mental models of dynamic systems.

However, the differential equations that describe complex, non-linear behavior are

generally very difficult, if not impossible, to solve analytically (von Bertalanffy, 1968);

their solutions can only be approximated using advanced numerical methods executed on

computers. Thus, prior to the widespread availability of computers, quantitative analysis

of complex dynamic systems was severely limited to the examination of simple, linear

dynamics at coarse resolutions. Developments in numerical analysis and continuous

improvements in computer speed and accessibility, however, have recently eroded those

limits.

Dynamic computer modeling is now a well accepted and widely used technique in

scientific analysis. The “system dynamics” methodology of Forrester (1968), for

example, has been used to study and manage a wide range of complex systems cutting

across multiple disciplines in both the natural and social sciences. In the early 1970s, the

World2 (Forrester, 1971) and World3 (Meadows et al., 1972) global models pioneered

the use of these techniques to quantify complex human-environment interactions, and

since then dynamic modeling has been effectively used in a wide variety of

environmental research and management contexts (cf. Costanza and Ruth, 1998); the

Millennium Ecosystem Assessment (MA, 2005) is a recent example.

4

In this thesis, dynamic modeling is used to build quantitative understanding of

energy resources and ecosystem services. In 2004, the U.S. Department of the Interior’s

Minerals Management Service estimated that 49% of the oil and 57% of the natural gas

yet to be discovered offshore in the United States are located in the Gulf of Mexico Outer

Continental Shelf region (MMS, 2004). While the existence of these energy resources is

critical to the nation’s future economic well-being, of equal importance is the amount of

already extracted energy that will be required to deliver the new fuel to society in a useful

form; the difference between the two quantities is the net energy supply. “Energy return

on investment” (EROI) is an indicator of the net productivity of an energy supply

process; specifically, it is the ratio of gross energy production to total, direct plus indirect,

energy cost (Cleveland et al., 1984). Chapter 1 describes a dynamic model designed to

calculate the EROI of offshore energy extraction in the U.S. Gulf of Mexico from 1985 to

2004 under differing assumptions regarding energy cost and technology. In 2004, the

EROI of the process is estimated to range from 10 to 25 depending on how

comprehensively energy costs are defined. In comparison, the EROI of U.S. onshore

petroleum extraction in the 1930s was at least 100 (Cleveland, 1992).

Ecosystem services are those functions of ecosystems that support, directly or

indirectly, human welfare (Costanza et al., 1997; Daily, 1997). Although interest in

ecosystem services has surged in recent decades and is currently still on the rise, these

phenomena have yet to be universally quantified. The current Multi-scale, Integrated

Models of Ecosystem Services (MIMES) project is an ambitious attempt to do so through

dynamic, spatially explicit modeling. As a part of this broad initiative, Chapter 2 details

5

the development and testing of a model designed to measure and map the ecosystem

service “water regulation” at multiple scales. The model is an extension of the well

known and widely used “runoff curve number” method originally developed by the U.S.

Department of Agriculture; it is applied to the Winooski watershed (Vermont, U.S.A.)

and to the entire globe.

Energy limits and loss of ecosystem services have been identified as among the

most serious environmental problems facing present and future societies (Diamond,

2005; Tainter, 1988). When faced with such issues in the past, some societies (such as

the infamous Easter Islanders) unfortunately collapsed, while others culturally evolved to

prosper for long periods of time. Diamond (2005) concludes that a key determinant of

success or failure is how a society responds to the signals of emerging environmental

problems. By supplementing our mental models with innovative computer models such

as those presented in this thesis, we can both clarify those ecological signals and better

inform our managerial responses.

6

Chapter 1.

The EROI of U.S. offshore energy extraction: A net energy analysis of the Gulf of

Mexico

Abstract

In 2004, the U.S. Department of the Interior’s Minerals Management Service estimated

that 49% of the oil and 57% of the natural gas yet to be discovered offshore in the United

States are located in the Gulf of Mexico Outer Continental Shelf region. While the

existence of these energy resources is critical to the nation’s future economic well-being,

of equal importance is the amount of already extracted energy that will be required to

deliver the new fuel to society in a useful form; the difference between the two quantities

is the net energy supply. “Energy return on investment” (EROI) is an indicator of the net

productivity of an energy supply process; specifically, it is the ratio of gross energy

production to total, direct plus indirect, energy cost. This paper describes a dynamic

model designed to calculate the EROI of offshore energy extraction in the U.S. Gulf of

Mexico from 1985 to 2004 under differing assumptions regarding energy cost and

technology. In 2004, the EROI of the process is estimated to range from 10 to 25

depending on how comprehensively energy costs are defined. In comparison, the EROI

of U.S. onshore petroleum extraction in the 1930s was at least 100.

7

1. Introduction

The distinction between gross and net measures of production is a fundamental

concept in standard economic theories. Conventional macroeconomic theory, for

example, provides two estimates of a nation’s total economic output: gross national

product (GNP) and net national product (NNP). GNP is the total market value of all

goods and services produced by the citizens a nation over a period of time, whereas NNP

is equal to GNP less capital depreciation. Similarly, conventional microeconomic theory

provides two measures of a firm’s production: revenue and profit. Revenue is the total

market value of a firm’s output over a period of time, while profit is equal to revenue

minus the total market cost of the factors of production.

The output of any economic production process, be it an individual firm or an

aggregate national economy, should be considered in both gross and net terms. But this

point is often missed in regards to one of the most critical economic production

processes: energy supply. The energy supply process is the “fuel line” of an economy; it

provides the low-entropy free energy required to power all of the various economic

sectors (including its own). Cottrell (1955) termed the net output of energy production

“surplus energy” and defined it as the difference between the energy delivered by a

process and the energy invested in the delivery.

Surplus energy may be the most economically relevant measure of energy

production because it represents the ability to produce final demand goods and services.

Yet in a review of the data accessible from the United States Energy Information

Administration’s official website (http://www.eia.doe.gov/) no references to surplus

8

energy could be found; all production figures, both historical and forecasted, are in gross

terms. From a net perspective, these data may look quite different.

In contrast, the academic community has recognized the importance of surplus

energy for many years. Numerous separate studies have estimated the net productivities

of a variety of energy supply processes, including ethanol production (Farrell et al., 2006;

Hammerschlag, 2006), nuclear energy generation (Tyner et al., 1988; Kidd, 2004), and

petroleum extraction (Cleveland, 1992; Cleveland, 2005), to name a few. However, there

currently is no standard protocol for net energy analysis, and so the results of these

studies are often inconsistent and difficult to interpret; the recent debate over the net

energy yield of corn ethanol production is a telling example (cf. Farrell et al., 2006;

Hagens et al., 2006; Cleveland et al., 2006).

In this paper, we develop a standard framework for net energy analysis using the

“energy return on investment” (EROI) productivity index, which is the ratio of gross

energy production to total, direct plus indirect, energy cost (Cleveland et al., 1984). We

then construct a dynamic computer model to apply this analytical framework to the

extraction of offshore energy in the U.S. Gulf of Mexico (GOM).

9

2. EROI theory

2.1. The stationary state

Fig. 1.1 – A generic energy supply process defined over the duration [0,T].

Figure 1.1 illustrates a generic energy supply process that is characterized by its

energy input and output flows. For every time t contained within the process duration,

[0,T], its state may be specified analytically by a 3-tuple as follows:

{EI(t), EO(t), EC(t)} where 0 ≤ t ≤ T (1)

The three coordinates in Eq. (1) are cumulative, non-decreasing functions of time; each

represents a distinct energy flow common to all energy supply processes. EI(t) is the raw,

“in situ” energy input, or energy in its natural form (e.g., wind, water, oil “in the

ground”). EO(t) is the transformed energy output, or energy at its social “point of use”

(e.g., electricity, gasoline “at the pump”). EC(t) is the total, direct plus indirect, energy

cost of the transformation. Collectively, these three functions provide a static “snapshot”

of the process at each time-step of its duration.

10

Given the information in Eq. (1) for a process operating at time-step t (where 0 t

T), various metrics can be derived that describe its performance up to and including

that particular moment. EROI, for example, can be formally defined based on Eq. (1) as

follows:

EROI(t) = EO(t) / EC(t) (2)

Expressed as a function of time, the EROI index is the ratio of delivered end-use energy

to the energy cost of delivery; both quantities are cumulative up to the specified time t.

EI(t) is not required to calculate EROI, however, it is used in other performance

indicators (such as “energy capture efficiency”: EI(t) / EC(t) + EO(t)).

Operationalizing this analytical model depends largely on the availability of

existing data, or the feasibility of deriving reliable data, for the two ratio components.

While the measurement of delivered end-use energy is relatively straightforward and data

are readily available, determining the energy cost of its delivery is significantly more

subjective and data are extremely limited. Energy cost data, therefore, often must be

derived essentially “from scratch”. To do so properly, the boundary of the energy supply

process must first be clearly established.

We will define the “frontier” of the energy supply process as encompassing all

anthropogenic activities (e.g., exploration, extraction or capture, processing, refinement,

storage, transportation) required to transform and deliver a particular quantity of in situ

energy to its social point of use. The process environment is the natural human

environment: a backdrop of ecosystem structures and processes that support and sustain

production. The energy cost of the process thus consists of 1) the total, direct plus

11

indirect, energy embodied in all economic feedbacks necessary to power the

transformative human activities, and 2) the energy cost of any damages to the external

environmental support structure.

These energy costs can be divided into four “tiers” of increasing

comprehensiveness. “Tier 1” (T1) energy costs include only direct fuels, which are the

already-delivered energies whose point of use is the production (or more correctly, the

reproduction) of new fuel. Consider a vehicle that transports diesel fuel to the

distribution station, while running on the same product. Indirect energy costs are more

difficult to identify and assess, but often are more significant than direct costs (cf.

Cleveland, 2005); they are distributed amongst the three upper tiers. “Tier 2” (T2)

energy costs include direct fuels as well as the energy embodied in the built capital and

other industrial goods and services used in the process. “Tier 3” (T3) energy costs

include T2 costs plus the energy equivalent of labor and government services. “Tier 4”

(T4) costs are the most comprehensive; they consist of T3 costs plus the energy cost of

any damages resulting from the depletion or pollution of the external process

environment, which can be measured in terms of ecosystem services. Figure 1.2 depicts

this energy cost tier structure, in which each tier is inclusive of everything below. In Fig.

1.3, these costs are presented in the context of a typical energy supply system.

12

Fig. 1.2 – The energy cost tier structure.

Fig. 1.3 – A typical energy supply system, adapted from Cleveland and Costanza

(1984).

13

2.2. EROI dynamics

Energy supply processes exhibit certain long run productivity dynamics. For

example, the EROI of non-renewable resource production naturally decays with the

depletion of the in situ resource stock. This is because, as Daly (1996, p.66) has pointed

out, surplus energy is a natural subsidy to the economy; it represents “value added” by

nature. Energy resources with more natural value added require less labor and capital for

delivery, sell for a lower market price, and therefore get produced and used up first.

Onshore oil from Texas, for example, was a much greater natural subsidy than is offshore

oil from the GOM. We refer to this phenomenon as the “depletion effect”.

The depletion effect does not apply to the production of renewable energy

resources because their supplies are unlimited. However, the available sites at which

renewable energies may be captured are limited, as is the maximum potential rate of

capture at each site. A long-term increase in the overall rate of renewable resource

production thus requires that a portion of the remaining available capture sites become

“saturated” with production. Because the most highly “subsidized” sites are saturated

first, EROI declines as production rates increase; we refer to this phenomenon as the

“saturation effect”.

Technological progress can offset or overcome depletion or saturation effects

through improvements in the energy efficiency of production. In the long run, a balance

of these two opposing forces determines EROI dynamics. If technology cannot

compensate for the effects of depletion or saturation, then EROI declines and the quality

14

of the resource diminishes. Conversely, if technology can overcome depletion or

saturation effects, then EROI increases and the quality of the resource is enhanced.

3. The offshore process

Gross production of U.S. offshore oil and natural gas has surged over the past

fifty years (Fig. 1.4). Historically, the GOM has been a hotspot for offshore extraction,

and in 2004 the U.S. Department of the Interior’s Minerals Management Service (MMS)

confirmed that production will continue in the region for yeas to come, estimating that

49% of the oil and 57% of the natural gas yet to be discovered offshore in the United

States are located there (MMS, 2004). While the existence of these energy resources is

critical to the nation’s future economic well-being, of equal importance is the amount of

already extracted energy that will be required to deliver the new fuel to society in a useful

form.

15

0

1

2

3

4

5

6

1960

1962

1964

1966

1968

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

Year

Qu

ad

rillio

n B

TU

Crude oil

Natural gas

Fig. 1.4 – Gross production of offshore oil and natural gas in the U.S., 1960 – 2004.

Source: Energy Information Administration.

To derive the EROI of GOM offshore extraction, the boundaries of this process

must first be established. As defined here, the “offshore process” refers exclusively to

the “upstream” sector of the offshore industry, including all activities necessary to find

and physically extract crude oil and natural gas from the offshore environment, but

excluding any further processing, storage, refinement, marketing, distribution, etc., of the

extracted fuel. Ei is in situ offshore crude oil and natural gas; Eo is extracted crude oil

and natural gas (to be used as input to the next process in series); Ec is the total energy

cost of the extraction.

16

Figure 1.5 illustrates an important characteristic of the offshore process: over

time, the depletion effect extends production from shallow waters to more challenging

deepwater environments. GOM offshore extraction can thus be viewed at various stages

of development by disaggregating the region by water depth and treating extraction in

each depth region as an independent process; processes operating in shallow water

regions are in later stages of development relative to those in deepwater regions.

0

10

20

30

40

50

60

70

80

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

Year

Pe

rce

nt

Crude oil

Natural gas

Fig. 1.5 – Percentage of gross energy production in the U.S. GOM from depths

greater than 200 m, 1992 – 2005. Source: Energy Information Administration.

17

4. Model specification

We designed a dynamic model to calculate the EROI of GOM offshore extraction

using Simile, an object-based, graphical modeling environment (Simulistics, Ltd.;

www.simulistics.com). The model diagram in Fig. 1.6 has been simplified from the final

version to highlight the model’s major components. The two box compartments, Eo and

Ec, are the model’s “state variables”; consistent with our analytical definition of process

state in Eq. (1), these variables cumulatively increase over time and uniquely define the

model at each time-step of its duration. The other relevant features of the model are

outlined below.

Fig. 1.6 – Simplified model diagram.

4.1. Temporal and spatial articulation

The model runs for a twenty-year period (1985 – 2004) at a yearly time-step. A

longer duration would have been preferred, however, the temporal extent was constrained

18

by data availability. The GOM is spatially disaggregated into four distinct sub-regions

defined by water depth: 0 to 60 m, 61 to 200 m, 201 to 900 m, and deeper than 900 m.

Extraction in each sub-region is considered a unique instance of the general offshore

process.

4.2. EROI calculation

The model calculates the EROI of offshore extraction in each of the four depth

regions and in the entire GOM at each time-step of the simulation. Annual gross

production includes both crude oil and natural gas; those data were obtained from the

MMS online database system (www.gomr.mms.gov). Energy cost data, however, are not

available and therefore must be calculated by the model internally. The approach is to

first derive monetary costs, and then convert them to energy costs.

The MMS has identified 11 major activity phases of the GOM offshore industry

(Dismukes et al., 2003). Nine phases are used in the model to derive monetary cost

(Table 1.1); two (“gas processing and storage: O&M” and “gas processing and storage:

construction”) are not because the frontier of the offshore process as defined above

excludes them. For each phase, the MMS has determined a standard physical cost unit

and its annual monetary cost (Table 1.1), as well as a sector-specific expenditure profile

(e.g., Table 1.2). By combining this information with data obtained from the MMS

online database system, the total monetary cost of each phase by water depth is derived

and then allocated to the appropriate economic sectors.

Sector-specific monetary costs can be converted to energy units using the energy

intensity factors of the various economic sectors. The energy intensity of an individual

19

economic sector is the energy cost per dollar of sector production (BTU/$). Based on the

input-output (I-O) techniques of Leonteif (1941) and methods described by Bullard and

Herendeen (1975) and Costanza (1980), Costanza and Herendeen (1984) have derived

energy intensities using both T1 and T3 energy costs for an 87-sector breakdown of the

1972 U.S. economy. These data are adjusted for inflation (to constant 1998$) and

technology (see below), and then are used to convert sector-specific monetary costs to

their energy equivalents, which are summed across sectors to determine the total energy

cost of each activity phase by water depth.

Table 1.1 – Activity phases of the offshore process and their annual per unit costs by

water depth (Dismukes et al., 2003).

Activity Phase 0-60 m 61-200 m 201-900 m 900 m+

Exploratory and development drillinga

Cost per well drilled ($000) 4,238 3,007 5,971 10,178

Production

Cost per producing well 240,908 253,764 263,152 271,070

Platform fabrication and installationb

Cost per platform ($ Million) 19.491 75.894 127.108 133.791

Pipeline construction and installationb

Cost per mile of pipeline 541,315 891,654 1,509,284 3,850,385

Pipeline operations and maintenance

Cost per MMBTU produced .0520 .0642 .0660 .0767

20

Workoversc

Cost per workover per well 13,704 14,385 14,566 14,566

Oil spills

Cost per gallon spilled 107.19 67.88 45.45 45.45

Platform abandonment and removalb,d

Cost per platform 878,555 1,816,058 9,664,348 12,710,826

All costs in constant 1998$.

a Exploratory drilling and development drilling, two distinct activity phases, are

aggregated into one general “drilling” category due to a lack of differentiation in the data

between wells drilled for development purposes and those drilled for exploratory

purposes; the average of the two costs is used for each depth.

b Denotes a fixed cost category; fixed costs are amortized evenly over the entire process

duration.

c Workover costs are the average of three major types of workovers: recompletions,

major workovers, and wireline services. It is assumed that each producing well has a

70% probability annually of having to undergo one of these three types, regardless of

water depth.

d Abandonment costs for each water depth are the average of several removal methods for

4-pile and 8-pile platforms.

21

Table 1.2 – Expenditure profile for platform abandonment and removal (Dismukes

et al., 2003).

IMPLAN

Sector

Sector

Description

0-60 m 61-200 m 201-900 m 900+ m

38 Oil & gas operations 0.14855 0.16929 0.17309 0.20139

50 New gas utility facilities 0.03732 0.04683 0.05043 0.05972

53 Misc. natural resource

facility construction

0.05050 0.03210 0.01563 0.01667

57 Other oil & gas field services 0.17102 0.11066 0.10253 0.01389

436 Water transport 0.58534 0.62886 0.64319 0.69028

506 Environmental/engineering

services

0.00728 0.01226 0.01513 0.01806

Total 1.00000 1.00000 1.00000 1.00000

4.3. Technology

The energy intensity factors calculated by Costanza and Herendeen (1984) reflect

1972 technology and therefore are not appropriate for this model considering its temporal

extent. To resolve this issue, the 1972 intensities are scaled based on a relative index of

the overall energy intensity of the U.S. economy. The most commonly used measure of

aggregate energy intensity is the “energy to gross domestic product” (E/GDP) ratio. This

measure, however, tends to overstate the extent to which improvements in energy

22

efficiency have occurred in an economy due to a disregard for structural change (cf.

Cleveland et al., 1984).

The U.S. Department of Energy’s Office of Energy Efficiency and Renewable

Energy has recently developed a new system of energy intensity indicators, the “energy

intensity indices”, that provide a more accurate measure of changes in the energy

throughput of an economy that actually result from changes in energy efficiency (i.e.,

from technological change). We use an adjusted E/GDP ratio, the “index of aggregate

intensity”, to scale the 1972 sector intensities so that they reflect 1985 technology. The

intensities can then be varied throughout a model run based on relative changes in the

index of aggregate intensity to simulate technological change; alternatively, they can be

held constant at 1985 levels to isolate the depletion effect.

23

5. Results and conclusions

0

5

10

15

20

25

30

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

Year

ER

OI

Tier 1

Tier 3

Fig. 1.7 – EROI of GOM offshore extraction using two alternative treatments of

energy cost (T1 and T3) and simulated technology, 1985 – 2004.

The EROI of GOM offshore extraction ranged from 10.1 to 25.4 in 2004

depending on how comprehensively energy costs were defined (Fig. 1.7; see also

Appendix A). This range is understated because the environmental damages incurred by

the process, which include for example the degradation of wetland ecosystems and the

storm protection services that they provide, are not accounted for. Nevertheless, the

results confirm the significance of indirect energy costs and emphasize the importance of

the energy cost tier structure (Fig. 1.2). In comparison, the EROI of U.S. onshore

24

petroleum extraction in the 1930s was at least 100 (Cleveland, 1992). More recent EROI

estimates for various methods of electric power generation are given in Fig. 1.8, however,

because energy costs are not specified, comparisons must be made with caution.

Fig. 1.8 – EROI for various methods of electric power generation (Kubiszewski and

Cleveland et al., 2007).

25

0-60 m

201-900 m

61-200 m

901 m+

201-900 m

901 m+

0-60 m

61-200 m

0

10

20

30

40

50

60

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

Year

ER

OI

Tier 1

Tier 3

Fig. 1.9 – EROI of GOM offshore extraction by water depth using two alternative

treatments of energy cost (T1 and T3) and constant 1985 technology, 1985 – 2004.

The productivity dynamics of the individual depth regions are presented in Fig.

1.9. Two distinct patterns prevail; the most striking is the dramatic increase in EROI for

the two deepwater regions (the primary cause of the recent increase in aggregate GOM

EROI). Because technology is held constant in this particular model run, these results

seem counterintuitive. What is increasing EROI if not technology, and what of the

depletion effect? To resolve these apparent inconsistencies, we must recall that the

deepwater processes are in early stages of development, and that the depletion effect is

predominantly a long run phenomenon. Thus, some other economic force, perhaps

economies of scale, must temporarily be at work.

26

In contrast, EROI in the 0 – 60 m and 61 – 200 m regions has steadily declined

since 1992 and 1996, respectively (see also Appendix B), indicating that resource

depletion may have just recently begun to decrease productivity in those regions.

However, when the impacts of technological progress are considered (Fig. 1.10), these

effects are almost completely offset. We therefore conclude that depletion in the GOM

has not yet significantly influenced the overall quality of the remaining reserves; thus far,

technology has provided sufficient compensation.

61-200 m

0-60 m

0

2

4

6

8

10

12

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

Year

ER

OI

Constanttechnology

Simulatedtechnology

Fig. 1.10 – T3 EROI of extraction in the 0 – 60 m and 61 – 200 m regions using

constant 1985 technology and simulated technology, 1985 – 2004.

In 2004, the MMS announced that, spurred by government incentives, crude oil

and natural gas production in the GOM were expected to increase by 43% and 13%,

27

respectively, over the following ten years (Melancon et al., 2004). Substantial increases

in depletion rates along with continuously “maturing” deepwater processes may prove to

be technologically insurmountable in the near future. To illustrate the implications of a

decline in EROI for future production in the region, we extended the computer generated

GOM T3 EROI curve to create two differing productivity scenarios based on two

alternate worldviews. The first scenario is technological optimism, represented by an

increasing EROI; the second is technological skepticism, represented by a declining

EROI (Fig. 1.11).

0

2

4

6

8

10

12

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

2009

2011

2013

Year

ER

OI

Technologicaloptimism

Technologicalskepticism

Fig. 1.11 – Historical GOM T3 EROI (1985 – 2004) and two alternate scenarios for

the near future (2005 – 2013).

28

0

2

4

6

8

10

12

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

2012

2013

Year

Qu

ad

ril

lio

n B

TU

Grossproduction

Netproduction

Technologicalskepticism

Technologicaloptimism

Fig. 1.12 – Historical GOM energy production (1985 – 2004) and two alternate

scenarios for the near future (2005 – 2013).

Figure 1.12 depicts the net production curves that correspond to the two alternate

EROI scenarios; they were calculated based on the MMS gross production forecast

(Melancon et al., 2004). An increasing EROI results in the convergence of gross and net

production, while a declining EROI causes them to diverge. This emphasizes the

fundamental difference between gross and net energy: whereas gross energy is strictly a

measure of resource quantity, net energy accounts for both quantity and quality. Net

energy is therefore a superior measure of fuel supply and should be a key driver of the

overall energy strategy of a society.

29

References

Bullard, C.W., Herendeen, R.A., 1975. The energy costs of goods and services. Energy

Policy 3, 268-278.

Cleveland, C.J., 1992. Energy quality and energy surplus in the extraction of fossil

fuels in the U.S. Ecological Economics 6,139-162.

Cleveland, C.J., 2005. Net energy from the extraction of oil and gas in the United States.

Energy 30(5), 769-782.

Cleveland, C.J., Costanza, R., 1984. Net energy analysis of geopressured gas resources

in the U.S. Gulf coast region. Energy 9, 35-51.

Cleveland, C. J., Costanza, R., Hall, C.A.S., Kaufmann, R., 1984. Energy and the United

States economy: a biophysical perspective. Science 225, 890-897.

Cleveland, C.J., Hall, C.A.S., Herendeen, R., 2006. Energy returns on ethanol

production. Science 312,1746.

Costanza, R., 1980. Embodied energy and economic valuation. Science 210, 1219-1224.

Costanza, R., Herendeen, R.A., 1984. Embodied energy and economic value in the

United States economy: 1963, 1967, and 1972. Resources and Energy 6,129-164.

Cottrell, W.F., 1955. Energy and Society: The Relation between Energy, Social Change

and Economic Develolpment. McGraw-Hill, New York.

Daly, H.E., 1996. Beyond Growth. Beacon Press, Boston, Massachusetts.

Dismukes, D.E., Olatubi, W.O., Mesyanzhinov, D.V., Pulsipher, A.G., 2003. Modeling

the Economic Impacts of Offshore Oil and Gas Activities in the Gulf of Mexico:

Methods and Applications. Prepared by the Center for Energy Studies, Louisiana

State University, Baton Rouge, La. U.S. Department of the Interior, Minerals

Management Service, Gulf of Mexico OCS Region, New Orleans, La. OCS Study

MMS 2003-018.

Farrell, A.E., Plevin, R.J., Turner, B.T., Jones, A.D., O’Hare, M., Kammen, D.M., 2006.

Ethanol can contribute to energy and environmental goals. Science 311, 506-508.

Hagens, N., Costanza, R., Mulder, K., 2006. Energy returns on ethanol production.

Science 312, 1746.

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Hammerschlag, R., 2006. Ethanol's energy return on investment: A survey of the

literature 1990 - Present. Environmental Science & Technology 40(6), 1744-1750.

Kidd, S., 2004. Nuclear: is there any net energy addition? Nuclear Engineering

International 49(603), 12-13.

Kubiszewski, I., Cleveland, C.J., Endres, P.K., 2007. Energy return on investment

(EROI) for wind energy. In: Cleveland, C.J., editor. Encyclopedia of Earth.

Leontief, W.W., 1941. The structure of American economy, 1919, 1929: an empirical

application of equilibrium analysis. Harvard University Press, Cambridge,

Massachusetts.

Melancon, M.J., Baud, R.D., Boice, A.G., Bongiovanni, R., DeCort, T., Desselles, R.,

Kazanis, E.G., 2004. Gulf of Mexico Oil and Gas Production Forecast: 2004-2013.

U.S. Department of the Interior, Minerals Management Service, Gulf of Mexico

OCS Region, New Orleans, La. OCS Study MMS 2004-065.

Minerals Management Service (MMS), 2004. Assessment of undiscovered technically

recoverable oil and gas resources of the nation’s outer continental shelf, 2003

update. MMS Fact Sheet RED-2004-01.

Tyner, G., Costanza, R., Fowler, R.G., 1988. The net-energy yield of nuclear power.

Energy 13, 73-81.

31

Appendix A

The EROI of GOM offshore extraction using two alternative treatments of energy cost

and simulated technology.

0 – 60 m 61 – 200 m 201 – 900 m 900 m+ GOM

Year T1 T3 T1 T3 T1 T3 T1 T3 T1 T3

1985 20.7 8.52 21.1 8.744 12.91 3.987 0 0 19.4 7.67

1986 22.2 9.251 21.6 8.992 13.58 4.251 0 0 20.4 8.17

1987 22.9 9.528 21.7 9.08 14.77 4.653 0 0 20.9 8.38

1988 23 9.548 21.7 9.078 15.08 4.743 0 0 21 8.39

1989 23 9.557 21.7 9.08 15.36 4.829 0 0 21 8.39

1990 23.3 9.657 21.5 8.981 16.63 5.225 0 0 21.2 8.45

1991 23.4 9.732 21.6 9.016 18.71 5.908 0 0 21.4 8.54

1992 23.5 9.82 21.7 9.112 21.25 6.73 0 0 21.7 8.68

1993 23.5 9.805 21.7 9.085 23.58 7.487 0 0 21.8 8.71

1994 23.6 9.824 21.7 9.094 25.99 8.26 0.203 0.06 21.9 8.78

1995 23.7 9.841 21.7 9.077 28.52 9.061 0.644 0.18 22.1 8.85

1996 23.7 9.857 21.8 9.122 31.5 10 1.226 0.34 22.4 8.94

1997 23.8 9.88 21.9 9.169 34.27 10.86 2.708 0.76 22.7 9.04

1998 23.9 9.912 22 9.21 37.72 11.94 5.041 1.41 23.1 9.19

1999 23.9 9.922 22.1 9.23 43.22 13.67 7.901 2.2 23.6 9.37

2000 23.8 9.874 22 9.216 47.89 15.13 11.45 3.18 23.9 9.51

32

2001 23.8 9.865 22.1 9.242 51.91 16.38 15.5 4.3 24.4 9.68

2002 23.7 9.835 22 9.192 55.01 17.36 20.46 5.66 24.8 9.83

2003 23.6 9.796 21.8 9.13 56.89 17.98 26.26 7.25 25.2 9.97

2004 23.5 9.73 21.6 9.043 57.95 18.32 31.71 8.75 25.4 10.1

33

Appendix B

The EROI of GOM offshore extraction using two alternative treatments of energy cost

and constant 1985 technology.

0 – 60 m 61 – 200 m 201 – 900 m 900 m+ GOM

Year T1 T3 T1 T3 T1 T3 T1 T3 T1 T3

1985 20.74 8.52 21.13 8.74 12.91 3.99 0.00 0.00 19.40 7.67

1986 21.83 9.10 21.21 8.84 13.37 4.19 0.00 0.00 20.09 8.04

1987 22.43 9.35 21.26 8.90 14.49 4.57 0.00 0.00 20.51 8.22

1988 22.49 9.35 21.23 8.89 14.77 4.65 0.00 0.00 20.55 8.21

1989 22.48 9.34 21.18 8.87 15.02 4.72 0.00 0.00 20.53 8.20

1990 22.64 9.40 20.91 8.74 16.18 5.08 0.00 0.00 20.60 8.22

1991 22.69 9.44 20.91 8.74 18.15 5.73 0.00 0.00 20.74 8.29

1992 22.75 9.49 21.00 8.80 20.53 6.50 0.00 0.00 20.92 8.38

1993 22.67 9.45 20.90 8.75 22.74 7.22 0.00 0.00 20.97 8.40

1994 22.62 9.42 20.82 8.72 24.93 7.92 0.19 0.05 21.04 8.42

1995 22.58 9.40 20.69 8.66 27.23 8.65 0.61 0.17 21.13 8.45

1996 22.56 9.37 20.72 8.68 29.94 9.51 1.16 0.33 21.29 8.50

1997 22.50 9.34 20.72 8.67 32.34 10.26 2.55 0.71 21.44 8.54

1998 22.42 9.30 20.65 8.64 35.28 11.17 4.71 1.31 21.64 8.61

1999 22.26 9.23 20.52 8.58 40.05 12.66 7.29 2.03 21.90 8.71

2000 21.98 9.10 20.32 8.50 43.97 13.89 10.44 2.90 22.06 8.75

34

2001 21.76 9.01 20.19 8.44 47.13 14.86 13.92 3.85 22.27 8.82

2002 21.51 8.91 19.89 8.33 49.50 15.62 18.13 5.01 22.43 8.88

2003 21.24 8.80 19.57 8.21 50.77 16.04 23.02 6.35 22.57 8.93

2004 20.91 8.66 19.21 8.06 51.26 16.21 27.49 7.57 22.60 8.94

35

Chapter 2.

On semantics and scale: Developing a dynamic multi-scale model of the ecosystem

service water regulation

Abstract

Interest in ecosystem services (i.e., the set of ecosystem functions that contribute to

human welfare) has surged in recent decades and is currently still on the rise. Although

by now these phenomena have become relatively well established and understood from a

qualitative perspective, they have yet to be universally quantified. This paper details the

initial development and testing of a dynamic, spatially explicit, computer simulation

model of the ecosystem service “water regulation”, which has been created as a part of

the broader Multi-scale, Integrated Models of Ecosystem Services (MIMES) initiative.

We discuss: 1) the conceptualization of this service as the process of hydrologic

abstraction; 2) its formalization, which extends the conventional functionality of the well

known and widely used “runoff curve number” method of the United States Department

of Agriculture; and 3) the application of the formal model to the Winooski watershed

(Vermont, U.S.A.) and to the entire globe.

1. Introduction

Ecosystem services are defined as the set of ecosystem functions that support,

directly or indirectly, human welfare (Costanza et al., 1997; Daily, 1997). Table 2.1 is a

list of ecosystem services and their corresponding ecosystem functions. The services

36

listed are fundamentally diverse in several ways. For example, some are critical to

human wellbeing (e.g., climate regulation, food production), while others simply enhance

it (e.g., recreation, aesthetics). Furthermore, ecosystem services, like ecological patterns

and processes in general, operate on a wide range of characteristic scales, from local and

regional scales (e.g., water regulation, soil formation) up to the global scale (e.g., climate

regulation). Despite these inherent dissimilarities, all ecosystem services do share an

important unifying feature: they represent benefits that bypass the monetary economy and

accrue directly to the general public, as opposed to any single private entity. Thus, they

have long been considered “free gifts of nature” according to the major doctrines of

economic value. Unfortunately, this situation has the potential to result in their

undervaluation, abuse, and subsequent destruction, i.e., the “tragedy of the commons”

(Hardin, 1968).

Table 2.1 – A list of ecosystem services and their corresponding ecosystem functions

(Costanza et al., 1997).

Number Ecosystem Service Ecosystem Functions

1 Gas regulation Regulation of atmospheric composition.

2 Climate regulation Regulation of global temperature, precipitation, and

other biologically mediated climatic processes at

global or local levels.

3 Disturbance regulation Capacitance, damping and integrity of ecosystem

response to environmental fluctuations.

37

4 Water regulation Regulation of hydrological flows.

5 Water supply Storage and retention of water.

6 Erosion control and

sediment retention

Retention of soil within an ecosystem.

7 Soil formation Soil formation processes.

8 Nutrient cycling Storage, internal cycling, processing and acquisition

of nutrients.

9 Waste treatment Recovery of mobile nutrients and removal or

breakdown of excess or xenic nutrients and

compounds.

10 Pollination Movement of floral gametes.

11 Biological control Trophic-dynamic regulations of populations.

12 Refugia Habitat for resident and transient populations.

13 Food production That portion of gross primary production

extractable as food.

14 Raw materials That portion of gross primary production

extractable as raw materials.

15 Genetic resources Sources of unique biological materials and

products.

16 Recreation Providing opportunities for recreational activities.

17 Cultural Providing opportunities for non-commercial uses.

38

Fortunately, following the recent introduction of the concept there has been a

significant burst of interest in ecosystem services. The vast majority of the initial

research has been of a subjective nature, focusing mainly on their description and

classification (e.g., MA, 2003), and especially their valuation. For example, based

primarily on preference-oriented, or “willingness-to-pay”, valuation techniques, the non-

market values of the various individual ecosystem services listed in Table 2.1 have been

estimated in hundreds of separate studies, for a range of different ecosystems. A

comprehensive synthesis of this research has suggested that the total value of the world’s

ecosystem services far exceeds the value of conventional marketed economic goods and

services (Costanza et al., 1997).

In comparison to this relative abundance of primarily qualitative information,

quantitative knowledge of ecosystem services is currently lacking. Kremen (2005) has

pointed out that measurement of the underlying biophysical role of ecology in providing

ecosystem services has generally been neglected, and that quantifying this role is an

important pending research agenda. The current Multi-scale, Integrated Models of

Ecosystem Services (MIMES) project is an ambitious attempt to build such quantitative

understanding through dynamic, spatially explicit, computer simulation modelling. By

formally representing ecosystem function in this manner, the resulting suite of models (in

combination with geographic information system (GIS) technology and web-based

facilities) will provide land managers, policymakers, and the general public with a

sophisticated, standard toolset to analyze the dynamics of the ecosystem services in any

39

particular area of interest and estimate how their value and function may change under

various management and policy scenarios.

As a part of the larger MIMES initiative, we have developed a model to measure

and map the ecosystem service “water regulation” at multiple scales. In this paper, we

discuss: 1) the conceptualization of that service as the process of hydrologic abstraction;

2) its formalization, which extends the familiar “runoff curve number” method originally

developed by the United States Department of Agriculture (USDA); and 3) the

application of the formal model to the Winooski watershed (Vermont, U.S.A.) and to the

entire globe.

2. Semantics

Quantifying an ecosystem service requires clear semantics. For example, what

exactly is the meaning of “water regulation”? Costanza et al. (1997) describe its

underlying ecological function generally as “Regulation of hydrological flows” (Table

2.1), while Farber et al. (2006) describe it simply as “Flow of water across the planet

surface”. As examples of the human-derived benefits that result from this function,

Costanza et al. provide “Provisioning of water for agricultural (such as irrigation) or

industrial (such as milling) processes or transportation”, whereas Farber et al. offer

“Modulation of the drought-flood cycle; purification of water”. While these qualitative

descriptions and examples provide simple and concise introductions to the concept, they

offer little immediate insight on how it might be measured, mapped, or formally modeled.

40

A more meaningful and unambiguous conceptualization of water regulation is

needed; we develop one here based on the above citations. First, we assume that the

“flow” referred to in both functional descriptions pertains only to freshwater hydrologic

flows occurring at the watershed scale. Second, we assume that the examples given by

Farber et al. (namely, the “modulation of the drought-flood cycle” and the “purification

of water”) are the two primary benefits to human populations that this service embodies.

It follows that direct runoff is a key biophysical force involved in water

regulation. Direct runoff is the result of rainfall excess; it occurs, for example, when the

rate of rainfall exceeds the infiltration capacity of a soil (Hortonian overland flow), or

when rainfall continues after a soil profile has become completely saturated (saturation

overland flow). The magnitude of direct runoff is dependent on a variety of physical and

meteorological factors, some of which (e.g., land cover characteristics) are highly

susceptible to anthropogenic change. In general, more direct runoff increases the peak

discharge rates of rivers and decreases groundwater recharge, thus increasing the relative

frequency of floods and droughts in a watershed. Conversely, less direct runoff decreases

peak discharge rates and increases groundwater recharge, thus tempering, or

“modulating”, the drought-flood cycle.

In addition, there is a strong connection between direct runoff and water

purification. Runoff water bypasses the natural filtration system that soils provide.

Moreover, as the water moves, it picks up various natural and human-made pollutants,

which is the primary cause of problematic nonpoint source pollution.

41

A simple expression of conservation of mass summarizes the rainfall to runoff

conversion:

Q = P – L (1)

where Q = direct runoff; P = rainfall; and L = hydrologic abstractions, which in the short

term consist primarily of interception storage, surface storage, and infiltration to the

subsurface. Based on this expression and the foregoing discussion, we conceptualize

water regulation as follows: “unregulated water” is the quantity Q of direct runoff that

results from a rainfall event, whereas “regulated water” is the quantity L, i.e., the

abstracted portion of that event. The meaning of water regulation is now clear; it is the

process of hydrologic abstraction, which can be measured universally in terms of

regulated water volume. Based on these simple, yet powerful semantics, a formal method

of measurement can be devised.

3. Scale

Scale refers to the temporal or spatial dimension of a particular phenomenon, and

scaling to the transfer of knowledge across and between scales (Turner et al., 1989).

Most ecological patterns and processes occur at certain “characteristic scales”, or

characteristic ranges of scales, which best reflect their intrinsic behavior (Clark, 1985).

Ecosystem services, for example, operate at their own distinctive scales, or ranges of

scales, at which their dynamics can be most accurately described and easily understood.

Characteristic scale is often described in terms of a typical spatial extent or

temporal frequency. However, for many natural phenomena this information is generally

42

not known a priori, and must be either detected (e.g., through fractal analysis) or

described by subjective observation (Wu, 1999). Based on the conceptualization of water

regulation presented above, it may be inferred that the process inherently operates within

the watershed range of spatial extents and at a daily event frequency.

There also exist several types of scale that may be associated with, but are not

inherent to, an ecosystem service. For example, the scale at which an ecosystem service

is modeled (i.e., the “modeling scale”) may be dependent on the scale of the policy-

making that the model is intended to inform (i.e., the “policy scale”). In general, laws

and regulations concerning a particular ecosystem service should be implemented at a

scale that is commensurate with the intrinsic scale of that service. In practice, however,

this may not always be the case. For example, environmental policies are rarely

implemented at the watershed scale; more often, they are implemented at the state,

national, or even global scales. Thus, when modeling a service such as water regulation

scaling may be required to bridge “scale gaps”.

Scaling involves altering one or both of the two primary components that

characterize scale: resolution (or grain, in spatial contexts) and extent. Resolution is the

precision of measurement, and extent is the total spatial or temporal expanse under

consideration (Tuner et al., 1989). “Upscaling”, for example, is translating information

from a finer resolution or smaller extent (i.e., a local scale) to a coarser resolution or

larger extent (i.e., a broader scale), whereas “downscaling” is translation in the opposite

direction.

43

Spatial scaling is a core problem in ecosystem service modeling because

ecosystem services are dependent on the spatial patterns of land use and land cover,

which are heterogeneous across most landscapes. Spatial scaling with dynamic models

typically consists of two distinct steps: 1) correctly defining and quantifying the fine

scale heterogeneity, and 2) properly aggregating the heterogeneous information to obtain

predictions at a broader target scale (King, 1991). Using GIS and remote sensing

technologies, spatial heterogeneity can be explicitly quantified in the form of digital maps

that become model parameters and inputs. Aggregation of this heterogeneity generally

poses a greater challenge as it involves the alteration of those parameters and inputs. Wu

and Li (2006) provide a detailed summary and comparison of a variety of dynamic

modeling spatial aggregation schemes.

4. A formal model of water regulation

Formal rainfall-runoff modeling has a relatively lengthy history. A large variety

of models and methods spanning wide ranges of conceptual, temporal, and spatial

complexities have been developed, from early single-event empirical methods, such as

the “rational method” of Mulvaney (1850), to recent continental-scale macro-models,

such as those of Vörösmarty et al. (1989) and Arnell (1999). It is notable that models and

methods at all points along this spectrum are currently in use. No single model is

appropriate for every possible task, its usefulness must be judged with the specific task at

hand in mind.

44

For the present modeling purpose, we have adopted the USDA Soil Conservation

Service (SCS) “runoff curve number” method, which is detailed in the National

Engineering Handbook Section 4: Hydrology (NEH-4) (USDA-SCS, 1985). The curve

number method is a well known and widely used empirical procedure for the estimation

of direct runoff from storm rainfall; it is based on the following rainfall-runoff relation:

Q = (P – Ia)2 / (P – Ia) + S if P > Ia; Q = 0 otherwise (2)

where Q = direct runoff (in); P = rainfall (in); S = maximum potential retention (i.e.,

rainfall not converted to runoff) that could possibly occur if rainfall were to continue

without limit, which consists mainly of the infiltration that happens after runoff begins

(in); and Ia = initial abstraction, which consists mainly of the interception, infiltration,

and surface storage that occur before runoff begins (in).

In order to remove the independent parameter Ia from Eq. (2), the SCS has

suggested a linear relationship between Ia and S:

Ia = S (3)

where = initial abstraction ratio, which has been assigned a default value of .2 based on

empirical findings ( = .2). This value, however, can vary as figures ranging from 0.0 to

0.3 have been reported (Ponce and Hawkins, 1996).

Assuming = .2 and substituting Eq. (3) into Eq. (2) yields the more familiar

version of the rainfall-runoff expression that is most commonly applied in practice:

Q = (P – 0.2S)2 / (P + 0.8S) if P > 0.2S; Q = 0 otherwise (4)

For convenience in application, the SCS has mapped S, which ranges from 0 to , to the

dimensionless parameter CN, which ranges from 0 to 100:

45

S = (1000 / CN) – 10 0 CN 100 (5)

where CN is considered constant for a particular storm event and is determined based on

the “soil cover complex”, a combination of the existing soil and land cover conditions.

The SCS has estimated CN for a variety of soil-cover complexes based on: 1) hydrologic

soil group (HSG) classified as A, B, C, or D according to the soil’s minimum infiltration

rate; 2) land cover classified according to Anderson et al. (1976); 3) hydrologic surface

condition; and 4) antecedent moisture condition (USGS-SCS, 1985).

The curve number method is thus a simple, predictable, and stable empirical

procedure for estimating the direct runoff that results from a given rainfall event.

Moreover, the relatively few required environmental inputs (HSG, land cover, rainfall)

are ordinarily available for most watersheds. Thus, the method is extremely popular,

albeit somewhat criticized (cf. Ponce and Hawkins, 1996), and is featured in many of the

hydrologic computer models currently in use, such as AGNPS (Young et al., 1987), EPIC

(Williams, 1995), and SWAT (Arnold et al., 1996).

We modified and extended the traditional curve number method in several

different ways:

1. Average hydrologic surface and antecedent moisture conditions are assumed; CN is

thus uniquely determined by the combination of HSG and land cover. Within the

MIMES framework, land cover is classified according to 11 biomes, or ecosystem

types, which together encompass the entire surface of the planet: Open Ocean,

Coastal Ocean, Forests, Grasslands, Wetlands, Lakes/Rivers, Deserts, Tundra,

Ice/rock, Croplands, and Urban. This ecological classification is an aggregation of

46

the16-biome scheme used by Costanza et al. (1997). Table 2.2 is the initial “default”

CN table for this 11-biome scheme; it was derived based on the CN tables originally

published by the SCS for the Anderson et al. classification (USGS-SCS, 1985).

Table 2.2 – Default CN parameterization for the 11-biome MIMES land cover

scheme and HSG.

A B C D

Open ocean NA NA NA NA

Coastal ocean NA NA NA NA

Forests 36 60 73 79

Grasslands 49 69 79 84

Wetlands 65 65 65 65

Lakes/Rivers 98 98 98 98

Deserts 55 72 81 86

Tundra 55 71 81 89

Ice/Rock 98 98 98 98

Croplands 67 78 85 89

Urban 89 92 94 95

2. After solving Eq. (5) and then Eq. (4) for direct runoff (Q), regulated water (L) is also

determined by subtracting Q from the given precipitation (P) based on Eq. (1). Q and

L are then converted from depths to volumes based on the given area of study.

3. The extended method is embedded in a dynamic system and run as a continuous

simulation driven by time-varying daily rainfall data, where each day represents a

47

unique storm event. Daily volumes of direct runoff and regulated water are

determined at each time-step and cumulatively summed over time. Simile, a

declarative modeling a simulation environment (Simulistics Ltd.;

www.simulistics.com) was the design tool.

4. The dynamic model is spatially distributed and augmented with GIS and remote

sensing technologies. Simile, billed as “system dynamics plus objects”, allows for

spatially explicit modeling through object-based representation. The dynamic “unit

model” is instantiated multiple times across a spatially disaggregated landscape

composed of either square unit cells or polygons. The individual instances are all

created from the same model object, but each is uniquely parameterized according to

spatially referenced data (HSG, land cover, rainfall) that correspond to its associated

geographic location. At each time-step, unique volumes of direct runoff and

regulated water are calculated across the modeled landscape and are summed to

determine area totals. Using this spatially explicit approach, the model can be

directly extrapolated (cf. King, 1991) to any spatial extent where the required data are

available.

In addition, this approach extends the format of a GIS, which can be used process,

organize, and store all spatially referenced data to be used in the model. For example,

digital land cover and HSG maps of matching homogeneous spatial units can be

overlain in a GIS to generate the soil-cover complex map, which in the model

determines CN for each spatial unit.

48

5. The spatially explicit model is adjusted to run at multiple spatial resolutions. Coarse

gaining the model (i.e., upscaling by increasing grain size) increases the size of each

spatial unit and decreases their overall number. If a larger spatial unit becomes

heterogeneous in terms of soil-cover complex, then the direct runoff for each existing

complex can be individually calculated and then weighted to determine a “composite”

estimate of runoff for the entire spatial unit:

Qcomp = (Qi Ai) / Ai (6)

where Qcomp = composite runoff (in); i = index for each soil-cover complex that exists

in the spatial unit; Ai = area of complex i, expressed as a percentage of the total unit

area (%); and Qi = estimated runoff for complex i (in). (CN weighting may also be

performed, however, because the weighting occurs prior to the runoff calculation,

aggregation error is introduced (USDA-SCS, 1985).)

Solving Eq. (6) at the broader scale requires that the fine scale soil-cover complex

information is aggregated and maintained as a percentage distribution of the total

area. Each broad scale spatial unit must be associated with an array of percentage

values, not a single scalar value as in simpler “lumping” aggregation schemes, such

as “majority rule” (Fig. 2.1). Eq. (6) thus minimizes aggregation error and can be

distributed across at any spatial resolution, from the maximum resolution (limited

only by computer resources) to a single aggregated spatial unit; only proper

aggregation and adjustment of the soil-cover complex input parameter is required.

Figure 2.2 is a simplified graphical representation of the final multi-scale model.

49

Fig. 2.1 – Two alternative methods of scaling: a) by “majority rule” and b) by

maintaining a percentage distribution.

Fig. 2.2 – Simplified model diagram.

50

5. Results and discussion

5.1. Calibration and validation

When applied to gauged watersheds, the model can be calibrated and validated by

comparing the modeled runoff to observed gage data. Because the primary purpose of

the model is to estimate the total volume of water regulated by an area over a given time

period (rather than the specific pattern of regulation within that time period), its

performance can be evaluated at the conclusion of each model run by calculating the

relative error between the total modeled runoff and the corresponding observed total.

Model calibration thus involves minimizing this error by first “coarse tuning” the model

by adjusting (Eq. (3)), and then “fine tuning” it by tweaking the various CN parameters.

We applied the model to the Winooski watershed (Vermont, U.S.A.; area ≈ 2,712

km2). The land cover pattern for this area has been mapped via remote sensing circa

1992 and 2001; the 1992 data were used for model calibration and the 2001 data for its

validation. Because the model does not yet account for the direct runoff that results from

snowmelt, the temporal extent was limited to June 1 through October 31 of each year

(153 daily time-steps). The analysis was conducted at a 330 m gain (56,100 spatial

units); the input data are briefly summarized below:

Daily mean streamflow data (ft3/s) for 1992 and 2001 were obtained from the

USGS via the National Water Information System: Web Interface

(http://waterdata.usgs.gov/nwis). They were recorded at the furthest downstream

gauging station on the Winooski River (near Essex Junction), to which the

majority of the watershed drains. The open-source Hydrograph Separation

http://waterdata.usgs.gov/nwis

51

Program (HYSEP) (Sloto and Crouse, 1996) was used to separate each

streamflow hydrograph into its baseflow and direct runoff components, and the

resulting direct runoff portion was used to evaluate the accuracy of the modeled

runoff.

Daily rainfall data (in) for 1992 and 2001 were obtained from the National

Climatic Data Center (NCDC). Although spatially distributed rainfall data would

have been ideal, these data are not easily obtainable for many watersheds, and

they are computationally impractical for most daily analyses. Thus, point

measurements from seven weather observation stations located throughout the

watershed were used to derive daily watershed averages, which were assumed to

fall uniformly across the modeled landscape.

Land cover data (30 m) for 1992 and 2001 were obtained from the University of

Vermont (UVM) Spatial Analysis Lab (SAL). The “Land Use/Land Cover for the

Lake Champlain Basin, Circa 1992 and Circa 2001” raster layers were previously

derived using the National Land Cover Database (NLCD 2001), ancillary GIS

data, and Landsat satellite imagery. These data were reclassified into the 11-

biome MIMES land cover scheme; the reclassified 2001 layer is displayed in Fig.

2.3.

HSG data (90 m) were also obtained from the UVM SAL. The HSG raster layer

was constructed based on the information currently contained in the “Hydrologic

Group” column of the component table of the NRCS SSURGO-2 dataset. This

layer was used for both 1992 and 2001; it is displayed in Fig. 2.4.

52

Fig. 2.3 – 2001 land cover pattern (30 m) of the Winooski watershed.

Fig. 2.4 – HSG pattern (90 m) of the Winooski watershed.

53

The results of the analysis are presented in Figs. 2.5, 2.6, and Table 2.3. The

model was most sensitive to changes in and, because the Winooski watershed is

predominantly forested, the forest cover curve numbers. These were the only parameters

that required calibration (Table 2.4).

0.00E+00

1.00E+06

2.00E+06

3.00E+06

4.00E+06

5.00E+06

6.00E+06

7.00E+06

8.00E+06

6/1/

01

6/8/

01

6/15

/01

6/22

/01

6/29

/01

7/6/

01

7/13

/01

7/20

/01

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/01

8/3/

01

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/01

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/01

9/7/

01

9/14

/01

9/21

/01

9/28

/01

10/5

/01

10/1

2/01

10/1

9/01

10/2

6/01

Day

Dir

ect

ru

no

ff (

m3

/d

ay)

Modeled runoff

Observed runoff

Fig. 2.5 – Modeled and observed runoff in the Winooski watershed, June 1 –

October 31, 1992.

54

0.00E+00

1.00E+06

2.00E+06

3.00E+06

4.00E+06

5.00E+06

6.00E+06

7.00E+06

8.00E+06

6/1/

01

6/8/

01

6/15

/01

6/22

/01

6/29

/01

7/6/

01

7/13

/01

7/20

/01

7/27

/01

8/3/

01

8/10

/01

8/17

/01

8/24

/01

8/31

/01

9/7/

01

9/14

/01

9/21

/01

9/28

/01

10/5

/01

10/1

2/01

10/1

9/01

10/2

6/01

Day

Dir

ect

ru

no

ff (

m3

/d

ay)

Modeled runoff

Observed runoff

Fig. 2.6 – Modeled and observed runoff in the Winooski watershed, June 1 –

October 31, 2001.

Table 2.3 – Results of model calibration (1992) and validation (2001).

Year Grain (m) Total modeled

runoff (m3)

Total observed

runoff (m3)

Relative

error (%)

Total regulated

water (m3)

1992 330 9.58e+07 1.01e+08 -4.92 9.78e+08

2001 330 6.71e+07 6.40e+07 4.92 7.57e+08

55

Table 2.4 – Calibrated parameters.

Parameter Default value Calibrated value

.2 .044

CN Forests A 36 36

B 60 54

C 73 68

D 79 75

The resulting modeled and observed hydrographs are in reasonable agreement for

both years with a few exceptions, which are assumed to be artifacts of spatially lumping

the rainfall data. More importantly, the relative errors between total modeled and

observed runoff for both years are well below 10%, which is an acceptable error

threshold for this analysis. Based on these results, we report that the Winooski watershed

regulated 9.78e+08 m3 of water from June 1 through October 31 in 1992, and 7.57e+08

m3 of water for the same time period in 2001.

Figure 2.7 displays the spatial distribution of the total regulated volume for 2001.

The areas that provided more regulation are lightly shaded, while those that provided

relatively less are more heavily shaded. This information could be aggregated in various

ways (e.g., by town or county) and could certainly be of practical use in a variety of land

management and environmental policy contexts; for example, it could be used as input to

a “payment for ecosystem services” (PES) system.

56

Fig. 2.7 – Total water regulation (thousand m3) in the Winooski watershed from

June 1 – October 31, 2001 at 330 m grain.

5.2. Scenario analysis

With the model calibrated, a wide variety of land cover and rainfall scenarios are

possible. We ran two general land cover scenarios for 2001 with the goal of determining

a relative scale by which the watershed’s regulatory performance could be rated. A

completely forested scenario determined the scale’s upper bound (i.e., maximum total

regulation, minimum total runoff), and a completely urbanized scenario determined its

lower bound (i.e., minimum total regulation, maximum total runoff). The results (Table

2.5) indicate that from June 1 – October 31, 2001 the regulatory performance of the

57

Winooski watershed was near full potential; it regulated 86.42% of the total portion of

rainfall that was available for either regulation or runoff during that time. Using the

hydrograph corresponding to the historical land cover data as a baseline scenario, Figs.

2.8 and 2.9 emphasize the benefits that were provided in terms of the modulation of the

drought-flood cycle. This relative rating system could be effectively used to track the

regulatory performance of a single watershed over time or to compare the performance of

multiple watersheds.

Table 2.5 – Scenario analysis.

Year Land cover scenario Total regulated

water (m3)

Water regulation

service rating (%)

2001 100% forest 7.88e+08 100.00

2001 Historical pattern 7.57e+08 86.42

2001 100% urban 5.58e+08 0.00

58

0.00E+00

1.00E+06

2.00E+06

3.00E+06

4.00E+06

5.00E+06

6.00E+06

7.00E+06

8.00E+06

6/1/

01

6/8/

01

6/15

/01

6/22

/01

6/29

/01

7/6/

01

7/13

/01

7/20

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7/27

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8/3/

01

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/01

8/24

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8/31

/01

9/7/

01

9/14

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9/21

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10/5

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10/1

2/01

10/1

9/01

10/2

6/01

Day

Dir

ect

ru

no

ff (

m3

/d

ay)

100% forested

Historical data

Fig. 2.8 – Modeled runoff in the Winooski watershed June 1 – October 31, 2001

using two alternate land cover scenarios: historical data and completely forested.

0.00E+00

5.00E+06

1.00E+07

1.50E+07

2.00E+07

2.50E+07

6/1/

01

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01

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6/29

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01

9/14

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9/21

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9/28

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10/5

/01

10/1

2/01

10/1

9/01

10/2

6/01

Day

Dir

ect

ru

no

ff (

m3

/d

ay)

100% urban

Historical data

Fig. 2. 9 Modeled runoff in the Winooski watershed June 1 – October 31, 2001

using two alternate land cover scenarios: historical data and completely urbanized.

59

5.3. Scale effects

To investigate scale effects, i.e., changes in the results of an analysis caused by

changing the scale at which the analysis is conducted, the model was coarse-grained and

executed multiple times using resampled 2001 data (Fig. 2.10). The scale effects (Table

2.6) were essentially negligible. Although grain was increased to almost 20 times its

initial size (resulting in a significantly greater decrease in the number of spatial units), the

model lost very little precision; relative error changed by a total of only .10%. Moreover,

the model did not require re-parameterization at each new spatial resolution.

These results represent a very favorable tradeoff in terms of computer resources.

Spatially distributed models often suffer from excessive computational demand, which

increases exponentially with the number of spatial units. A very large number of spatial

units can be a major problem even for the most advanced computing facility. We have

shown that coarse graining this model can alleviate its computational demand at the

expense of very little precision. Thus, the model can be applied at whatever resolution is

appropriate for the location at hand and the computer resources available.

60

a) b)

c) d)

Fig. 2.10 – Total water regulation (thousand m3) in the Winooski watershed, June 1

– October 31, 2001 at 4 grain sizes: a) 450 m, b) 900 m, c) 2700 m, and d) 6000 m.

Table 2.6 – Scale effects.

Grain

(m)

Number of

spatial units

Total modeled

runoff (m3)

Total observed

runoff (m3)

Relative

error (%)

Total regulated

water (m3)

330 56,100 6.71e+07 6.40e+07 4.92 7.57e+08

450 30,098 6.71e+07 6.40e+07 4.91 7.57e+08

900 7,575 6.71e+07 6.40e+07 4.90 7.57e+08

2700 850 6.71e+07 6.40e+07 4.84 7.57e+08

6000 192 6.71e+07 6.40e+07 4.82 7.57e+08

61

5.4. The global application

Although there may be several conceptual and empirical problems inherent in

applying this model at the global scale, we proceeded with caution for two primary

reasons: 1) to emphasize the need for mapping and modeling ecosystem services at all

scales; and 2) to provide an initial “default” estimate (however crude it might be) of the

global pattern of water regulation. The analysis was performed at a 1 deg grain (50,400

spatial units); the data that were used are as follows:

A global land cover (1 km) raster layer, classified according to the 11-biome

MIMES classification scheme, was obtained from the UVM SAL. This layer

represents a reclassification of the Global Land Cover 2000 (GLC2000) dataset.

Because a direct mapping from the 22-class GLC2000 scheme did not exist, a

series of geo-processing tasks and ancillary data sets (e.g., ETOPO2 global digital

elevation model, World Wildlife Fund Terrestrial Ecoregions) were employed; the

resulting layer is displayed in Fig. 2.11.

A global HSG (5 arcmin) raster layer was also obtained from the UVM SAL. To

generate this layer, an intermediate global dataset indicating the percent

composition of clay in topsoil, relative to sand and silt, was derived from the Food

and Agriculture Organization (FAO) “Digital Soil Map of the World”. These

intermediate data were then reclassified according to the following rules: 1 – 10%

= A; 11 – 20% = B; 21 – 40% = C; and 41 – 100% = D. Global HSG is displayed

in Fig. 2.12.

62

Fig. 2.11 – Global land cover pattern (1 km).

Fig. 2.12 – Global HSG pattern (5 arcmin).

Global precipitation data were not used in this analysis. Instead, the model was

run in a static context assuming 2 in of uniform rainfall across the entire surface of the

planet. Water regulation in each spatial unit is expressed as the regulated percentage of

the 2 in event (Fig. 2.13). These results are not calibrated and were obtained using the

63

model’s default parameter settings (Table 2.2). However, they do represent a first

approximation of global water regulation and can be used to make general comparisons

across the globe.

Fig. 2.13 – Global water regulation (1 deg) as the regulated percentage of a 2 in

rainfall event.

6. Conclusion

As the concept of ecosystem services continues to gain momentum, the need to

develop a standard quantitative understanding of these services is becoming more critical.

While the model presented in this paper is certainly in need of additional refinement,

testing, and review, it is a successful “proof of concept” and represents an important

initial step towards building such an understanding. It also highlights the importance of

the broader MIMES initiative and demonstrates the large amount of research and

development that will be needed to bring that project to fruition. The significance of such

64

research is profound, as it may largely determine the precision with which we can

manage and conserve ecosystem services in the future.

65

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dynamic modeling to inform environmental management

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