Volume 51, Number 2/1999

and more . . .

Bringing Life into the Picture p. 2

Where the Waves Are p. 16

Shallow Water, Deep Science p. 26
. A practical, objective set of

nalytical solutions, numerical

onal case studies is under

 include massively parallel

memory computers combined

mpling networks using mobile

ient mapping and adaptive

ork simulation and control that

odel input/output is underway.

ecture driven by evolving

s is a design goal.

g and prediction research and

d in universities, the Naval

nis Space Center, Mississippi

other Navy and government

. A principal mission is to

s and prediction tools to the

ate transition of products to

orology and Oceanography

uch as the Fleet Numerical

raphy Center and the Naval

coordinates its research efforts

Warfare Systems Command

METOC Data Acquisition,

ion Program funded by the

 The challenge of advancing

ational ocean modeling and

engineering, interdisciplinary

ration, procurement, training,

lected topics in basic research

nt. The state-of-the-art in data

sampling are reviewed. An

, finite element modeling is

articularly relevant to coastal

geometry. Understanding and

ve research are examined. The

omprehensive, but rather to

important current activities

astal ocean prediction.

Tom Curtin

Office of Naval Research

After an initial career in aerodynamics, George Mellor turned his scientific interests to atmospheric and oceanic turbulent boundary layers. He established the Program in Atmospheric and Oceanic Sciences at Princeton University, which is associated with NOAA’s Geophysical Fluid Dynamics Laboratory (GFDL). Mellor’s research involvesthe study of estuarine and oceanic dynamics through the use of numerical ocean models. Professor Mellor is the author ofmore than one hundred journal articles covering turbulent boundary layers, ocean modeling and other topics in fluid dynamicsand a textbook on Introductory Oceanography. He is a fellow of the American Meteorological Society and the AmericanGeophysical Union. The Princeton Ocean Model (POM), developed by Mellor and Alan Blumberg in the 1970s, is usedwidely by scientists, institutions and industry, including the U.S. Navy, NOAA’s National Environmental Center and theNational Ocean Service.There is an internet users group of over 350 users worldwide. POM includes an imbedded secondmoment turbulence closure sub-model to provide vertical mixing coefficients, a sigma vertical coordinate scaled on waterdepth, orthogonal curvilinear horizontal coordinates and an “Arakawa C” finite differencing scheme. The horizontal griddifferencing is explicit whereas the vertical differencing is implicit. The latter eliminates time constraints for the verticalcoordinate and permits the use of fine vertical resolution in the surface and bottom boundary layers. The model has a freesurface and a split time step. Complete thermodynamics have been implemented. The turbulence closure sub-model is oftencited in the literature as the Mellor-Yamada turbulence closure model, but the model is based on turbulence hypotheses byRotta and Kolmogorov which were extended to stratified flow.

Current users of POM are the beneficiaries of forty years of research. The branch of this evolution at Princeton is

illustrative. In the 1960s, turbulent boundary layer experiments and models were investigated by H.J. Herring and students.In 1969, GFDL was established at Princeton under J. Smagorinsky. In the early 1970s, T.Yamada developed atmosphericboundary layer formulations accounting for turbulence. In the late 1970s based on these advances, the first version of POMwas created by G. Mellor and A. Blumberg. From 1980-83, Dynalysis, a company formed by Blumberg and Herring,applied POM to Gulf of Mexico circulation studies. Simultaneously, L-Y Oey modeled the Hudson/Raritan Estuary. Sincethe mid-80s, improved versions of POM have been developed for Delaware Bay (Galparin), the Arctic Ocean (Kantha,Hakkinen), the Mediterranean Sea (Zavatarelli), the North Atlantic (Ezer) and the coastal zone of the eastern United States(Aikman).

Further information including a list of journal publications can be found in http://www.aos.princeton.edu/wwwpublic/

htdocs.pom/

Dr. George Mellor

Program in Atmospheric and Oceanic Sciences

Princeton University

Princeton, NJ
Volume 51, Number 2 1

Bringing life into the picture

Coupled Physical/Biological Models for

the Coastal Ocean

by Daniel R. Lynch

Where the waves are

Improving Wind Wave Prediction on the

Ocean

by Charles L. Vincent and Robert E. Jensen

Shallow water, deep science

Adaptive Sampling for Ocean Forecasting

by Allan R. Robinson and Scott M. Glenn

Modeling by assimilation

Oceanographic Data Assimilation in the

1990s: Overview, Motivation and Purposes

by Paola Malanotte-Rizzoli

Profiles in Science

Dr. George Mellor

2

16

26

39

53
2 Naval Research Reviews

Building a realistic model of the coastal ocean is still a

long way from reality—but scientists believe they are

on the threshold of that possibility. In the past, scientists

have approached the challenge by modeling the physical

and biological aspects of the environment separately.

While physical models have progressed to a high degree of

realism, biological modeling is just now blossoming due to

advanced computer capabilities. Coupled physical-biological modeling—where the biological model depends on

output from the physical model—is an ultimate modeling

goal. Military and civilian scientists are interested in developing models that include both the physical and biological

aspects of the coastal ocean in this coupled manner.

As the Navy and Marine Corps are increasingly concerned with operating in the littoral, or coastal, regions,

their interest in understanding the biological phenomena in
Volume 51, Number 2 3

these waters has grown correspondingly. The Navy traditionally has

used physical models for ocean forecasting. Coupling these powerful tools to biological modeling will help decision-makers assess

the potential effects of naval operations on local biology. The

Navy-Marine Corps team is far from indifferent to environmental

issues, which occupy them not only during combat—recall the

concerns during the Gulf War over Iraqi ecological vandalism—but

also during peacetime. Most naval operations are carried out during peacetime under civilian regulations. Concern over the effects

of an oil spill on local marine life, ability to predict hazardous algae

blooms, understanding zooplankton population dynamics, controlling greywater discharge, and so on, are no longer fringe issues.

In this article, Daniel Lynch discusses physical modeling techniques and how they might be coupled to biological models.

Lynch’s suggestions offer researchers some interesting directions

for future work. - D.B.
4 Naval Research Reviews

Daniel R. Lynch

Dartmouth College

Hanover, NH

Coupled Physical/Biological Models for the

Coastal Ocean

Abstract

Prospects are reviewed for site-specific models, which

couple physics and biology. Physical models have advanced

to the point where real-time operational systems (combining

land- and ship-based elements) can be built with entry-level

resolution relative to biological needs. Coupling biology to

these presents a vast frontier of opportunity. Some general

and simple guidelines are offered in a hierarchy beginning

with abiotic motion and moving progressively through

several biotic features: behavior, growth and development,

and reproduction. Examples from the Gulf of Maine are

provided.

Introduction

This discussion concerns models, which simulate

biological processes occurring within, and influenced by, a nontrivial physical environment. We

begin with the premise that spatially explicit models

are desirable. This is evident from several perspectives. First, all data is obviously spatially explicit.

Second, all ecosystems are spatially explicit and

each occupies a potentially unique niche in parameter space. And third, all-important operational

questions including ecosystem management and emergency

decision-making are fundamentally tied to a specific system

and its details. We therefore address the notion of constructing spatially explicit, coupled physical-biological simulations.

The simulation of the physical environment in the coastal

ocean has now advanced to a high degree of sophistication

and realism. We are endowed with a set of canonical

equations; several decades of progress in computational

mathematics and machinery; remarkable advances in

observational technology; and, an emergent cohort of bright,

energetic computational scientists. All of these support the

conjecture that skillful spatially explicit circulation models

can be constructed and operated in many of the world’s

coastal oceans. The importance of this cannot be overstated:

that it is possible to construct a 4-D (three space dimensions

plus time) physical environment comprising motion, turbulence, and hydrographic fields at “entry-level” resolution

(order 1 km). This sets the stage for spatially explicit coupled

models. And because the coupling is strictly one-way in the

oceanic context — i.e. physics affecting biology but not

vice-versa — continued progress in physical simulation has a

momentum of its own which will lead to continuous improvements in simulated physical environments.

Biological simulation of the coastal ocean is, relative to its

potential, far less advanced. The potential biological statespace is enormous and in practice not

realizable on any computer; and while

some canonical sets of equations have

emerged, their parameterization remains

elusive in realistic systems. Further, the

biological observational base is generally

far less developed than its physical

counterpart. As a result of this, many

biological simulations will necessarily be

posed, parameterized, initialized, and

forced by hypothesis rather than from

observation. The vague question ‘what are the dynamics of

the biological system?’ is not generally meaningful under

these conditions.

Despite these difficulties, extremely valuable site-specific

coupled simulations can be constructed. Clearly, it is

necessary to simplify the biological relationships being

modeled if any practical progress is to be made. The most

potent simplifications are those that accompany clarification

and refinement of specific hypotheses. Given that a “comprehensive” coupled model is not possible, what ideas can be

examined with the tools at hand, which include a 4-D sitespecific physical environment? Pursuit of scientific objectives along this direction can lead to very productive and

SPATIALLY

EXPLICIT MODELS.

Models that portray

phenomena within real

shelf systems, with

realistic topography,

forcing, and biota.
Volume 51, Number 2 5

revealing coupled simulations. The very fact that biological

simulation is less advanced means that the most exciting

opportunities are likely to occur along this frontier.

We thus arrive at a practical view of coupled physicalbiological simulation, which emphasizes problem-driven

simulations in a site-specific context. The principles are:

• use the best available circulation model to provide a sitespecific realistic physical environment; know its

strengths and weaknesses;

• know the organisms under study – their basic life

histories, their patterns of abundance and distribution,

and their mysteries (Mangel, 1993);

• formulate the least complex biological model needed to

answer focused questions about the system which can be

tested against observation. It is likely that these will

initially center around space-time relationships relevant

to specific organisms or assemblages, implied by the

circulation;

• seek and accept inescapable conclusions from

the simplest modeling exercises needed to

support them; and

• refine the biological questions carefully,

building a hierarchy of inference. A likely

hierarchy suggested below is to begin with

abiotic (passive tracer) simulations, then to

add behavioral features, and finally to add

feeding and reproduction.

Below we will illustrate these ideas in the context

of an ongoing study of the Gulf of Maine system.

Modeling Physics

Gulf of Maine: The Gulf of Maine is a semienclosed coastal sea on the eastern North American shelf, stretching from the Cape Cod Islands

eastward to the Bay of Fundy and the Nova

Scotian shelf, and from the coast of Maine/New

Brunswick seaward to the shelf break on the

southern edge of Georges Bank.

The basic Gulf-wide circulation is depicted in

Figure 1 – a composite schematic that summarizes

numerous observational, theoretical, and modeling data.

Many important shelf processes are operative in the Gulf,

including two primary and distinct inflows across the Scotian

Shelf and through the Northeast Channel; deepwater formation in the three major Gulf basins; tides, tidal mixing, and

tidal rectification; wind; stratification and frontal circulation;

freshwater inflow along the coast; and local estuarine

processes.

The Gulf has served as a development laboratory for the

Dartmouth Shelf Models for a decade. Fortunately, we have

been guided by earlier seminal work by D. Greenberg and

colleagues (Greenberg, 1990). These studies defined the

basic barotropic modes of the system and established many

essential modeling principles for the Gulf, which remain

relevant and “right” today.

Nested and Graded Meshes: In a survey of contemporary simulation experience, Lynch et al. (1995) observed that

achieving adequate resolution in coastal ocean simulations

remains a widely shared concern. In the Gulf of Maine, for

example, tidal rectification and frontal circulation can

demand resolution of order 1-2 km, while properly equilibrated inflows from the Scotian Shelf demand upstream

spatial coverage of order 4 shelf widths, i.e. horizontal

coverage of order 1000 km. Similarly in the vertical, proper

resolution of surface and bottom heat and momentum

transfers demands vertical resolution of order 1 m, with total

depth reaching 300 m in the Gulf basins and 1000 m or more

at the shelf break. Uniform gridding over these ranges

produces an estimated 250,000 horizontal cells, with perhaps

on average 200 vertical cells. Coupling these spatial needs

with the requirements of simulating nonlinear dynamics in

tidal time produces a formidable computational challenge.

We have used the finite element method to meet this challenge. In this method the horizontal is discretized in unstructured grids of triangles. This permits the use of freely

variable resolution to fit topography and circulation features;

Fig. 1 – Gulf of Maine topography and circulation.

[Source: McGillicuddy et al., 1998]
6 Naval Research Reviews

seamless nesting of near-and far-field domains; and locally

enhanced resolution for detailed studies coupling biological

and physical processes.

Figure 2a shows an example mesh that covers the Gulf of

Maine plus the Gulf of St. Lawrence and the Grand Banks.

This mesh is configured for separate or coupled studies of

these regions. Our primary Gulf of Maine domain lies within

it, extending from the Laurentian Channel to the western tip

of Long Island, and seaward to roughly the 1000 m isobath,

beyond which it terminates in a gently sloping idealized

ocean. Baseline resolution on Georges Bank is of order 3 km,

and approaches 1-2 km across the steep northern flank. The

flexibility of the finite element method allowed us to fill this

domain with only 6756 horizontal nodes and 12877 triangles

as a baseline mesh.

Several refinements and alterations have been added for

individual studies. Examples of sub-meshes appear in

Figures 2b, c for the Maine Coastal Current and Georges

Bank. We have used these smaller, more refined meshes in a

nested fashion, driving open water boundary conditions with

the results of larger-domain simulations. Some experiences

with the nesting are reported by Lynch et al. (1997); and

with mesh refinement, by Lynch et al. (1995) and Luettich

and Westerink (1995).

The finite element method has served remarkably well in this

capacity. It supports a single wide-area calculation with

variable resolution; and facilitates nested calculations by

making possible natural (e.g. topography-following) terminations of local meshes. And overall, the highest possible

resolution is achieved by avoiding wasted resolution, which

inevitably results from structured-grid approaches.

Climatology, Hindcast, Forecast: Our earliest modeling

experiences have concentrated on the production of a

climatology for the Gulf. This occupied considerable

energies in the assembly of forcing data, the establishment of

boundary conditions, mesh refinement, and finally scrutiny

of the solutions. The end result has been the archival of a

standard climatology realized as a sequence of six bimonthly

realizations of tide and subtidal residual flow fields (Naimie,

1995; Lynch et al., 1996, 1997). These are displayed in

Figure 3. The general circulation features displayed in figure

1 are clearly present: a cyclonic circulation around the Gulf

with substructures over the deep basins; anticyclonic

circulation over Georges Bank with partial recirculation; and

throughflow from the Scotian Shelf. The seasonal modulation of these features is significant. To date this climatology

and its diagnostic predecessor have been compared with

moored current measurements (Lynch et al., 1993; Naimie et

al., 1994; Naimie, 1996); turbulence dissipation rates (Horne

et al., 1996); and drifter trajectories (Naimie et al., 1999)

with satisfying results.

This climatology has been used in numerous coupled

Fig. 2a – Northwest Atlantic Shelf

mesh. [Source: Greenberg et al., 1998]

Fig. 2b – Maine Coastal Current mesh.

[Source: Lynch et al., 1997]

Fig. 2c – Georges Bank mesh. [Source:

Lynch et al., 1998]
Volume 51, Number 2 7

physical-biological studies to date, some of which are

reviewed below. The premise in this type of modeling is that

long-term mean tendencies of the coupled system can be

“explained” by the union of average physical fields and

average biology. This is not to say that either the physics or

the biology is linear or lacks variation; only that at the points

of coupling, the climatological mean interaction is prominent

in the mean outcomes. If we conceptualize the biological and

physical fields as the sum of climatological means (m, n) and

variations (d, e) about those means, then their average

interaction would have two contributions: the mean interaction mn plus the covariance E(de), a Reynolds’ stress-like

term. Failure of the mean interaction to replicate long-term

system tendencies is an indication that the covariance of

physics and biology is important. In itself this would be a

substantive conclusion.

The climatology is the starting point for several subsequent

investigations. Containing as it does a complex set of 4-D

structures with seasonal modulation, it constitutes the best

prior estimate for circulation at any particular time. In the

absence of observations, this estimate is the only substitute

for the null case (zero motion) which would be a foolish

choice. Beyond climatology, we have two types of physical

simulations: hindcast and forecast. In both cases the

problem is to make reasonable adjustments to the climatology to fit specific observations.

An example of a hindcast is shown in Figure 4. In this case

we were concerned with hindcasting the detailed circulation

on Georges Bank during a 2-week period for which both

hydrography and CTD data were available. The general

procedure is to force a prior estimate with climatological

boundary conditions and observed wind, heat flux and

hydrography. Adjusting the open-water boundary conditions

minimizes discrepancies between simulated and observed

velocities. Figure 4a shows the observed velocity; tides are

dominant. The remaining unexplained velocity, posthindcast, is depicted in Figure 4b. In essence this is a leastsquares problem, with a nonlinear forward model. It is

solved iteratively as in Figure 5. The availability of a fast,

linearized inverse is critical. Details can be found in Lynch et

al. (1998).

The forecasting problem is distinguished by the timing of

data availability and the necessity of making a sequence of

simulations, each assimilating a growing observational base

(Figure 6). In April-June of 1999, the first Gulf of Maine

Fig. 3 – Gulf of Maine climatological circulation.

Illustrated is the streamfunction governing mean

subtidal flow in each of six bimonthly seasons.

Contour interval is 0.1 Sverdrup. [Source: Naimie,

1995]

Fig. 4b – Residual (unexplained)

velocity after inversion of EN265

ADCP data. This is the discrepancy

between modeled velocity and the

data in figure 4a, following

assimilation. Note the change in

scale from figure 4a. [Source: Lynch

et al., 1998]

Fig. 4a – Observed ADCP data for

cruise EN265 on Georges Bank.

[Source: Lynch et al., 1998]
8 Naval Research Reviews

level resolution relative to biological needs. The design skill

lies in assembling the right combination of prior estimate,

networked instruments and databases, and interactive

nesting/refinement of calculations to support specific tasks.

Observational System Simulation Experiments:

Perhaps the most challenging opportunity for modeling today

is in the design of field sampling plans. A realistic sitespecific simulation can be used as “truth” and sampled

according to a real or proposed sampling program. Measurement error may be incorporated into the model output

sampling. These measurements may then be used to reconstruct the circulation using a candidate assimilation procedure, and the errors in the reconstructed field quantified

against the “truth.” This general idea provides a complete

evaluation of sampling plan plus assimilation procedure, and

is a gateway to exploring the limits of inference imposed by

practical computational and observational equipment, as well

as available theory. OSSE’s are the practical design tool for

the construction of systems as depicted in Figure 7.

Observational System Simulation Experiments have been

conducted relative to Georges Bank hydrographic (Lynch

and Naimie, 1998) and zooplankton (McGillicuddy et al.,

1999) fields.

Coupling Biology

Assume the existence of a comprehensive physical simulation. What can be done with it, given the litany of difficulties

mentioned in the introduction? We suggest starting with the

simplest aspects of the coupled system, and working outFig. 5 – Inversion procedure. The forward model

QUODDY (green) is a comprehensive 3-D simulation

with full nonlinearity and advanced turbulence

closure. The inverse model (red) is based on a

linearization of the forward. It deduces boundary

condition improvements needed to minimize the

unexplained velocity data. Because of the

nonlinearity, the loop is closed by iteration.

Fig. 6 – Forecast system time lines.

Fig. 7 – The future of ocean modeling. Data will be

obtained from a variety of networked instruments

and services and integrated seamlessly into dataassimilated simulations running concurrently on

land- and ship-based platforms.

operational modeling exercise was carried out at sea, with

daily forecasts of the Georges Bank circulation. This realtime assimilation procedure is using a climatological prior

estimate of forcing and circulation; sequential forecasts of

atmospheric forcing and related oceanic wind-band

pressure boundary conditions; and assimilation of CTD,

drifters, and ADCP data into forecast products on the local

mesh shown in Figure 2c. The experiment showed that

using today’s workstations, a 3-day limited-area forecast

can be computed at sea within a half-day of the closing time

for atmospheric data; and that forecasts could be expected to

predict drifter trajectories within a few km over a few days.

Archived results from this at-sea experience will provide an

experimental testbed for evaluating different assimilation

strategies.

These and other experiences support the position that sitespecific real-time operational systems, combining land- and

ship-based elements as in Figure 7, can be built with entry-
Volume 51, Number 2 9

wards/upwards from there. First we review two basic

modeling strategies. Then we suggest an approximate 4-level

hierarchy of complexity.

The Physical/Biological Interface: There are two basic

approaches for constructing coupled physical-biological

simulations. The first, conventional approach mimics that

which has been successful in the physical modeling: construct Eulerian fields representing densities of organisms in

various categories, and write partial differential equations for

their transport and evolution. The canonical form is the

advective-diffusive-reactive equation

(1)

with c the Eulerian density, v the fluid motion, J the

nonadvective (dispersive) flux, R the net source. An essential

additional feature is the behavioral transport vector q,

representing active motion relative to the ambient fluid. Note

we do not assume anything about its divergence.

Many coupled systems have been cast in this framework

(e.g. Franks et al., 1986; Fasham et al., 1990);

computationally it requires only a natural extension of

algorithms used to transport physical fields, plus the closure

of the biological terms q and R. Experience shows successful

simulations with relatively large numbers of Eulerian

variables; and in particular nonlinear, density-dependent

relations in the source term R are natural computationally.

However, the specific rendering of biological ideas about e.g.

development and behavior, into closures for q and R, can be

awkward, because one is dealing only with an aggregation,

not individual organisms per se. We refer to this modeling

strategy as the Eulerian or Concentration-Based Model

(CBM).

A distinctive alternative is the Lagrangian, Individual-Based

Model (IBM) (DeAngelis and Gross, 1992). In this approach,

one simulates individual organisms separately, writing a set

of ordinary differential equations for individual evolution

through physical (x) and biological (b) spaces:

(2)

(3)

The terms ε are stochastic terms representing individual

variability. The basic formulation is for each individual; the

population is the assembly of many such individuals,

appropriately initialized. This formulation provides a direct

and natural means of simulating specific organisms with

specific behavioral and other relationships to the environment.

Incorporation of experimental information can be quite

natural in this setting; and natural variability in biotic

processes is easily incorporated through the stochastic terms.

As a result, detailed biological resolution is possible at the

level of individuals and populations, provided the balance of

the physical and biological system is available as Eulerian

fields. (See e.g., Werner et al., 1996; Carlotti and Wolf,

1998; Bryant et al., 1998). The simulation of density

dependence is fundamentally problematic in this approach,

as it poses a classical n-body problem, which can be very

unfavorable for large systems.

Both types of models are in common use; see the recent issue

of Fisheries Oceanography (Coombs et al., 1998) for a

sampling of contemporary applications. We have used both

to advantage in the Gulf of Maine work described below.

Because of their complementary strengths and weaknesses, a

mature simulation is likely to have both types of models

interacting; for example an IBM approach to specific target

species, coupled to a more general CBM model for the

balance of the ecosystem.

Considerable care must be exercised in the specification of

the random variables ε. The biological variation represents a

substantive aspect of the system and an opportunity to

exploit the natural strength of the IBM approach. The motion

variation is typically treated as a random walk process, with

parameters derived from the modeled hydrodynamic

turbulence. Although this is simple in the case of uniform

mixing, such is rarely the case in the coastal ocean. The

specification of random walk models in heterogeneous media

is a significant subject in itself and several detailed studies

are available. (Thompson, 1987; Hunter et al., 1993; Okubo,

1986). The simplest generalization to the inhomogeneous

case is likely to have the unintended consequence of concentrating individuals in low-mixing areas, an unphysical result.

Motion and its implications: The first, baseline requirement is “know your circulation fields”. Given the availability

of 4-D physical fields (motion, turbulence, hydrography) on

complex topography, there are millions of space-time

trajectories of potential interest. These can be explored with

the simplest abiotic models. Doing so in a way that illuminates biological issues is the first level of coupled modeling

– in this case, coupling the physics to a biological question.

It is important to give this seemingly elementary step its

proper respect. The motion imposes a set of potentially

complex space-time patterns as an abiotic- or null-model

baseline. Understanding and recognizing them is critical.

Contributing to these patterns are

• the basic advective pathways in the system and the

space-time relations which they imply for organisms;

• the presence of convergence/divergences in the flow and

their ability to concentrate organisms;

• the basic residence times for organisms entrained in

various circulation features;
10 Naval Research Reviews

• the impact of spatially variable hydrodynamic dispersion

– either shear dispersion or eddy diffusivity.

As an example, we recently completed a study of Calanus

finmarchicus, a dominant copepod in the Gulf of Maine. This

animal is observed in population centers in the deep basins

of the Gulf during summer, with development arrested in a

nearly mature developmental stage (diapause). Activation in

the December/January timeframe results in the individuals

moving toward the surface, maturing to adulthood and

beginning the production of two to three generations of

offspring prior to the end of the growing season, perhaps

June. The offspring move through 12 developmental stages,

with the earliest stages presumed important in the diet of

larval Cod and Haddock. Questions surrounding this

population include the relationships among time and place of

activation and the subsequent pathways to the bank; the vital

rates along these pathways; the space-time patterns of

Calanus occurrence on the bank, especially the production

of the earliest offspring; and the presence or absence of selfsustaining annual pathways which would return offspring to

the deep basins from which their grandparents originated.

Many of these issues can be addressed with carefully

constructed passive (or nearly passive) tracer studies. In

particular, the initial resting stock may be expected to live for

2 months or more, and therefore a simulation of their

transport alone, subject to baseline mortality (decay), is a

simulation of the transport of reproductive potential. An

example appears in Figures 8a, b. These are the results of

clouds of passive tracer initially present in one of the deep

basins, transported in either the vertically averaged flow or

concentrated in a near-surface layer. The outcomes are

complex, and different. The surface layer moves about twice

as fast and is more effective in delivering animals to Georges

Bank; the vertically averaged flow is slow and follows the

deeper topography. Additionally,

the surface layer concentrates

surface-seeking organisms at

downwelling zones which create

transport lanes and aggregation

hot spots. And, the surface layer

cloud has developed a bifurcation. Using these and other

nearly passive simulations, we

have been able to confirm that

the deep basins of the Gulf are

capable of populating most of

Georges Bank, each having its

own distinctive space-time

signature. Inflow from the

Scotian Shelf also contributes to

the Southern Flank of the Bank

in its own characteristic pattern.

These passive features are the

manifestation of fundamental

constraints on all of the coupled physical/biological outcomes. It is important to accept them as natural tendencies of

the system. Comparison with available data allowed the

refinement of a three-layer, 3-field model accounting for the

initial generation -- a deep immobile reservoir of resting

copepodites; an intermediate layer of copepodites exiting

diapause and transported in the vertically averaged flow;

and a surface layer of newly-molted adults. These simulations allowed us to deduce the size of the previously unmeasured near-bottom population, from the observed persistence

higher in the water column; the unmeasured population

appears to be comparable to that measured. A related

conclusion is that source regions in the Gulf provide a

persistent, rather than an impulsive, loading of adults to

Georges Bank. The exit from diapause appears to be prolonged over 2 months.

Finally, any activation of adult reproduction in this model led

immediately to an undeniable problem: although the adult

populations were correctly placed in space/time, the offspring were far too early relative to the data. The most likely

explanation for this phenomenon emerged as a reproductive

delay due to limited food supply during the transit from the

deep basins to the Bank; and this is consistent with observations of primary productivity. The resulting conceptual

model is summarized in cartoon form in Figure 9.

Behavior as an adjunct to the hydrodynamic motion: The above case study calls attention to biological

behavior as an important mediator of the motion. The passive

tracers which are confined to the surface layer move faster

and in different directions than their depth-mean counterparts, and show the concentrating (diluting) effect of layer

convergence (divergence). Implied is a behavioral assumption that the animal being modeled can regulate its depth in a

complex physical environment — in that sense, it is not

passive at all.

Fig. 8a – Passive transport of

Calanus initialized over Jordan

Basin; vertically-averaged flow.

[Source: Lynch et al., 1998]

(a) (b)

Fig. 8b – Same as figure 8a, but the

cloud is confined to a 25-meter thick

surface layer. [Source: Lynch et al.,

1998]
Volume 51, Number 2 11

As a rule of thumb,

individual organisms can be

expected to sustain

swimming of the

order one bodylength per second.

This adds a behavioral transport

vector to the

hydrodynamic

transport; and as in

the hydrodynamics,

it can be divided

conceptually into

advective (mean

individual tendency)

and non-advective

(individual variability) parts. Closure

of this behavioral transport in terms of the physical environment (velocity, turbulence, light, stratification), the biotic

environment (food, predators), and the target organism itself

(developmental stage, nutritional status, prior stress, etc.) is a

fundamental issue for any biological simulation in a complex

circulation field.

As an example, Werner et al. (1993) simulated the egg and

larval stages of Cod and Haddock spawned on Georges Bank

using simple IBM’s. Initially, observed depth distributions

were used to close the behavior. It was found immediately

that the assumed near-surface positioning of the egg stage

resulted in transport off the bank (a fatal trajectory) of the

entire cohort; this led to the serious reexamination of the

appropriateness of the sparse data for this stage. Generally,

these early and inescapable results have endured. Later

simulations with refined physical fields and IBM’s continue

to show near-surface individuals are swept off the bank,

while deeper individuals are more likely to be retained and

advected to areas with chances for successful survival.

Essentially, the right behavior is critical to larval survival in

this system.

Comparing these simulations with data, one must guard

against an inherent bias toward the survivors. Fundamentally,

in nature we are able to observe only the survivors, which for

these populations is a tiny percentage. The literature suggested that older larvae in this system preferred deeper

positioning, and also horizontal positioning closer to the

center of the bank. The simulations indicate that these two

tendencies are exhibited by the passive behavioral system,

since near-surface trajectories leave the system (die) and

deeper (surviving) trajectories which sample the bottom

boundary layer have a shoalward tendency. While the passive

system does not account completely for these observed

effects, it nevertheless highlights the danger in interpreting

outcomes of a coupled system in terms of biological behavior alone, especially when the observable outcomes in nature

are biased toward the survivors.

As in the case of the Calanus calculations above, these are

very simple biological simulations that have provided

significant insight about the nature of the system and its

observation.

Feeding and development: The individual-based

modeling context is naturally extended to include feeding

and development, provided there are suitable relations for

ingestion and growth, and a suitable model for the prey field.

As an example, Werner et al. (1996) added an energetic

model which balanced food ingestion against metabolic costs

to determine net growth for an individual larval fish. The

trophodynamic relations in this case were available from

rearing studies. These were integrated into the larval fish

behavioral IBM described above. The resultant state of each

individual therefore consisted of position, weight, and age.

The environment included hydrodymanics (velocity and

turbulence) and food in various size classes. The spatially

variable food data were assembled from historical observations. Example results appear in Figure 10 that express the

relative effects of feeding success and transport on larval

survival on Georges Bank. Essentially, survival in these

simulations requires a) retention in the Georges Bank

system; and b) integrated growth in excess of the “death

barrier” as illustrated in Figure 10. These simulations called

attention to an apparent critical gap in the food supply,

whereby simulated first-feeding larvae were systematically

undernourished, and to the likely role of other species (e.g.

microzooplankton) in the diet at this life stage.

Lynch et al. (1999) extended this study by incorporating

reproducing populations of two prominent zooplankton

species, in order to avoid the sparse observations of the

earliest/smallest prey life stages. Using the same IBM for

Fig. 9 – Conceptual model resulting form the union of simulation and Calanus data: a)

horizontal; b) vertical. [Source: Lynch et al., 1998].

(a) (b)
12 Naval Research Reviews

larval fish, and simplified prey population dynamics from

Lynch et al. (1998) and McGillicuddy et al. (1998), maps of

feeding rate were constructed for the Bank (Figure 11).

These results indicate the surprising opportunity for Calanus

eggs to be an important dietary item for first-feeding larvae.

One of the findings in this study was the critical role of

turbulence in affecting predator-prey encounter rates, and

successful ingestion. Increasing turbulence favors the former,

but disfavors the latter. The balance of these appears critical

to the first-feeding larvae, for which high levels of turbulence has a net negative effect. The turbulent dissipation rate

used in these studies was taken from the modeled hydrodynamics as part of the physical environment experienced by

the individual larva. Continued study of the proper parameterization of turbulence and its impact on larval feeding is

needed.

Reproduction: The larval fish IBM’s discussed so far have

had no need to close the life cycle, since the period of

interest has been limited to the first few months of a surviving individual’s full life span. In the zooplankton case,

however, the life cycle involves several generations in a

single year, and reproduction is a necessary ingredient in a

relevant model.

In the Eulerian model such as that described above for

Calanus, this is incorporated by introduction of separate

Eulerian fields for every important development stage. A

developmental conveyor-belt effect then occurs as the

population ages, with residence times in each stage given as

the inverse of the stage duration. In effect we have ‘advection’ through the conveyor belt. But as in hydrodynamic

advection, artificial diffusion inevitably occurs and we obtain

premature breakthrough from egg to adult unless the duration

in each stage is small. So the control of developmental

diffusion can become a limiting computational problem. In

Lynch et al. (1998) we subdivided developmental stages

which had a duration of greater than one day; the result was a

total of 87 Eulerian variables to describe the population.

Needless to day, this can quickly become a limiting consideration.

The alternative IBM modeling approach is elegantly suited

to this problem. In Miller et al. (1998) this idea was implemented for Calanus finmarchicus in order to simulate the

occurrence of up to 3 generations of copepods in a single

growing season. Each individual carries a biological state

which includes developmental stage and age-within-stage;

and matures according to a blend of deterministic and

stochastic relationships which can be related to laboratory

rearing data. Upon reaching adulthood, the population

differentiates sexually, and females begin reproducing

Fig. 10 – Individual-based model simulation of larval

fish spawned on Georges Bank. The top panel

partitions the losses between advection and

starvation. The lower panel shows the growth curve

of the survivors. [Source: Werner et al., 1995]

Fig. 11 – Map of larval growth rate on Georges Bank.

The growth rates are computed with the larval fish

individual-based model; the prey fields are computed

using simplified population dynamics and observed

adult concentrations of Calanus finmarchicus and

Pseudocalanus spp. [Source: Lynch et al., 1999]
Volume 51, Number 2 13

depending on their biological state and the environment.

Artificial developmental diffusion is completely eliminated

in this approach. In addition, individuals may preserve a

complete identity including place of birth, origin and status

of mother, generation number, and ultimate source population. The only real addition to the IBM technology is the

requirement that new particles be ‘spawned’ as necessary.

Care is needed to manage these computations – for example

in Miller et al. an initial population of order 500 individuals

grows to 500,000 surviving individuals over a few months!

And many more were spawned and died along the way.

When these numbers become too large for simulation,

statistical subsampling of the population is necessary

(Batchelder and Miller, 1989). Figure 12 shows a typical

output of these simulations.

In another example of the same model, we studied the longterm effects of restricted fishing in certain areas (Lewis et

al., 1999). In this example we looked at scallops, whose

larvae are spawned in the fall, and settle on the bottom after

a pelagic period of roughly 40 days. The fall period is a peak

recirculation time in the Georges Bank climatology, resulting

in relatively high retention of the local population. The

operative question in this study concerns the effectiveness of

Fig. 12 – Individual-based model for Calanus exiting

diapause in Jordan Basin. Each adult spawns roughly

50 eggs per day which are transported and mature in

the circulation system. A subsample of particle

locations are plotted with color indicating

developmental stage. [Source: Miller et al., 1998]

Fig. 13 – Results of 40-day Scallop larval drift from

indicated areas, indicating retention and self-seeding

charactistics. [Source: Lewis et al., 1999]

closing certain areas to fishing and the long-run effects on

stock rebuilding.

Figure 13 illustrates the retention effect of the circulation

over a single 40-day pelagic period within the fall climatology. There is exchange among areas 1 and 2, with area 1

being largely self-seeding and area 2 seeding both areas.

Figure 14 illustrates the long-run consequences of the closed

areas. In this calculation, spawning occurs once per year.

Initially, adults are seeded everywhere. Larvae drift for 40

days and then settle and remain immobile until the following

year when spawning occurs again. Natural mortality is

enhanced by fishing mortality everywhere in the left panel;

in the right panel, there is no fishing mortality in the closed

areas. The mortality and fecundity relations in this simulation are very simple; but the impact of the closure on stock

rebuilding is dramatic and invites refined modeling.

Conclusion

Today we are facing enormous opportunities for scientific

progress in coupled physical/biological simulations of the

coastal ocean. Site-specific physical simulations are advancing remarkably fast, making possible a huge variety of

simulations. We are still a long way from being able to claim

“comprehensive” simulations on the biological side; and

nearly all physical simulations are claiming the need for

higher resolution. Nevertheless, by sticking to a few basic

principles we can forecast significant model-assisted
14 Naval Research Reviews

Fig. 14 – Results of a 10-year Scallop simulation.

Individual surviving scallops are plotted with color

indicating age (red = old). Right panel: fishing

restricted in the three closed areas. Left panel: no

fishing restrictions. [Source: Lewis et al., 1999]

advances in our understanding of these systems. Among

these principles are:

• Know your circulation fields

• Know your organisms

• Ask simple baseline questions focused on specific

hypotheses which are testable

• Accept and accumulate the conclusions from these

Implied is a hierarchy of biological complexity, starting with

the abiotic (passive tracer) case and progressively adding

behavior, development and feeding, and reproduction as

necessary.

Finally, it is important to recognize that models do not make

important simulations – rather modelers make them. We are

fortunate today that there is a developing cohort of highcaliber modeling professionals in ocean science. Their

continued encouragement and development is by far the most

important priority as we move toward site-specific, coupled

simulations on an operational basis.

Acknowledgments

Several individuals have worked with me over the past

decade to refine the ideas expressed here. Particularly worthy

of mention are D.McGillicuddy, C. Davis, W. Gentleman, D.

Greenberg, C. Hannah, M.Holboke, C. Lewis, G. Lough, C.

Miller, C. Naimie, I. Perry, and F. Werner, who contributed

many of the graphics from the cited papers.

References

1. H.P. Batchelder and C.B. Miller, “Life history and population

dynamics of Metridia pacificus: results from simulation

modeling,” Ecol. Model, 48, 113-136 (1989).

2. A.D. Bryant, D. Hainbucher and M. Heath, “Basin-scale

advection and population persistence of Calanus

finmarchicus,” Fisheries Oceanography, 7(3/4), 235-244

(1998).

3. F. Carlotti and K.U. Wolf, “A Lagrangian ensemble model of

Calanus finmarchicus coupled with a 1-D ecosystem model,”

Fisheries Oceanography, 7(3/4), 191-204 (1998).

4. S. Coombs, R. Harris, I. Perry and J. Alheit (eds.), GLOBEC

Special Issue, Fisheries Oceanography, 7(3/4), Sept/Dec

(1998).

5. D.L. DeAngelis and L.J. Gross (eds.), Individual-Based

Models and Approaches in Ecology: Populations,

Communities, and Ecosystems, (Chapman and Hall, New York,

1992), p. 525.

6. M.J.R. Fasham, H.W. Ducklow and S.M. McKelvie, “A

nitrogen-based model of plankton dynamics in the oceanic

mixed layer,” J. Mar. Res., 48, 591-639 (1990).

7. P.J.S. Franks, J.S. Wroblewski and G.R. Flierl, “Behavior of a

simple plankton model with food-level acclimation,” Marine

Biology, 91, 121-129 (1986).

8. D.A. Greenberg, “Chapter 5, Modeling Marine Systems,” The

contribution of modeling to understanding the dynamics of the

Bay of Fundy and Gulf of Maine vol. 2, A.M. Davies (ed.),

(CRC Press, Boca Raton, 1990), pp. 107-140.

9. D.A. Greenberg, F.E. Werner and D.R. Lynch, “A diagnostic

finite element ocean circulation model in spherical-polar

coordinates,” J. Atmospheric and Oceanic Technology, 15(4),

942-958 (1998).

10. E.P.W. Horne, J.W. Loder, C.E. Naimie and N.S. Oakey,

“Turbulence dissipation rates and nitrate supply in the upper

water column on Georges Bank,” Special Volume on Georges

Bank, Deep Sea Research II, 43, 7-8, 1,683-1,712 (1996).

11. J.R. Hunter, P.D. Craig and H.E. Phillips, “On the use of

random walk models with spatially variable diffusivity,” J. of

Computing Physics, 106, 366-376 (1993).

12. C.V.W. Lewis, D.R. Lynch, M.J. Fogarty and D. Mountain,

“Effect of Area Closures on Georges Bank Bivalves: Larval

Transport and Population Dynamics,” http://

www.nml.dartmouth.edu/~lewis/closed_areas/index.html, 25

February 1999.

13. D.R. Lynch, A.M. Davies, H. Gerritsen and C.N.K. Mooers,

“Closure. Quantitative Skill Assessment for Coastal Ocean

Models,” Coastal and Estuarine Studies, American

Geophysical Union, D.R. Lynch and A.M. Davies (eds.), 47,

501-506 (1995).

14. D.R. Lynch and C.E. Naimie, “The M2 Tide and its Residual

on Georges Bank,” J. Phys. Oceanography, 23, 10, 2,222-

2,253 (1993).
Volume 51, Number 2 15

15. D.R. Lynch, J.T.C. Ip, C.E. Naimie and F.E. Werner,

“Convergence Studies of Tidally-Rectified Circulation on

Georges Bank,” Coastal and Estuarine Studies, American

Geophysical Union, Quantitative Skill Assessment for Coastal

Ocean Models, D.R. Lynch and A.M. Davies (eds.), 48, 153-

174 (1995).

16. D.R. Lynch, J.T.C. Ip, C.E. Naimie and F.E. Werner,

“Comprehensive coastal circulation model with application to

the Gulf of Maine,” Continental Shelf Research, 16(7), 875-

906 (1996).

17. D.R. Lynch, M.J. Holboke and C.E. Naimie, “The Maine

Coastal Current: spring climatological circulation,”

Continental Shelf Research, 17(6), 605-634 (1997).

18. D.R. Lynch, C.E. Naimie and C.G. Hannah, “Hindcasting the

Georges Bank Circulation, Part 1: Detiding,” Continental Shelf

Research, 18, 607-639 (1998).

19. D.R. Lynch and C.E. Naimie, “Hydrographic data assimilation

on Georges Bank,” M.L. Spaulding and A.F. Blumberg (eds.),

Estuarine and Coastal Modeling V, (American Society of Civil

Engineers, Reston, VA, 1998), pp. 523-540.

20. D.R. Lynch, W.C. Gentleman, D.J. McGillicuddy Jr. and C.S.

Davis, “Biological/Physical Simulations of Calanus

finmarchicus Population Dynamics in the Gulf of Maine,”

Mar. Ecol. Prog. Ser, 169, 189-210 (1998).

21. D.R. Lynch, C.V.W. Lewis and F.E. Werner, “Can Georges

Bank Larval Cod Survive on a Calanoid Diet?” Special

Georges Bank Issue, Deep-Sea Research II, in press (1999).

22. M. Mangel, “Models, physics and predictive biological

oceanography: KNOW your organism,” U.S. GLOBEC News,

4, 1-2 (1993).

23. C.B. Miller, D.R. Lynch, F. Carlotti, W. Gentleman and C.

Lewis, “Coupling of an Individual-Based Population

Dynamics Model for Stocks of Calanus finmarchicus with a

Circulation Model for the Georges Bank Region,” Fisheries

Oceanography, 7(3/4), 219-234 (1998).

24. D.J. McGillicuddy, D.R. Lynch, A.M. Moore, W.C. Gentleman

and C.S. Davis, “An Adjoint Data Assimilation Approach to

the Estimation of Pseudocalanus spp. Population Dynamics in

the Gulf of Maine-Georges Bank Region,” Fisheries

Oceanography, 7(3/4), 205-218 (1998).

25. D.J. McGillicuddy Jr., D.R. Lynch, P. Wiebe, J. Runge, W.C.

Gentleman and C.S. Davis, “Evaluating the USGlobec

Georges Bank Broad-Scale Sampling Pattern with

Observational System Circulation Experiments,” Special

Georges Bank Issue, Deep-Sea Research II, in press (1999).

26. C.E. Naimie, J.W. Loder and D.R. Lynch, “Seasonal variation

of the 3-D residual circulation on Georges Bank,” J.

Geophysical Research, 99(C8), 15,967-15,989 (1994).

27. C.E. Naimie, “Georges Bank residual circulation during weak

and strong stratification periods – Prognostic numerical model

results,” J. Geophysical Research, 101(C3), 6,469-6,486

(1996).

28. C.E. Naimie, R. Limeburner, C. Hannah and R. Beardsley,

“Comparison of observed and modeled drifter trajectories in

the Georges Bank region,” Deep-Sea Research, submitted

(1999).

29. C.E. Naimie, J.W. Loder and D.R. Lynch, “Seasonal Variation

of Three-Dimensional Residual Circulation on Georges Bank,”

J. Geophysical Research, 99(C8), 15,967-15,989 (1994).

30. C.E. Naimie, “Georges Bank bimonthly residual circulation –

Prognostic numerical model results,” Dartmouth College

Numerical Methods Laboratory Report NML, September 1995,

Hanover, NH.

31. A. Okubo, “Dynamical aspects of animal grouping: swarms,

schools, flocks, and herds,” Advances in Biophysics, 22, 1-94

(1986).

32. D.J. Thompson, “Criteria for the selection of stochastic models

of particle trajectories in turbulent flows,” J. Fluid Mechanics,

180, 529-556 (1987).

33. F.E. Werner, F.H. Page, D.R. Lynch, J.W. Loder, R.G. Lough,

R.I. Perry, D.A. Greenberg and M.M. Sinclair, “Influences of

mean advection and simple behavior on the distribution of cod

and haddock early life stages on Georges Bank,” Fisheries

Oceanography, 2(2), 43-64 (1993).

34. F.E. Werner, R.I. Perry, R.G. Lough and C.E. Naimie,

“Trophodynamic and advective influences on Georges Bank

larval cod and haddock,” Special Volume on Georges Bank,

Deep-Sea Research II, 43(7-8), 1,793-1,822 (1996).

35. R.A. Luettich and J.J. Westerink, “Continental shelf scale

convergence studies with a barotrophic tidal model,”

Quantitative Skill Assessment for Coastal Ocean Models,

Coastal and Estuarine Studies, American Geophysical Union,

D.R. Lynch and A.M. Davies (eds.), 48, 349-371 (1995).

The Author

Daniel R. Lynch is MacLean Professor of Environmental Engineering at Dartmouth College in

Hanover, NH. Dr. Lynch earned a BS and MS in

mechanical engineering from MIT in 1972. In 1975

he returned to Princeton University to pursue study in

Water Resources. Upon completion of the PhD in

estuarine circulation in 1978, he joined the faculty of

engineering at Dartmouth.

At Dartmouth, Lynch pursues research at the intersection of advanced computation and large-scale

environmental simulation, with a focus on

continiental shelf simulation.

Dr. Lynch served as Director of Graduate Studies and

Associate Dean of Engineering at Dartmouth from

1985-1989, and was appointed MacLean Professor in

1993. From 1993 to 1996 he served as Executive

Director of the Regional Association for Research on

the Gulf of Maine. Since 1998 he also serves as

Adjunct Scientist at the Woods Hole Oceanographic

Institution.
16 Naval Research Reviews
Volume 51, Number 2 17

redicting the weather is hard enough. Predicting

waves is maddeningly difficult—it makes weather

forecasting look like something that could be done

by, well, those people on the television news who split

their time between cold fronts, chatting with the sports

anchor, and sending out birthday greetings to

centenarians.

One of the big problems is collecting data.

Waves are greatly influenced by local conditions, and

ocean scientists rarely have the degree of data

granularity they would need to forecast waves even

for relatively small coastal regions. When it comes to

the open ocean or larger coastal areas, you can

almost forget about it—sampling buoys are

expensive, short-ranged, and in relatively short

supply. Observation from space is promising, but even

with new, sophisticated satellites it’s difficult to

balance the necessarily high level of detail with the

equally necessary timeliness and extent of coverage.

In the following article, Vincent and Jensen

describe how advanced modeling techniques can fill

in the data gaps and give ocean scientists powerful

new tools for wave forecasting and nowcasting.

- J.P.
18 Naval Research Reviews

Charles L. Vincent

Office of Naval Research

Arlington, VA

and

Coastal and Hydraulics Laboratory, US Army Engineer Research and Development Center

Vicksburg, MS

Robert E. Jensen

Coastal and Hydraulics Laboratory, US Army Engineer Research and Development Center

Vicksburg, MS

Introduction

Every sailor who has ventured onto the open ocean and every

Marine and SEAL who has worked on a beach knows the

power of wind generated ocean waves (Figure 1). Major

storms produce individual waves that can exceed 30 m in

height. Naval and maritime history are replete with accounts

of ships lost and battles affected by these whims of nature.

Today, Naval operations are not only affected by such large

waves, but by waves that are tame by the mariner’s ordinary

standards. Littoral operations near beaches (such as those

required by Joint Logistics Over the Shore Operations) can

be severely affected by waves as low as sea-state 3 (1-2 m

waves). Other Naval operations can be affected by relatively

Ocean waves are difficult to measure or to predict accurately

for two fundamental reasons. First, wind waves are the most

dramatic and obvious issue of the coupling of the atmosphere

and ocean. Poor prediction of the wind stress over the ocean

leaves small hope of estimating the waves accurately. Waves

evolve as an integration of the wind stress over time and

space in complex, imperfectly understood ways. Moreover

the feedback between the growing waves, the atmosphere,

and the ocean’s mean circulation is not yet understood in

detail. Waves can grow rapidly over short times and distances. For example, a tropical storm (winds less than 30 m/

sec) may grow into a category 4 hurricane (winds greater

than 65 m/sec) in one day, with the waves rising from 4 to 15

meters in height, and may remain relatively localized. In

such a storm the region of very high

waves may cover a region only 100 km in

diameter.

Second, waves are dispersive: the energy

injected into the ocean at one place

radiates across the ocean. Waves generated in the Indian Ocean, for example,

can produce high surf on the California

coast. Swells with twenty-second periods

from the Halloween Nor’Easter of 1991

(located off New England) pounded the

coast of Florida nearly 2,000 km away.

Ocean currents and bathymetry can

influence wave propagation (Figure 2). If

the bathymetry is known, its effect can be

estimated, but the effects of ocean

currents are rarely considered. The effects

of bathymetry or currents on the wave field can be dramatic

over short distances, with important variations occurring

Improving Wind Wave Prediction

 on the Ocean

Fig. 1 – Large wave with very long crest. The flat trough just before this

wave will feel like a hole the ship falls into.

low waves of an inconvenient period that cause resonance or

relative motions between vessels.
Volume 51, Number 2 19

over distances shorter than a kilometer, especially in very

shallow water.

Given such variability in time and space, observation or

monitoring programs based on in-situ instrumentation are not

practical on a global basis. Satellite oceanography is beginning to provide additional information but it remains

inadequate for addressing routine operational needs. Today

(and for the foreseeable future) most analyses (“nowcasts”)

and forecasts remain based on numerical prediction models

driven by numerical weather prediction models. Indeed much

of the recent improvement in wave prediction has come from

advances in weather prediction.

These models must now be run at large weather prediction

centers with major computing power. However as the speed

of computers increases and the distribution of information

via web-based technologies advances, many practical wave

models may be run in ships—or even on laptops on the

beach.

In this article we review the current state of the art in wave

modeling at a number of spatial scales and outline research

efforts underway to improve wave prediction. We discuss

two types of models: phase-averaged (spectral) models and

phase-resolving models. Phase-averaged models predict the

statistical composition of the sea surface. Phase-resolving

model individual waves. Development of site specific coastal

models that can be coupled to in-situ or locally remote

sensed data collection systems offer significant opportunities

for improving wave estimates for Naval operations.

Representing Ocean Waves

Intuitively we describe the sea’s roughness in terms of wave

height. The traditional definition of roughness uses a

statistical index called the “significant wave height.”

Significant wave height is defined as the average of the

highest third of the waves measured in an observing period

of, typically, 5-40 minutes. This rather odd definition arose

during World War II to reflect and quantify observers’ visual

estimates of wave height. The advent of modern measurement technology lets us relate this to several more statistically relevant measures of either the variance of the poŸ...tion

of the sea surface or the probability of distribution of

individual waves. In the deep ocean if the significant height

has a value Hs

, the maximum wave that expected is less than

2.0Hs and the average wave height is about 0.6Hs. Other

parameters of interest are a characteristic period (or frequency) and wave travel direction.

The sea surface usually forms out of a complicated mixture

of waves from different sources. Waves generated by local

winds (sea), and waves from several distant sources (swell)

all contribute. Each of these systems has a characteristic

height, period and propagation direction. Thus the commonly

used significant wave height (with period and direction)

rarely describe the sea state well, other than as a general

index of its severity.

Modern wave measurement and prediction technology is

based on the concept of the directional spectrum of the sea

surface. The sea surface over some small finite spatial region

is a wavy surface with periods ranging from 0.5 second to 25

seconds. The directional spectrum of the ocean is generally

represented as a polar contour plot (Figure 3) of energy

density versus frequency and direction (f,θ). It is either

Fig. 2 – Wave Field In the Entrance of San Francisco

Bay. Here the surface current speed due to the

waves is mapped in color: darker blues are troughs,

greens to reds are crests. The wave field is affected

both by the water depth and the outflow from the

bay. The image covers about 1 by 1.5 km.

Fig. 3 – Directional spectrum measured off Pt. Reyes,

California. Non-black color intensity denotes energy level

as a function of frequency (radially out from center) and

direction. Here we see the largest waves at about 14 s

from the northwest, with a higher frequency wave train,

perhaps sea, at 9 s from the WNW. There is some hint of

a small swell from the Southern Ocean from the S at 18s.
20 Naval Research Reviews

computed from the Fourier transform of some parameter of

the sea surface or estimated by a wave model. Examinating

the spectrum allows us to identify and track the energy level,

period-range and direction of movement of different wave

systems. because the directional spectrum is a statistical

distillation of information about the sea surface, it is neither

a complete nor a unique description of that surface. For this

we need to add the phase relationships of all the waves. Most

operational wave models predict the spectral characteristics

of the sea surface in which the phase information has been

averaged and lost. Newer, more complicated models that

calculate the phases of waves are under development. While

phase-averaged spectra typify ocean conditions over minutes

or hours, phase-resolving models are valid over a few

minutes at best.

Measuring Waves

The Navy would like maps or databases in which the sea

state is displayed as a function of several forecast time

periods, or in which the wave climate has been summarized.

Given the temporal and spatial variation of wave systems, a

resolution of 1 degree by 1 degree may be barely adequate

on a global scale—recall that the eye of a major tropical

cyclone can easily fit within such a box. For coastal applications where the waves may be greatly affected by bathymetry, a kilometer by kilometer square may be inadequate. Yet

measurements of the wave field at either of these resolutions

is not available on a routine basis, largely due to cost.

The advance of signal processing and

electronics technology since World War

II has permitted development of a

number of different gauges or buoys for

making wave measurements. In the

1950’s few gauges existed around the

world, and all data were gathered by

hand and recorded on strip charts.

Today’s newer instruments may contain

data chips on board that collect the raw

signals and then either process and store

them or telemeter them to databases. But

there remain fewer than fifty buoys

maintained in relatively deep water with

data available for use in global wave

analyses, and most of those are located

near the US and European coasts. While

of great local value, they do not provide

a robust sampling of the wave field on

most days. Small ship-deployable

systems exist, and these are useful for

local purposes, but they remain expensive.

Contrast the state of wave prediction

with the much happier condition of

weather prediction. Satelites that can

sample some meteorological parameters

almost continuously have remarkably advanced the state of

the weather prediction art. Now, ocean waves can be

observed from space, but the present set of sensors—

altimeters and synthetic aperture radar (SAR)—must be

flown in low earth orbits. These instruments can therefore

measure or infer continuous, narrow great circles of wave

information, but the low orbital tracks only permit them to

sample apart of the ocean in any day (Figure 4). Furthermore, the satelites usually repeat their tracks only every 17

and 34 days. So the waves at any fixed location are sampled

only a couple of times a month. In the long run these data

will build a wave climatology, but they are of limited

usefulness in making even a daily map of wave conditions.

The satellite data are, however, valuable in data assimilation

schemes by helping constrain the computations in wave

models driven with wind stress.

In the 1950’s pioneering work by Willard Pierson—who

noted that ocean waves could be represented spectrally—and

by Owen Phillips and John Miles—who developed source

terms that represented the input of energy from the air to the

sea— ushered in the modern era of wave modeling technology. Research by Klaus Hasselmann established the role of

nonlinear wave interactions in spectral evolution and so

further advanced the development of wave models. With

these theories and techniques, the spectral characteristics of

the sea surface can be estimated in detail from global

numerical wind products. The Navy’s Fleet Numeric

Meteorology and Oceanography Center (FNMOC) was a

pioneer in applying these models. Today several centers like

Fig. 4 – Satellite data off of Canadian Atlantic Coast March 3, 1997.

The red box is the area with an ERS-2 SAR image. The colored great

circles are all the nearby altimeter passes for the day color coded by

wave height. The SAR image does not tell wave height directly. The

altimeters suggest that the waves were somewhere between 5 and 10

m in height. To estimate wave heights off the track, one must

interpolate on model.
Volume 51, Number 2 21

the National Center for Environmental Prediction (NCEP),

the European Center for Weather Prediction (ECMWF), the

Atmospheric Environment Services (AES) in Canada, and

the British Meteorology Office (BMO) routinely produce

global forecasts. The Naval Oceanographic Office (NAVO)

at the Stennis Space Center in Mississippi also makes a

global forecast it uses to initialize smaller regional models.

The computer requirements for these models (at a 1 or 2

degree resolution) are no longer as formidable as they once

were (Figure 5).

At present the state of the art in wave models is generally

thought to be the WAM model (1). This model is run at

FNMOC, NAVO, NCEP, ECMWF, and AES-Canada, with

differences in geographical gridand spectral resolution. The

most significant differences in the wave forecast products are

due to the wind stress products used to drive the models.

WAM was developed in the mid-1980’s and came into wide

use in the 1990’s.

Komen et al.(1) provides a comprehensive review of the

physics and numerical approximations used in the WAM

wave model. The radiative transfer equation provides the

WAM’s general basis:

(1)

In which the left side accounts for the propagation of wave

energy and the right side represents the input of energy from

the atmosphere (Sin), dissipation due breaking (Sds), and

redistribution of energy within the spectrum by nonlinear

wave resonance (Snl4). Komen et al. (1) provides details of

the computation of each. The basic theory of wind wave

generation holds that:

(a) pressure fluctuations due to the turbulent wind field

build small steep waves which

(b) then are enahnced by modifying air flow over the

waves that

(c) interact with each other through third-order

four wave resonant originally described by

Hasselmann (2) shifting energy to longer waves, and

(d) with dissipation due to white capping occurring as individual waves become too steep.

The WAM model is often called a third-generation

model because it attempts to estimate the four-wave

resonance directly and does not constraint the

frequency spectrum to a pre-determined form as did

two earlier generations of wave models. Recently,

Tolman et al. (3) revised the WAM model and

produced alternate formulations of the source terms.

This model is run at NCEP.

Improvement of wave models was hampered by the

quality of the wind fields used to drive the models. So

little wave gauge data and insufficient certainty in the

meteorology usually made it possible to make

reasonable adjustments to the wind field analyses to force the

wave model results into acceptable agreement with the

measurements. But this only works where you have data.

Advances in meteorological data collection and modeling

have now greatly improved wind forecasts. Coupling these

with more wave data allows a more rigorous evaluation of

the wave models and allows weaknesses in the theories and

models to be pinpointed (4). Over the last ten to fifteen years

the RMS errors and biases for FNMOC wind wave predictions have been significantly reduced (Table 1). In research

studies where time is available to refine the wind analyses,

wave model predictions accurately reproduce what is

measured (Figure 6).

Evaluation of the wind wave prediction system suggests

systematic errors in the wave model. In very large storms

(when the wind fields are well reproduced) the model underpredicts wave height and period. Often swell periods are a

few seconds too short, and the model does not yield the

Fig. 5 – FNMOC Global WAM Run for June 8, 1999 00Z. Largest

waves (7 - 8 m) are in the southern hemisphere where it is

RMS Error

Bias

Scatter 

Index

SOWN

1985

a

0.83-2.76m

x

0.40-

0.59

GSOWM

1985

a

0.73-

1.86m

x

0.28-

0.40

GWAM

1995

b

0.75-

0.78

-.17-

+0.20 

0.22-

0.28

GWAM

1995-97

c

0.51

+0.02

0.21

Table 1 – Changes in Wave Height Prediction Accuracy at

FNMOC.

Note: Column (a) Reference (5), (b) Reference (6); (c) Reference

(7). Only (c) is based on a large sample from many locations.

The scatter index is the ratio of the RMS error to the mean value

and provides an index of relative error.
22 Naval Research Reviews

range of temporal variation in swell energy even though the

mean value is about right. Analyses of hurricane data

indicate poorer performance on the left side of the storm

(relative to the direction of its motion) and when the storm

stalls, or loops. For many years wave researchers have felt

that wave directions would tend not be as well predicted as

heights or periods, but recent evaluation of Naval predictions

suggest that the wave arrival directions are often well

predicted.

Research is beginning to offer clues to possible causes for

some errors. Resio et al. (8) has suggested that underprediction in big storms is due to how the PiersonMoskowitz spectrum has been parameterized for large winds.

The proposed new form allows larger and longer waves to

develop in big storms. Since long swell originates in big

storms, this may help alleviate the under-prediction of swell

periods. The new model of Tolman et al. (3) at NCEP has an

improved numerical scheme for wave propagation. Even

without the improved fully developed formulation this model

reproduces the range of variation in swell energy better than

the Navy WAM model. Improving the model in tropical

storms is difficult because of the lack of a good wind and

wave database. So we cannot partition the error into meteorological and wave model parts.

Regional And Coastal Spectral Models

People now routinely run global spectral models on about a

one-degree grid mesh. Compared to the first “global” models

run on about a 3-degree grid mesh, and mainly over the

northern hemisphere alone, resolution has increased by

almost an order of magnitude in grid computation points.

Even at this scale, however, the model cannot resolve

tropical storms or frontal passages, or define sheltering

effects due to islands and continental landmass configuration. Nor can these models represent mesoscale features in

the wind fields. A one-degree resolution is normally inadequate to represent variations in the wave field due to bottom

bathymetry irregularity if the water is shallow. The current

strategy uses a sequence of nested grids that refines the

model resolution to the areas where it is needed (Figure 7).

For example, near the Atlantic coast of the United States a

series of nested grids brings the model down to a 1

km spacing (Figure 8). Even though the most

sophisticated operational wind models like the

Navy’s Coupled Ocean/Atmospheric Mesoscale

Prediction System (9) are not run on this fine a

resolution, this grid is needed to represent gradients in the wave field due to changes in water

depths. If the bathymetry is particularly complex,

even finer resolutions are needed to represent its

effects on wave propagation and breaking. For

selected operational purposes even higher grid

resolutions can be run. In the research model, wave

models are being evaluated down to 100-meter

grid resolutions that even include the surf zone.

Naval prediction systems now have the capability to take the

waves into harbors and bays as well.

Although the WAM model includes some aspects of shallow

water wave physics, it remains inadequate for true coastal

applications on sub-one-kilometer grid meshes. Research

currently sponsored by the Office of Naval Research aims at

improving our understanding of the physics of WAM-type

spectral models for shallow water. This research program

includes a major field experiment, the Shoaling Waves

Experiment (SHOWEX) off of the North Carolina coast

scheduled for the fall of 1999 to measure the source terms

that are appropriate extensions to equation (1) for shallow

water. More information on SHOWEX can be found on the

SHOWEX web page: http://cheyenne.rsmas.miami.edu/duck99/.

The Office of Naval Research is sponsoring concurrent

research to enhance practical aspects of shallow water wave

models through the Advanced Wave Prediction Program.

This effort will improve modeling of swell propagation over

irregular bathymetry and allow the assimilation of both insitu and remotely sensed wave data. Research has shown that

injection of on site wave data often improves wave estimates

locally, helping thereby to remove some of the errors

inherent in trying to force a model with wind fields. A

Fig. 6 – Waves of January-March 1993 using hindcast winds

and WAM and a second-generation model. Data from NDBC

buoy 44014 off North Carolina.

Fig. 7 – Model

Nesting Schemes.

Global Nested

Regional Grids,

and Bay are

WAM-type

models. Littoral/

Surf can be either

phase averaged

or resolving

models. Harbor

Models are

usually phase

resolving.
Volume 51, Number 2 23

variation of a WAM type model developed in the Netherlands and called SWAN (10) serves as the basis for improvement. SWAN has been made available to the general research

community for use and evaluation so that it will be tested in

a wider variety of coastal environments. More information

on SWAN can be found on the SWAN web page http://

swan.ct.tudelft.nl/. Updates on the Advanced Wave Prediction Program are posted on its web page: http://

www.onr.navy.mil/sci_tech/ocean/Info/cd99/advwvprd.htm .

Figure 9 demonstrates some of the capabilities of SWAN by

showing computations of the wave height field near San

Miguel Island in California. The Naval Research Laboratory

at Stennis Space Center performed these using the original

version of SWAN. The model is run on a 100 m resolution

and suggests that the bathymetry focuses wave energy more

sharply than the old model anticipated. The challenge now

lies in validating a model with such high resolution. The

potential value to the Navy would be a newfound ability to

pinpoint areas where littoral operations would or would not

be possible.

Phase Resolving Models

The WAM, SWAN and new NCEP models are

all phase-averaged spectral models. They

predict the directional spectrum of the sea

surface and thus permit estimation of significant wave height, period and direction of

travel. Their great advantage has been the

development of wind-wave generation

algorithms driven by wind stress predicted by

meteorological models. They do not, however, tell us much about the characteristics of

individual waves, and yet very large, unexpected individual waves often cause great

damage to ships, installations, and offshore

platforms.

Information on extreme wave characteristics and wave

groups must be inferred; it cannot be calculated. In shallow

water important aspects of the interaction of the incoming

waves with the wave generated current field and surf beat

cannot presently be calculated using purely phased averaged

physics. Research is underway to investigate whether phase

resolving models that predict both the amplitude and phase

of the waves offer more promise.

One place that phase resolution may be very useful in deep

water is in predicting the appearance of rogue waves in the

open ocean. Phase resolving models (11), are being evaluated under the Office of Naval Research’s Mobile Offshore

Base (MOB) program to see if the occurrence of unusually

high, long crested waves that might occur during a big storm

can be predicted. Such waves are of interest in the design

specifications for a MOB, conceived as a mile long floating

structure that can move from one operational area to another.

Phase resolving models suggest that these rogue waves may

arise out of nonlinear wave effects in an otherwise random

sea. Last year in hurricane Bonnie NASA measured a wave

50 feet high with a crest about a mile long using an airborne

Scanning Radar Altimeter in conjunction with the MOB

program. Such a wave would look something like Figure 1 to

a hapless ship in a storm. Conventional wisdom had suggested that this wave would only have a crest about 3,000 ft

long.

Naval operations on beaches are affected by breaker heights,

swash incursion on the beach, and nearshore currents.

Models like SWAN can be applied to predict waves on the

space scales of the surf zone (with a resolution of 100 meters

or less). Tests of these models suggest that on many beaches

these models can predict both the wave height and many

aspects of the directional spectrum. But applying wave

models to drive nearshore circulation models on barred

beaches has been less successful than investigators had

hoped.

Figure 10 shows phase resolving model simulations of a

Fig. 8 – Grid Nesting for the North Atlantic.

Fig. 9 – High Resolution Wave Predictions Using SWAN.
24 Naval Research Reviews

simple swell interacting with a shore and a bar having a rip

current channel. The simulations were made with a

Boussinesq wave model of the nearshore developed at the

University of Delaware (12). The Delaware model has the

ability to predict nearshore waves and currents simultaneously. Although the input wave field is steady, the

wave-driven nearshore current develops a rip current

in the bar gap that is not steady, but pulsates in both

time and position, shedding eddies. These results are

in general agreement with the patterns observed in the

laboratory and field (Figure 11). The key to reproducing these effects is the model’s ability to transfer

energy to sub- and super-harmonics of the incident

wave field and allow shear instabilities in the

nearshore current field to develop and interact with

the incoming wave field. Phase-averaged models do

not at this point incorporate the physics required to

replicate these processes.

Although phase-resolving models appear to offer

significant new insights into wave predictions, they

are no panacea. First of all, they are incredibly

computationally intensive. Even in a research mode it

is impractical to run them for more than a few square

kilometers. Secondly, they must either be initiated

with phase information about the wave field (which

cannot be inferred but must be measured) or the

phase field must be simulated using statistical

techniques (which then require many realizations to

obtain statistical stability). Thus their potential for

the near term may lie in improving our understanding of the physics to allow development of better

phase averaged models.

Summary

Over the past decade advances in computers and

electronics, in satellite meteorology and oceanography, and in numerical weather prediction have

allowed development of practical ocean phase

averaged spectral wave models. These models are

now run on temporal and spatial scales appropriate

to the available wind forcing information and

bathymetry. Phase resolving models are under

development that allow highly detailed simulations

of the ocean surface, and the interaction of waves

with bars, beaches and currents. Now that the

forcing wind data are better known, research is

underway to identify and correct deficiencies in the

wave models.

Challenges for the near future remain validation of

the details of the model’s predictions, and coupling

wave observation systems to the models to permit

application of data assimilation techniques. Users

and developers of the models must work to find

better ways of representing and interpreting the

wealth of information these models produce. For the

longer term, our goal is to improve the models so that they

used coupled physics to describe the interaction of the waves

and ocean, and waves and atmosphere in a physically

realistic manner.

Fig. 11 – Photograph of swell breaking on a beach and

generating a rip current near La Jolla, CA. (Elgar)

Fig. 10 – Phase

resolving model

simulation of a bared

beach showing the

wave field, the current

field, and the vorticity

field. The vorticity

patterns show eddylike structures that can

be seen in field

imagery.
Volume 51, Number 2 25

Acknowledgments

The figures for this article were obtained from the following

sources and are gratefully acknowledged: Figure (2), Richard

Goldstein of the Jet Propulsion Laboratory, California

Institute of Technology; (3) Website of the California Coastal

Data Information Program; (4) David Walker, ERIM

International; (5) Website of the Fleet Numerical Oceanography and Meteorology Center; (9) James Kaihatu, Naval

Research Laboratory; (10) Professor James Kirby, University

of Delaware; (11) Dr. Steve Elgar, Woods Hole Oceanographic Institute.

The Authors

Charles L. Vincent is Senior Research Scientist for

Coastal Hydrodynamics at the U.S. Army’s Engineering Research and Development Center’s

Coastal and Hydraulics Laboratory. He also serves

as a Scientific Officer with the Office of Naval

Research’s Coastal Dynamics Program, where he

manages ONR’s Advanced Wave Prediction

Program. Dr. Vincent’s research interests include

wind wave prediction and modeling in deep and

shallow water, nearshore processes, inlet dynamics,

and integrated coastal systems models. He earned a

bachelor of arts with distinction in mathematics

(1969) and the master of science (1971) and Ph.D

(1973) in environmental sciences, all from the

University of Virginia. His awards and recognition

include a Department of the Army Meritorious

Civilian Service Medal, the Department of Army

Research and Development Achievement Award,

and the American Society of Civil Engineers Walter

Huber Prize for Research. He has co-authored over

100 papers and reports. Dr. Vincent will join the

staff of the Naval Research Laboratory in November 1999.

Robert E. Jensen is a Research Hydraulic Engineer at the Coastal and Hydraulics Laboratory of

the US Army Corps of Engineers Engineer Research and Development Center (ERDC). He holds

a baccalaureate in atmospheric and oceanographic

sciences and a bachelor of engineering in environmental science engineering, both earned at the

University of Michigan. His masters in ocean

engineering comes from Oregon State University,

and he received the Ph.D. in 1983 from Texas

A&M. Since 1983 he has been at the ERDC

(formally the Waterways Experiment Station)

working in the field of spectral wave modeling.

Presently Dr. Jensen heads the Wave Information

Study, a US Army Corps of Engineers sponsored

research and development unit sponsored by the US

Army Corps of Engineers. He was an active

member of the WAM group, is a member of the

WISE group and a co-leader of the Army/Navy

Wave Prediction Group.

References

1. G. Komen, L. Cavaleri, M. Donelan, K. Hasselmann, S.

Hasselmann and P. Janssen, Dynamics and Modeling of Ocean

Waves (Cambridge University Press, 1994), p. 532.

2. K. Hasselmann, “On the Non-Linear Energy Transfer in a

Gravity-Wave Spectrum – General Theory,” J. Fluid

Mechanics, 12, 481-500 (1962).

3. H. Tolman and D. Chalnikov, “Source Terms in a Third

Generation Wind Wave Model,” J. of Physical Oceanography,

26, 2,497-2,518 (1996).

4. V. Cardone et al, “Evaluation of Contemporary Ocean Wave

Models in Rare Extreme Events: The ‘Halloween Storm’ of

October 1991 and the ‘Storm of the Century’ of March 1993,”

J. of Atmospheric and Oceanographic Technology, 13, 198-230

(1996).

5. M. Clancy et al, “The Fleet Numerical Oceanography Center

Global Spectral Ocean Wave Model,” Bulletin of the American

Meteorology Society, 67(5), 498-512 (1986).

6. P. Wittmann, M. Clancy and T. Mettlach, “Operational Wave

Forecasting at Fleet Numerical Meteorological and

Oceanography Center,” 4th International Workshop on Wave

Hindcasting, Banff, Alberta, Canada, (Atmospheric

Environment Service, Downsview, Ontario, Canada, 1995), pp.

335-342.

7. J. Bidlot, M. Holt, P. Wittmann, R. Lalbeharry and H. Chen,

“Towards a systematic verification of operational wave

models,” Waves ’97, Ocean Wave Measurements Analysis,

American Society of Civil Engineers, 653-667 (1997).

8. D. Resio et al, “Wind Speed Scaling in Fully Developed Seas,”

J. of Physical Oceanography, accepted for publication (1999).

9. R. Hodur, “The Naval Research Laboratory’s Coupled Ocean/

Atmosphere Mesoscale Predication System (COAMPS),”

Monthly Weather Review (1996).

10. N. Booij, L.H. Holthuijsen and R.C. Ris, “The SWAN wave

model for shallow water,” Proceedings, 25th International

Conference on Coastal Engineering, 1, 668-676 (1996).

11. D. Dommermuth and D. Yue, “A Higher Order Spectral

Method for the Study of Nonlinear Gravity Waves,” J. of Fluid

Mechanics, 184, 267-288 (1987).

12. Q. Chen et al, “Boussinesq Modeling of a Rip Current

System,” J. of Geophysical Research, accepted for publication

(1999).
26 Naval Research Reviews
Volume 51, Number 2 27

he Navy has long been interested in ocean forecasting as a

way to anticipate the ocean’s influence on naval operations

both under and over the sea. In the past, most of the research

focused on deep-water environments where ships and submarines carried out their missions. Shallow coastal waters of the

world present an added challenge as the focus of future naval

operations will likely be in these littoral, or near-shore, areas. In

the littoral zone, Navy oceanographers are studying a cat’s

cradle of challenges: tidal pulses, beach profiles, reefs, bars,

shallows, shoals, channels, sediment transport, turbidity, rain

rates, river run-off, biological components and the complex

weather patterns inherent in any coastal region.

Today’s oceanographers study the littoral zone the same

way they study deep water—through sampling. Although the

methodology is traditional, the tools of the trade now include

satellite and remote-sensing technologies and sophisticated

ocean-modeling software.

With advances in technology, oceanographers can increasingly provide the Navy with data collection, analysis and

recommendations in near real time. In the old days, studies took

weeks—even months—to return enough data for analysis. Today,

most sampling systems, including the HOPS and LEO-15 versions

mentioned in the article that follows, incorporate both observation and modeling techniques to maximize the benefits of both

capabilities. The systems gather data on an ongoing basis from

autonomous platforms, allowing the researchers to adapt sampling patterns as needed to generate useful forecast models. In

a continuous feedback loop, adaptation of future sampling is

based on model simulation results. - D.B.
28 Naval Research Reviews

Abstract

Real-time regional forecasting of the coastal ocean is a

challenging task, complicated by the ocean’s episodic nature,

the lack of extensive observations, and the combined

influence of internal processes and interactions with boundaries on the evolution of the forecast fields. Adaptive

sampling is an evolving methodology for the efficient

sampling of ocean phenomena in support of real-time

nowcasting and forecasting activities. Ocean Observation

and Prediction Systems (OOPS) provide a framework for

acquiring, processing and assimiliating data in a dynamical

forecast model which can then generate forecasts of 3-D

fields and error estimates that can be used to optimize

adaptive sampling schemes for specific goals. Modern OOPS

applications with adaptive sampling are presented for the

Harvard Ocean Prediction System (HOPS) and the Rutgers

University Long-term Ecosystem Observatory (LEO-15).

Interdisciplinary models, new assimilation methodologies,

new sensors, autonomous platforms, and automated system

responses will further improve adaptive sampling capabilities in the next decade.

Real-Time Regional Forecasting

The ocean is intermittent, eventful, and episodic. It is an

essentially turbulent fluid whose circulation is characterized

by a myriad of dynamical processes occurring over a vast

range of nonlinearly interactive scales in space and time.

Ocean forecasting is essential for effective and efficient

operations on and within the sea, and such forecasting has

been initiated, e.g. for military operations, coastal zone

management and scientific research. Observations are used

to initialize dynamical forecast models, and further observations are continually assimilated into the models as the

forecasts advance in time. Such observations are generally

difficult, costly and sparse. If a region of the ocean were to

be sampled uniformly over a predetermined space-time grid

adequate to resolve scales of interest, only a small subset of

those observations would have significant impact on the

accuracy of the forecasts. The impact subset is related to

intermittent energetic synoptic dynamical events. For most of

the energetic variability in the ocean, the location and timing

of such events is irregular and not a priori known. However,

a usefully accurate forecast targets such events and forms the

basis for the design of a sampling scheme tailored to the

ocean state to be observed. Such adaptive sampling of the

observations of greatest impact is efficient and can drastically reduce the observational requirements, i.e., by one or

two orders of magnitude.

The ocean evolves in time, both as a direct response to

external surface and body forces, and also via internal

dynamical processes. The former include, for instance, tidal

forces, winds and surface fluxes of heat and fresh water.

Where air-sea interactions are important, an accurate

meteorological forecast is needed for the ocean forecast.

Oceanic internal instabilities and resonances, which include

meanders of currents, frontogenesis, eddying and wave

propagation, are generally analogous to atmospheric weather

phenomena and are called the internal weather of the sea.

The spatial scales of important internal ocean weather

phenomena are short and require ocean forecasts to be

carried out regionally rather than globally. The regional

forecast problem then has additional forces appearing as

fluxes through horizontal boundaries, representing both

larger scales of direct forcing, remote internal dynamical

events and land-sea interactions in the littoral zone. The

development of a regional forecast system and capability

depends both upon the scales and processes of interest and

the scales and processes that are dominant in the region. The

design of sampling schemes is constrained both by generic

and special regional issues. The forecast region or region of

influence is often necessarily larger than the region of

operational interest. Additional challenging issues in sampling design include efficient real-time forecast protocols

and the acquisition of data adequate for both updating and

verification purposes.

Adaptive Sampling for Ocean Forecasting

Allan R. Robinson

Harvard University

Cambridge, Massachusetts

Scott M. Glenn

Rutgers University

New Brunswick, New Jersey
Volume 51, Number 2 29

Ocean science and marine technology today are increasingly

interdisciplinary. Fields of forecast interest include physical,

acoustical, optical, biological, chemical and sedimentological state variables. Velocities, temperatures, sound speed,

scattering, irradiances, plankton concentrations, chlorophyll

and suspended particles are some examples. Interdisciplinary

compatibility requirements constrain multi-disciplinary

sampling schemes. Some variables are of direct interest

while others are useful for interdisciplinary field estimation,

e.g., acoustic travel times for the estimation of temperature

gradients. Thus, as the scope of ocean prediction expands,

the challenging adaptive sampling problem that emerges is

the design of sampling schemes for the acquisition of multiscale compatible interdisciplinary data sets based upon realtime observations and realistic forecasts. The specific

purpose of the forecast which will utilize the data guides

both the design of the sampling and the choice of a forecast

skill metric. The adaptive sampling problem defined in the

last two sentences is the topic of this paper.

Characterization of the Coastal Ocean

The short term evolution (1-5 days) of the mesoscale ocean

circulation at times is controlled by nonlinear internal

processes associated with the density-driven flows, especially in deeper water. As water depths decrease, forcing

from the boundaries (surface, bottom, offshore, inshore, and

lateral) and turbulent mixing is often of similar importance

or greater (ex. Keen and Glenn, 1998).

Atmospheric momentum and

buoyancy fluxes produce daily

to seasonal variations in the

upper mixed layer and the

seasonal thermocline. Coastal

upwelling/downwelling is

caused by the Ekman transport,

which in the deepwater limit is

associated with alongshore

winds and Coriolis forces, but

in the often neglected shallow

water limit is associated with

cross-shore winds.

Bottom interactions on the

continental shelf are complicated by the effects of surface

waves that feel the bottom, and by a moveable sediment bed.

Both the nonlinear wave-current interaction in the wave

boundary layer, and the increased roughness due to ripple

formation, act to increase the bottom stress felt by the lowerfrequency currents, while suspended sediment induced

stratification acts to decrease the bottom stress.

At the outer boundary, interactions with deepwater eddies

and boundary currents can produce cross-shelf exchanges or

along-shelf pressure gradients that force the outer-shelf.

Along the coastal boundary, estuaries are a source of

freshwater, producing buoyant plumes and alongshore

surface jets on the inner-shelf. Entering through lateral crossshelf boundaries, coastal-trapped, externally generated waves

can propagate along the coast through a region of interest.

The observation and prediction of coastal circulation is

further complicated by the presence of a continuum of wave

motions of similar magnitude or greater than the boundary or

internally forced currents. Surface waves, internal waves and

solitons, barotopic and baroclinic tides, and inertial waves

may occur simultaneously, and each may interact with the

mean flow by modifying the turbulence, especially near the

thermocline where the largest shears are often encountered.

We have chosen to emphasize the features, variabilities and

complexities of the physical coastal ocean (Robinson and

Brink, 1999) and will only briefly mention the equally, if not

more important, multi- and inter-disciplinary processes.

Coastal conditions support vigorous marine ecosystems and

are of utmost importance for living marine resources.

Primary production occurs in phytoplankton blooms in

response to seasonal stratification, wind-driven and topographic upwelling, tidal-mixing and nutrient advection

events. The dynamics of interactive, multi-scale physicalbiological variabilities (phytoplankton and zooplankton

patchiness) is currently a research topic of critical importance for both understanding and managing coastal seas. The

forward and inverse acoustic propagation problems across

the shelfbreak and in shallow waters involve critical bottom

interactions and require careful treatment of attenuation,

scattering and reverberation.

Adaptive Sampling Concept

The concept of experimental and observational sampling

being well matched to the phenomena of interest is deeply

rooted in modern scientific methodology. The success of

Newtonian physics was based upon the rigorous requirement

of subjecting dynamical hypotheses to quantitative testing by

experimental facts. An iterative process has evolved, with

feedbacks between theory and experimentation, which

involves both agreements with pre-existing data and predictions of new measurements. Practical material and human

resource constraints demand efficient measurements, an

issue of particular concern in oceanography. Efficient

sampling requires a priori knowledge of scales that may be

simple (e.g. periodic) or complex (e.g. multi-scales arising

from nonlinear interactions).

If scales are known for intermittent episodic phenomena,

adequate uniform sampling is possible but not very efficient.

Coarser sampling misses entirely or at best aliases the

phenomena (MODE Group, 1978, Section 1). Finer sampling

is redundant. Optimal sampling requires a priori estimates of

the state of the ocean during the sampling interval. To carry

out such observations adaptively requires flexible and

efficient platforms well matched to the phenomena. Consider

THERMOCLINE. The

transition layer between the

mixed layer at the surface and

the deep water layer. The

definitions of these layers are

based on temperature.

EKMAN TRANSPORT. The

net movement of water

influenced by friction

(typically the wind or bottom

drag) and the rotation of the

earth.
30 Naval Research Reviews

a scenario in which two (or more) platforms are available

together with a real-time data telemetering capability. One

platform provides continuous good coverage from a fixed

position or predetermined track (saturated data, e.g. from a

coastal CODAR or satellite altimeter). The second platform,

generally costly to operate in the forecast region, provides

targeted data (sparse data, e.g. from a ship, aircraft or AUV)

on events identified but incompletely sampled in the realtime saturated data stream. Additionally, if a usefully reliable

forecast model exists, present and future events can be

identified from model nowcasts and forecasts instead of from

a saturated data stream, but more powerfully in conjunction

with such a data stream.

The adaptive sampling strategy will attempt to minimize a

selected error measure and the estimate of the error must take

into account data type, sampling and assimilation scheme.

Contemporary scientific methodology is tripartite,

involving theory, experimentation and realistic

simulations now possible because of rapidly

increasing computational resources. Observational

System Simulation Experiments (OSSEs) now play

an essential role in quantitatively assessing

adaptive sampling strategies (Robinson et al.,

1998).

Historically oceanographers have always adaptively sampled

with respect to known scale information. Early examples

include biological sampling (or harvesting) of estuarine

ecosystems at appropriate phases of the tidal cycle and the

design of physical time series with regard to Nyquist

frequency considerations. The existence of dominant

mesoscale variability in the ocean which was discovered in

the 1960s, and described and quantified in the 1970s

(Robinson, 1983), led naturally to the initiation of ocean

forecasting during the 1980s (Mooers et al., 1986). During

that decade the present authors independently carried out

adaptive sampling research, for example in conjunction with

the first real-time shipboard forecast of the California

Current evolution (Robinson et al., 1986) and with the

provision of strong ring-current advisories to dynamically

positioned deep water oil drilling vessels (Glenn et al.,

1990). Together we devised weekly event-related P3 AXBT

flights in support of research/operational forecasting of Gulf

Stream meanders and rings for the US Navy from November

1986 to January 1989 (Glenn and Robinson, 1995). During

the 1990s the opportunities and requirements for multi-scale,

interdisciplinary ocean forecasting have sharpened, the term

adaptive sampling for ocean

observational networks was

articulated (Curtin et al., 1993),

and the concept of Ocean Observing and Predictions Systems has

firmly emerged.

Ocean Observing and

Prediction Systems (OOPS)

Advanced ocean observing and prediction systems (OOPS)

now exist for field estimation. An OOPS consists of an

observational network, data analysis and assimilation

schemes and a suite of interdisciplinary dynamical models.

Generally multiple interactive scales require compatible

observational and modeling nests, and efficiency requires a

well-chosen mix of sensors and platforms

for a particular problem. The concept of

advanced ocean prediction systems is

represented schematically (Figure 1a) by

the LOOPS (Littoral Ocean Observing and

Prediction System) architecture

(Patrikalakis et al., 1999). The LOOPS

system is modular, based on a distributed

information concept, providing sharable,

scalable, flexible and efficient workflow

and management for interdisciplinary data

collection, assimilation and forecasting.

The Harvard Ocean Prediction System

(HOPS), described below and illustrated in

Figure 1b, is at the heart of LOOPS. An

OOPS can be generic and portable (e.g.

HOPS (Robinson, 1999)), or designed and

implemented for specific regions or

processes (e.g. LEO-15 (Glenn et al.,

1998)).

Data assimilation, which melds observations with dynamics, provides the only

feasible basis for obtaining accurate

synoptic mesoscale realizations over the

Fig. 1 – a) Architecture of advanced high-level ocean observing and

prediction system; b) Architecture of Harvard Ocean Prediction

System (HOPS).

(a) (b)

ADAPTIVE SAMPLING.

Measurements whose

distribution in time and

space are adjusted according

to observed or predicted

gradients.
Volume 51, Number 2 31

space-time scales and domains of interest. Data assimilation

dynamically adjusts and interpolates data inserted into

models (Robinson et al., 1998). Data assimilation methods

being used or adapted today for ocean science have their

roots in engineering and meteorology and are generally

based on estimation theory, control theory or inverse

techniques. Error models are an intrinsic element of data

assimilation schemes and errors are propagated together with

forecast fields. Data assimilation or inverse methods allow

for the estimation of parameters such as eddy diffusivities

and rate parameters and the inference of processes from the

balance of terms in dynamical equations. The control of

predictability error via data assimilation

initiated by meteorologists is interesting for

the interdisciplinary ocean forecasting

problem in the light of the nonlinearities

inherent in coupled biological and physical

models.

Modern ocean observation networks use

multiple platforms including remote (satellites, aircraft and shore-based), stationary

(surface and subsurface), moveable (ships and

AUVs), and drifting (surface or vertically

mobile). The Rutgers LEO-15 system is

illustrated in Figure 2 and described below.

Advances in satellite, line-of-site radio, and

underwater acoustic communications enable

real-time data transmission, which prompts

development of automated processing and

visualization algorithms. Instantaneous

product dissemination via the World Wide

Web promotes the formation of distributed

networks, with different groups responsible

for individual systems. The proliferation of

distributed observation networks allows one

to envision a patchwork of well-sampled

coastal ocean regions in which the role of

sparse adaptive sampling will change relative to the role of

saturated measurements. In the well-sampled ocean, adaptive

sampling can begin to focus on observations that improve or

otherwise compensate for imperfect model physics, such as

unparameterized turbulent mixing mechanisms, as the

dominant source of forecast error.

Interdisciplinary ocean science involves a hierarchy of

complex coupled physical-acoustical-biogeochemicalecosystem dynamical models. Physical models are generally

primitive equation (PE) models, but small scale coastal

phenomena can be represented via non-hydrostatic models.

Boundary layers (top and bottom) and turbulence are

modeled through process parameterization, second order

closure, or large eddy simulation. Basic biological mechanisms are generally known (although not as well known as

physics) but much remains to be learned about their manifestations in real ocean processes and their appropriate representation in dynamical models. Mechanisms such as nutrient

uptake, grazing, mortality, etc. are highly nonlinear in nature.

There are an almost unlimited number of potential state

variables (species, life-stages, trophic levels, nutrients, etc.)

and the choice of aggregations appropriate for particular

problems (critical state variables) is a demanding aspect of

modeling. Higher trophic levels of biology require behavior

modeling. Acoustic propagation has a variety of approximate

dynamics, depending on frequency and complicated by

circulation, bottom and surface interactions, biological

interactions, etc.

Operational high-resolution (10-30 km) regional atmospheric

models may adequately resolve most atmospheric processes,

but coastal ocean fronts can occur at the kilometer scale. To

determine if the smaller scale ocean features feedback on the

atmosphere and influence their own evolution, an even

higher resolution atmospheric model can be nested within

the operational models, or a planetary boundary layer model

can be coupled to each grid point of the ocean model and

forced at the top with the operational resolution model. The

first approach drastically increases runtime, while the second

approach assumes the ocean influence is primarily local.

Research in progress and operational examples

Harvard Ocean Prediction System (HOPS): HOPS

(see Figure 1b) is a flexible, portable and generic system for

inter-disciplinary nowcasting, forecasting and simulations.

HOPS can rapidly be deployed to any region of the world

ocean, including the coastal and deep oceans and across the

shelfbreak with open, partially open or closed boundaries.

Fig. 2 – The LEO-15 observation network operated offshore of

Tuckerton, New Jersey during the annual Coastal Predictive Skill

Experiment.
32 Naval Research Reviews

Physical, and some acoustical, real-time and at sea forecasts

have been carried out for more than fifteen years at numerous sites (Robinson, 1999) and coupled at sea biological

forecasts were initiated in 1997. The present system is

applicable from 10m to several thousand meters and the

heart of the system for most applications is a primitive

equation physical dynamical model. Work is in progress to

extend the system to estuaries and to include a non-hydrostatic option. Multiple sigma vertical coordinates have been

calibrated for accurate modeling of steep topography.

Multiple two-way nests are an existing option for the

horizontal grids. The modularity of HOPS facilitates the

selection of a subset of modules to form an efficient configuration for specific applications and also facilitates the

addition of new or substitute modules. Data assimilation

methods used by HOPS include a robust (suboptimal)

optimal interpolation (OI) scheme and a quasi-optimal

scheme, Error Subspace Statistical Estimation (ESSE). The

ESSE method determines the nonlinear evolution of the

oceanic state and its uncertainties by minimizing the most

energetic errors under the constraints of the dynamical and

measurement models and their errors. Measurement models

relate state variables to sensor data. Real-time efficiency is

achieved by reducing the error covariance to its dominant

eigendecomposition.

HOPS utilizes a variety of observational networks in its

applications. Satellite sea surface temperature, height and

color are routinely utilized as available. HOPS, on shipboard,

has recently forecast physics and acoustics from data

gathered by the RV Endeavor during the ONR Shelfbreak

PRIMER experiment, and physics and biology from data

gathered by the RRS Discovery in the Northeast Atlantic

during the Plankton Patchiness Studies by Ship and Satellite

experiment. Interactive adaptive sampling with the MIT

Odyssey AUVs was initiated in shallow water during the

1996 ONR Haro Straits tidal fronts experiment (Nadis,

1997). In recent NATO Rapid

Response exercises, the observational networks included the

SACLANTCEN NRV Alliance,

additional NATO military and

research vessels and P3 aircraft

and ARGOS floats. A multiscale, interdisciplinary observational network is illustrated in

Figure 6 for the recent LOOPS

Massachusetts Bay Sea Trial

1998.

LEO-15 Observation and

Modeling System: The

Rutgers University Long-term

Ecosystem Observatory (LEO15) (Grassle et al., 1998) is an

instrumented natural littoral

laboratory that spans the 3 m to

30 m water depths offshore Tuckerton, New Jersey with a 30

km x 30 km well-sampled research space (Figure 2). This

inner shelf region has “often been ignored in the past because

of the very difficult operating conditions and the complex

dynamics, where the water is effectively filled with turbulent

boundary layers” (Brink, 1997). Real-time surface data from

remote sensing platforms, combined with real-time subsurface data from remotely-operated and autonomous nodes,

provide 3-D nowcasts to guide adaptive sampling with up to

five coastal research vessels and a fleet of AUVs (long-range

gliders, medium-range REMUS survey vehicles, and shortrange REMUS turbulence vehicles) (Glenn et al., 1998).

Coastal forecasts for adaptive sampling are generated using

Rutgers’ Regional Ocean Modeling System (ROMS), a

primitive equation model with a free sea surface, curvilinear

horizontal grid, a stretched (S-coordinate) vertical grid, and

open boundary conditions allowing two-way forcing

between small and large scales. Turbulence closure is

achieved using the KPP scheme (Large et al., 1994) modified

to include overlapping surface and bottom boundary layers

and wave-current interactions (Styles and Glenn, 1999). Data

assimilation options include nudging, optimal interpolation

and a reduced-state Kalman filter. Atmospheric forcing

options include operational Navy products that drive a

planetary boundary layer model, or direct coupling to a highresolution Regional Atmospheric Modeling System (RAMS).

HOPS examples: Figures 3 and 4 illustrate the use of

HOPS during recent NATO Rapid Environmental Assessment (Pouliquen et al., 1997) Rapid Response exercises in

1996 and 1998. A real-time nowcast for 18 Sept. 1996 is

shown in Figure 3a. This nowcast is the combination of a 3-

day forecast with AXBT data whose expected analysis error

is shown in Figure 3b. The data-forecast melding was

performed using ESSE assimilation. The sampling patterns

Fig. 3 – Surface temperature map for 18 Sept. 1996 in the Strait of Sicily region

overlaid with surface velocity vectors (a). The Atlantic Ionian Stream is a free jet

meandering from west to east with a strong thermal front between 25-26°C.; (b)

Normalized expected error (0-1) of the surface temperature mapped from the new

observations.

(a) (b)
Volume 51, Number 2 33

of data collection for ships and

aircraft (Sellschopp and

Robinson, 1997) were subjectively adapted in real-time,

combining shipboard predictions

with operational needs in order

to sample areas of influence for

the region of interest. Figure 4a

is a real-time nowcast for 21

March 1998, melding the field

forecast with all the past data up

to that day, via data assimilation.

Figure 4b is the forecasted error

standard deviation, from the

ESSE assimilation scheme, of

the temperature at 100m. The

error field and the associated dominant eigenvectors of error

covariance forecasts were utilized to design adaptive patterns

of AXBT flights for the region, in accord with practical,

operational and meteorological constraints.

Figure 5 and Figure 6 illustrate the interdisciplinary forecast

experiment that occurred for more than two months in

Massachusetts Bay in late summer and early fall of 1998.

This demonstration of concept real-time sea trial field

experiment was performed in collaboration with the LOOPS

(NOPP), Advanced Fisheries Management and Information

Service (AFMIS, NASA, Rothschild et al., 1998) and

Autonomous Ocean Sampling Network (AOSN, ONR,

Curtin et al., 1993) programs. The scientific focus was

phytoplankton and zooplankton patchiness, in particular, the

spatial variability of zooplankton and its relationship to

physical and phytoplankton variabilities. Simultaneous

synoptic physical and biological data sets in 4 dimensions

were obtained over a range of scales. This data was assimilated into HOPS using OI and ESSE. Real-time forecasts of

fields and error covariance eigendecompositions were

provided. These forecasts were utilized for adaptive sampling and for the calibration of the model parameters. Several

dynamical interactions among the circulation, productivity

and ecosystem systems were inferred.

Figure 5a shows the chlorophyll-a concentration at 10m,

overlaid with horizontal velocity vectors at the same depth.

Figure 5b is a cross-section of chlorophyll-a concentration

along the entrance of Massachusetts Bay, from Race Point to

Cape Ann. The multi-scale patchiness of the chlorophyll

field is clearly visible. Higher concentrations occur at the

northeast of Cape Ann and near Boston Harbor because of

the continued supply of nutrients, over Stellwagen Bank due

to tidal mixing, and at several locations along the coastline,

because of local wind driven upwelling and episodic wind

mixing.

Statistical error models previously developed for other ocean

regions (Lermusiaux,1999) were

calibrated and verified for use in

Massachusetts Bay. The initial

error subspace was set to the a

priori dominant, synoptic

mesoscale variability in the Bay,

which is related to the dominant

subspace of the so-called GFD

singular vectors (Palmer et al.,

1998). Adaptive sampling

methodologies were carried out

in real-time for two months, as

illustrated by Figure 6. The

multi-scale sampling strategies

were based on: (1) ocean field

forecasts assimilating all prior

data (regions of most active or interesting dynamics) and (2)

forecasts of error variances and of dominant

eigendecompositions of error covariances, using ESSE. The

optimal strategies were subject to weather and operational

constraints. Figure 6 shows the multiplicity of scales of such

strategies. The R/V Able-J (Panel a) was used to sample the

Fig. 4 – Melded estimate of temperature in the Gulf of Cadiz with velocity

vectors after data assimilation for 21 March 1998 (a) and forecast error estimate

Fig. 5 – Example chlorophyll-a concentration at 10m with horizontal velocity

vectors for MBST-98 (a) and vertical section of chlorophyll-a concentration from

Race Point to Cape Ann (b).

(a) (b)

(a) (b)
34 Naval Research Reviews

Bay scales and the external oceanic forcings (note the

adapted zigzag in the Gulf of Maine and over Georges

Bank). The R/V Oceanus (Panel b) sampled the mesoscales,

outside of Cape Cod Bay, and in the open boundary forcing

regions. The R/V Lucky Lady sampled the mesoscale (Panel

c) and submesoscales (Panel d), mainly in Cape Cod Bay.

The Odyssey AUV’s (Panel e) sampled the submesoscales in

Cape Cod Bay. Finally, the REMUS AUV’s (Panel f)

sampled the turbulent scales in Cape Cod Bay. All of the

sampling patterns of these platforms and sensors were

designed and made available in real-time, assimilating

yesterday’s data today for tomorrow’s forecast and sampling.

These accomplishments have resulted in a combined and

compatible physical and biological multi-scale data set

applicable to interactive process studies and data assimilation, adaptive sampling, and predictive skill OSSEs.

Coastal Predictive Skill Experiments at LEO-15: A

series of Coastal Predictive Skill Experiments (CPSE) were

begun at LEO-15 starting in 1998. The summer 1998 CPSE

focused on improving nowcast skill for adaptive sampling

using spatially extensive real-time data. The summer 1999

CPSE focused on improving model forecast skill for adaptive sampling via coupling to a regional atmospheric model,

improved turbulent closure, and real-time updates of the

offshore boundary conditions. Future CPSEs will emphasize

the coupling between physical and bio-optical components.

The phenomenological focus of the CPSEs is the development of recurrent coastal upwelling centers and their effect

on phytoplankton and suspended sediment distributions.

Figure 7a illustrates the initial development of an upwelling

center in which the ocean model has assimilated the more

Fig.6 – Adaptive sampling

methodologies carried out in

real-time for two months. (a)

The R/V Able-J was used to

sample the Bay scales and

the external oceanic forcings.

(b) The R/V Oceanus

sampled the mesoscales,

outside of Cape Cod Bay, and

in the open boundary forcing

regions. (c) The R/V Lucky

Lady sampled the mesoscale

and submesoscales (d),

mainly in Cape Cod Bay. (e)

The Odyssey AUV’s sampled

the submesoscales in Cape

Cod Bay. (f) The REMUS

AUV’s sampled the turbulent

scales in Cape Cod Bay.
Volume 51, Number 2 35

a cyclonic eddy embedded within the cold upwelling center

(Figure 7b). This data-based nowcast, a model forecast for

continued upwelling, and model sensitivity studies indicating

a dependence on turbulent closure in the vicinity of the eddy,

were used to define three cross-shelf transects for sampling

over a two day period. A ship-towed SWATH ADCP and an

undulating CTD/Fluorometer (Creed et al., 1998) were sent

to patrol the transect just north of the eddy center, and a

REMUS survey vehicle was sent to patrol the transect just

south. The REMUS turbulence vehicle was sent directly into

the eddy center to observe the changing turbulence characteristics as the vehicle drove out of the eddy and crossed the

upwelling front.

The alongshore current component (Figure 8, color contours)

acquired by the REMUS survey vehicles not only indicates

that the northward-flowing upwelling jet on the offshore side

is confined to the region above the thermocline, it also

reveals a southward-flowing, subsurface jet on the nearshore

side. The systems towed along the northern transect uncovered a similar velocity structure, with the highest phytoplankton concentrations of the season discovered within

the subsurface jet. The subsurface adaptive sampling data

suggest that phytoplankton concentration increases within

the upwelling center may be dominated by advection from

the north.

Eddy viscosities derived from the REMUS turbulence

vehicle were found to be two orders of magnitude greater on

the inshore side of the upwelling front compared to the

offshore side. Idealized tests of the modified KPP closure

(Figure 9) indicate that maximum eddy viscosities are

expected just shoreward of the upwelling front. Standard

Fig. 7(a) – Sea surface temperature and surface current

forecast of the initial formation of an upwelling center

generated by the Regional Ocean Modeling System

(ROMS) forced with operational Navy atmospheric

forecasts while assimilating surface current radial

velocity components from the individual CODAR sites.

Fig. 7(b) – Sea surface temperature and surface current

nowcast of a fully-developed upwelling center derived by

detiding and low-pass filtering the combined CODAR

vector velocities. Lines indicate the locations of the three

cross-shelf repeat transects chosen for subsurface

shipboard and AUV sampling.

extensive radial currents from each of two on-shore CODAR

HF-Radars (Kohut et al., 1999). The initial development is

characterized by the cyclonic curvature in the northward

flowing upwelling jet and the surfacing of the cold upwelled

water nearshore.

Three days later, the surface current and temperature nowcast

indicated that the upwelling jet was now meandering around

Fig. 8 – Alongshore (color contours) and cross-shore

(arrows) velocity components derived from the upward

and downward looking ADCPs on the REMUS Survey

AUV as it ran shoreward along the southern transect at a

depth near 8 m.
36 Naval Research Reviews

turbulent closure schemes produce the exact opposite, a

minimum in the eddy viscosity just shoreward of the front.

Coupled biological model sensitivity studies indicate that the

biological response can be even more sensitive to vertical

mixing parameterizations than the physical model.

Adaptive sampling research and the control of

errors

In modern ocean adaptive sampling, a goal characterizes the

ideal future sampling among the possible choices, in an

adaptive accord with the constraints and available forecasts

that have assimilated all of the past data. This goal can be

achieved either subjectively, with forecast information being

combined with the a priori experience to intuitively choose

the future sampling, or quantitatively, where forecast

capabilities serve as input to a mathematical sampling

criterion whose real-time, continued, optimization predicts

the adapted sampling. The parameters of the adaptive

sampling procedure are therefore the available forecasts, new

data acquired during the forecast, the constraints and the

goal, i.e. the properties to be optimized and the metrics used

to measure these properties.

Today, the forecast capabilities include the future evolution

of the ocean fields, of their variabilities and of their uncertainty or error statistics (Lermusiaux, 1999). There are

constraints from practical considerations (platforms and

sensors available, airport locations, ship speeds, AUV range,

weather conditions, etc), dynamical motives (search for

precursor of the primary phenomenon, dynamical model

verifications), and cost penalties (batteries, fuel, human

costs). There are scientific and technical constraints for the

measurement model to generate the actual state variables to

be assimilated. For example, adaptive sampling of coastal

currents may be severely

constrained by the sampling

requirements of a measurement

model that separates the

frequencies of interest (the

model velocity state variables

for assimilation) from the

spectrum of frequencies

observed (surface and internal

waves, tides, inertial waves,

etc.). Finally, several goals or

criterion are also possible, in

varied representations (e.g.

physical vs. Fourier space). For

example, the optimum can be

the sampling that minimizes the

forecast of the field error

variances over the global

domain and scales of interest,

subject to the cost penalties and

practical constraints. Other types

of optima are the sampling that

ideally determines specific properties of the future dynamics

(e.g., potential vorticity), irrespective of the past data and

other constraints, or, the sampling that allows the best skill

evaluation. In assimilation studies, the goal should be in

accord with the data assimilation criteria. For example, if the

assimilation aims at minimizing the field error with a

variance metric (i.e. trace of the error covariance), the

adaptive sampling criteria should aim at determining the

future sampling that also minimizes the trace of the error

covariance.

An important component involves the theoretical and

numerical optimization procedure, to be carried out in realtime. For linear systems, the optimization can be implemented beforehand, independently of the future data values,

only using the dynamical and measurement models and their

statistical uncertainties. However, for nonlinear models, the

data values matter, and forecast OSSEs need to be carried out

during the optimization process. To do so, the results of the

last decades in optimal control and estimation theory

(Robinson et al., 1998) are ready to be utilized and further

developed by the interdisciplinary oceanographer in the

quest for the most useful data.

Research Directions and Future Prospects

During the 1990’s interdisciplinary ocean science has been

rapidly evolving and now comprises an increasingly important and substantial component of marine science. This has

been based upon progress in the understanding of realistic

ocean dynamical processes in the sub-disciplines, and the

identification of new realistic coupled and interdisciplinary

dynamical processes is presently a research frontier. More

and more attention is being focused on the coastal ocean and

its deep sea and terrestrial interactions. The requisite four

Fig. 9 – Idealized cross-shelf transect of turbulent eddy viscosity (color

contours) and density (white lines) generated by the modified KPP closure,

with the largest viscosities found shoreward of the density front.
Volume 51, Number 2 37

dimensional field estimates necessary for continued progress

in multi-scale interdisciplinary ocean science and technology

can only be provided by advanced littoral ocean observing

and prediction systems with adaptive sampling. Ocean

science, ocean engineering and marine technology are

symbiotic among themselves and are deeply rooted in the

fundamental and engineering sciences. Complex ocean

systems research today is interdisciplinary with important

aspects of computer, information and communication

sciences.

Coastal ocean adaptive sampling is in its infancy and

methodological advances in the next several years will be

related to advances in the observing and prediction systems

components, the overall system concept and system integration, as well as dedicated theoretical research on objective,

automated sampling. Platform advances will include ocean

gliders, improved AUV capabilities and unmanned aircraft.

Fleets of robotic autonomous platforms will operate with

sampling patterns altered in consideration of data pooled and

analyzed aboard command platforms. New sensors are under

design, construction and test for hyperspectral ocean optics,

microwave salinity and coastal altimetry measurements.

Interdisciplinary multi-scale ocean models will be validated

for a variety of (interactive) processes; calibration and

sensitivity procedures will be established. Process feedbacks

for coupled regional atmospheric and oceanic models will be

better understood and some coupled systems will be undergoing verification from both regional and generic points of

view. Research issues involved in developing the methodology of quasi-optimal assimilation of interdisciplinary multiscale multi-fields in real-time should be clarified. The

advanced OOPS concept is of a flexible, modular, scaleable,

distributed system capable of efficiently managing large preexisting and novel databases. Fully integrated OSSEs, which

include both scientific process and engineering operational

constraints, will be underway. The suitability of adaptive

sampling goals for various purposes will be studied and

better understood and, hopefully, associated quantitative

metrics will not be strongly dependent upon the methodology of their implementation. With recent progress towards

the implementation of real-time optimal control and optimization algorithms, computed optimal samplings will give the

assimilation scheme the observations it needs most, hence

ideally improve the ocean field estimate. Such theoretical

adaptive sampling studies need to be carried out for both

covert and overt operations.

Experience of recent past decades indicates that the first

decade of the twenty first century should result in the

maturing and evolution of both interdisciplinary ocean

science and technology, and the ocean observing and

prediction system concept. Powerful new field estimation

and regional predictive capabilities can be expected to

transform overall operational capabilities for naval rapid

environmental assessment and societal environmental crisis

response and, supported by rapidly expanding observational

infrastructure and a strong national coastal program, to

provide the basis for effective and efficient management of

multi-use coastal zones.

Acknowledgments

We are grateful to Dr. Pierre F.J. Lermusiaux, Michael

Crowley and Wayne G. Leslie for essential contributions to

the preparation of this manuscript, and thank Prof. Henrik

Schmidt, MIT, for interesting remarks. We are both supported by grants from the Office of Naval Research and the

National Ocean Partnership Program.

References

1. K.H. Brink, “Observational coastal oceanography,” presented

at Advances and Primary Research Opportunities in Physical

Oceanography Studies (APROPOS) Workshop, 15-17

December 1997.

2. E.L. Creed, S.M. Glenn and R. Chant, Adaptive Sampling

Experiment at LEO-15, OCC ’98 Proceedings, Sea

Technology, November, 576-579 (1998).

3. T.B. Curtin, J.G. Bellingham, J. Catipovic and D. Webb,

“Autonomous Ocean Sampling Networks,” Oceanography,

6(3), 86-94 (1993).

4. S.M. Glenn, G.Z. Forristall, P. Cornillon and G. Milkowski,

“Observations of Gulf Stream Ring 83-E and Their

Interpretation Using Feature Models,” J. of Geophysical

Research, 95, 13,043-13,063 (1990).

5. S.M. Glenn and A.R. Robinson, “Verification of an

Operational Gulf Stream Forecasting Model,” Qualitative Skill

Assessment for Coastal Ocean Models, Coastal and Estuarine

Studies, American Geophysical Union, D. Lynch and A.

Davies (eds.), 47, 469-499 (1995).

6. S.M. Glenn, D.B. Haidvogel, O.M.E. Schofield, J.F. Grassle,

C.J. von Alt, E.R. Levine and D.C. Webb, “Coastal Predictive

Skill Experiments at the LEO-15 National Littoral

Laboratory,” Sea Technology, April, 63-69 (1998).

7. J.F. Grassle, S.M. Glenn and C. von Alt, “Ocean Observing

Systems for Marine Habitats,” OCC ’98 Proceedings, Sea

Technology, November, 567-570 (1998).

8. T.R. Keen and S.M. Glenn, “Factors influencing hindcast skill

for modeling shallow water currents during Hurricane

Andrew,” J. Atmos. Ocean. Tech., 15, 221-236 (1998).

9. J.T. Kohut, S.M. Glenn and D.E. Barrick, “SeaSonde is

Integral to Coastal Flow Model Development,” Hydro

International, April, 32-35 (1999).

10. W.G. Large, J.C. McWilliams and S.C. Doney, “Oceanic

vertical mixing: A review and model with a nonlocal boundary

layer parameterization,” Reviews of Geophysics, 32, 363-403

(1994).

11. P.F.J. Lermusiaux, “Data assimilation via error subspace

statistical estimation, Part II: Mid-Atlantic Bight shelfbreak

front simulations and ESSE validation,” Monthly Weather

Review, 127(8), 1408-1432 (1999).
38 Naval Research Reviews

The Authors

Allan R. Robinson is the Gordon McKay Professor of Geophysical Fluid Dynamics at Harvard

University. He holds BA (mcl), MA and PhD

degrees in physics from Harvard and honorary

doctorates from the Universities of Liege and

Massachusetts. His research includes dynamics of

rotating and stratified fluids and ocean currents,

and the influence of physical processes on biological dynamics in the ocean. He is recognized as a

pioneer and leading expert in ocean prediction and

data assimilation. He has served on numerous

national and international advisory committees and

has chaired many programs for international

cooperative science, including mesoscale dynamics, ocean prediction, and ecosystem dynamics. He

has authored and edited nearly 200 articles and

books and is currently editor-in-chief of THE SEA

and Dynamics of Atmospheres and Oceans.

Scott M. Glenn received his Sc.D. in Ocean

Engineering from the WHOI/MIT Joint Program in

1983. He currently is a Professor of Marine and

Coastal Sciences at Rutgers University, where he

co-directs the Coastal Ocean Observation Lab. His

recent research activities at LEO-15 include the

development of distributed multi-platform ocean

observation networks for real-time nowcasting,

improved algorithms for numerical ocean models to

increase coastal forecast skill, and new adaptive

sampling techniques using towed and autonomous

systems for interdisciplinary applications.

12. MODE Group, “The Mid-Ocean Dynamics Experiment,”

Deep-Sea Research, 25, 859-910 (1978).

13. C.N.K. Mooers, A.R. Robinson and J.D. Thompson, “Ocean

Prediction Workshop 1986: A status and prospectus report on

the scientific basis and the Navy’s needs,” Proceedings of

Ocean Prediction Workshop, Inst. Naval Oceanography,

National Space Technology Laboratory, MS.

14. S. Nadis, “’Real-time’ oceanography adapts to sea changes,”

Science, 275, 1881-1882 (1997).

15. N.M. Patrikalakis, P.J. Fortier, Y.E. Ioannidis, C.N. Nikolaou,

A.R. Robinson, J.R. Rossignac and A. Vinacua, “Distribution

Information and Computation in Scientific and Engineering

Environments.” D-Lib Magazine, 5(4), http://www.dlib.org/

dlib/april99/04abrams.html (1999).

16. E. Pouliquen, A.D. Kirwan Jr. and R.T. Pearson (eds.), “Rapid

Environmental Assessment,” Proceedings Int. Conference

Rapid Environmental Assessment, 10-14 March 1997, Lerici,

Italy.

17. A.R. Robinson (ed.), Eddies in Marine Science (Springer,

Berlin, 1983), p. 609.

18. A.R. Robinson, “Forecasting and simulating coastal ocean

processes and variabilities with the Harvard Ocean Prediction

System” Coastal Ocean Prediction, AGU Coastal and

Estuarine Studies Series, C.N.K. Mooers (ed.), (American

Geophysical Union, 1999), pp. 77-100.

19. A.R. Robinson and K.H. Brink (eds.), THE SEA: The Global

Coastal Ocean, Volume 11: Regional Studies and Syntheses,

(John Wiley and Sons, New York, 1999).

20. A.R. Robinson, J.A. Carton, N. Pinardi and C.N.K. Mooers,

“Dynamical forecasting and dynamical interpolation: An

experiment in the California Current,” J. of Physical

Oceanography, 16, 1561-1579 (1986).

21. A.R. Robinson, P.F.J. Lermusiaux and N.Q. Sloan, “Data

Assimilation,” THE SEA: The Global Coastal Ocean, Volume

10: Processes and Methods, A.R. Robinson and K.H. Brink

(eds.), (John Wiley and Sons, New York, 1998), pp. 541-594.

22. B.A. Rothschild, A. Robinson, A. Gangopadhyay, S.

Besiktepe, J. Bisagni, A. Cabeza, D. Cai, P. Fortier, P. Haley,

H.S. Kim, E. King, L. Lannerole, P. Lermusiaux, W. Leslie, C.

Lozano and M. Miller, “Management Information System and

the Precautionary Approach,” ICES Symposium on

Confronting Uncertainty in the Evaluation and Implementation

of Fisheries-Management Systems, 16-19 November 1998,

Cape Town, South Africa.

23. J. Sellschopp and A.R. Robinson, “Describing and forecasting

ocean conditions during Operation Rapid Response,”

Proceedings Int. Conf. Rapid Environmental Assessment, E.

Pouliquen, A.D. Kirwan Jr. and R.T. Pearson (eds.), 10-14

March 1997, Lerici, Italy, pp. 35-42.

24. R. Styles and S.M. Glenn, “Modeling Stratified Wave-Current

Bottom Boundary Layer Model for the Continental Shelf,” J.

of Geophysical Research, submitted (1999).
Volume 51, Number 2 39

ceanographers have recently made considerable

strides in model improvement, model-data synthesis,

and oceanic and climatic forecasting. They are moving

towards forecasting applications that vary from global

climate change simulations, through modeling of decadal

and interannual climate variabilities like El Niño, to extended seasonal forecasts, and finally to regional forecasts on a time scale of weeks.

Advances in data assimilation have been largely

responsible for the new ability to take good advantage of

the rapidly expanding dataset. These advances come not

only from meteorology, but from work as divergent as

solid-earth geophysics inverse theory and engineering

control theories. All of them have helped oceanographers

by giving them the formal tools necessary to constrain a

dynamical model with available data.

Different oceanographic applications call for different data assimilation methodologies. The diversity of the

objectives suggests that no single assimilation methodology can address all of our needs. More probably several techniques, like those addressed in the article that

follows, will jointly address the future needs of oceanographic assimilation. Each methodology will serve the

purposes to which it is best suited.

Here then is a review of some of this decade’s most

promising work. - J.P.
40 Naval Research Reviews

Paola Malanotte-Rizzoli

Massachusetts Institute of Technology

Cambridge, MA

Oceanographic Data Assimilation in

the 1990s:

Overview, Motivation and Purposes

Abstract

A brief non-technical overview is given of oceanographic

data assimilation in the 1990’s. First, a historical perspective

is presented that illustrates its main motivations and discusses the objectives of combining fully complex ocean

general circulation models (OGCM) and oceanographic data.

These objectives are divided into three main categories:

model improvement, model-data synthesis and ocean/climate

forecasting. Forecasting applications vary from global

climate change simulations on a time scale of 50-100 years;

through decadal and interannual climate variability, such as

the El Nino-Southern Oscillation and the Atlantic thermohaline variability; to extended seasonal forecasts and finally to

regional forecasts on a time scale of a few weeks. Appropriate assimilation methodologies for each class of oceanographic applications are discussed. For each ocean prediction

problem on different time/space scales the needs for data

assimilation approaches are pointed out where these are still

lacking as they might overcome some of the present deficiencies of the related modeling efforts.

Introduction

The term “data assimilation” emerged in meteorology about

30 years ago to describe a methodology in which observations are used to improve the forecasting value of operational

meteorological models. In the practice of operational

meteorology, all the observations available at prescribed

times are “assimilated” into the model by melding them with

the model-predicted values of the same variables in order to

prepare initial conditions for the forecast model run.

In the oceanographic context, however, “data assimilation”

has acquired a much broader meaning, covering a vast body

of methodologies that originate not only in meteorology, but

also in solid-earth geophysics inverse theories and in

engineering control theories. These methods all constrain a

dynamical model with available data. Furthermore, oceanographers often use data assimilation for very different purposes than those common in meteorology. In this past decade

they have come to focus on “model-data synthesis”, that is,

on obtaining a four-dimensional realization (the spatial

description coupled with the time evolution) of the oceanic

flow that is simultaneously consistent with the observational

evidence and the dynamical equations of motion. This

“synthetic” realization can be used for detailed process

studies.

In this paper I wish to provide a brief and non-technical

overview of the various assimilation problems and methodologies used in oceanography. My main focus is the objectives of oceanographic data assimilation, rather than the

methodologies used, and I will try to concentrate on what

still needs to be done rather than on reviewing the existing

body of work. I limit my attention to the use of oceanographic data with the most realistic and sophisticated tools

presently available to simulate oceanic flows, the ocean

general circulation models (OGCM). One assumes the future

of oceanographic data assimilation must lie there.

Many detailed technical references cover the various

assimilation methodologies used in oceanography. At the

most fundamental levels, inverse methods in oceanography

are similar to those used in geophysics. Some comprehensive

textbooks for this mature field are Geophysical Data

Analysis: Discrete Inverse Theory by Menke (1984) and

Inverse Problem Theory by Tarantola (1987). However, these

reviews do not meet oceanography’s requirement: an

analysis of these methods for application to nonlinear, timedependent dynamical models of three-dimensional ocean

circulation. Data assimilation methods most used and

relevant for meteorology are reviewed by Bengtsson et al.

(1981). From the point of view of the complexity of the
Volume 51, Number 2 41

physical systems, and of the associated dynamical models,

the analysis and applications discussed in Daley’s (1991)

book, Atmospheric Data Assimilation, are perhaps the most

useful.

Two major differences in objective still prevent oceanography from simply “borrowing” techniques from meteorology.

First, the motivation for oceanic data assimilation, is not as

narrowly focused on short term prediction as most meteorological efforts, although it must be added that ocean forecasting is rapidly emerging as a legitimate and important

motivation in itself. Second, the meteorological and oceanographic data sets are distinguished from one another by a

major difference, which I will discuss in the next section.

Thus methodologies that originate in meteorology cannot be

blindly applied to oceanic dynamical problems, but must be

revisited and sometimes profoundly modified to make them

feasible and successful for physical oceanography.

Reviews and syntheses of data assimilation methods for

oceanographic applications can be found in the special issue

of Dynamics of Atmospheres and Oceans devoted to Oceanographic Data Assimilation, Haidvogel and Robinson, eds.

(1989). The review paper by Ghil and Malanotte-Rizzoli

(1991) provides a very comprehensive review of the literature up to the early 90’s. A recent, thorough synthesis of

oceanographic assimilation methodologies appears in

Bennett (1992). A recent monograph by Wunsch (1996)

views ocean general circulation as an inverse problem.

Historical perspective

Over the past 25 years or so, since the initial efforts to

develop three dimensional ocean circulation models (Bryan,

1969), ocean modeling has made enormous progress.

Holland and Capotondi (1996) review the milestones in the

development and advancement of OGCM’s, up to the

complexity and sophistication of the present generation of

models, which are capable of most realistic simulations on

the global scale. Their review also offers a perspective from

which to view the future possibilities and trends of ocean

modeling. In parallel with advances in modeling, oceanic

observational techniques have also been thoroughly revolutionized. However, because oceanography lacks a single

focusing motivation for oceanic data assimilation like the

one meteorology gets from the need for Numerical Weather

Prediction (NWP), ocean models and observational techniques have developed quite independently of one another.

When oceanic models and observations started to converge,

they did so along different paths depending on the specific

objective of each effort.

The early days of oceanography saw dynamic calculations as

the main quantitative tool to combine data (temperature and

salinity) with “models” (thermal wind relations). From this

modest beginning—relying on highly simplified models with

no formal assimilation procedure—the next step was to

introduce a formal least square inverse methodology imported from solid earth geophysics and add the tracer

conservation constraints in order to solve the problem of the

level of no motion (Wunsch, 1978; Wunsch and Grant, 1982;

Wunsch, 1989a,b). This was done in the framework of coarse

resolution box models whose dynamics was still very simple,

although the inverse methodology used was very general.

At the other extreme of model complexity versus assimilation method sophistication, efforts began with “diagnostic

models” in which temperature and salinity data were simply

inserted into the dynamical equations of fairly complex

ocean models in order to evaluate the velocity field (Holland

and Hirschman, 1972). The results were very poor because

of inconsistencies in model-data-topography, and so at the

next stage a very simple assimilation methodology was

introduced into OGCMs, and this became known in the

oceanographic context as the “robust diagnostic” approach

(Sarmiento and Bryan, 1982). The same approach had

actually been introduced earlier in meteorology as the

“nudging” technique (Anthes, 1974) and the term “nudging”

has now become common in oceanography as well. In this

approach there is no effort to introduce least-square

optimality, and the data are just used to nudge the model

solution towards the observations at each time step through a

relaxation term added to the model equations. The result is

far superior to simple diagnostic models, but leaves much to

be desired due to the inability to use information about data

uncertainty or to estimate the errors in the solution obtained

(Holland and Malanotte-Rizzoli, 1989; Capotondi et al.,

1995a,b; Malanotte-Rizzoli and Young, 1995).

As the objectives of modeling and observational oceanography began to converge, more formal least square methods

taken from meteorology were also used in ocean models, in

particular the Optimal Interpolation (OI) method (Robinson

et al., 1989; Derber and Rosati, 1989; Mellor and Ezer, 1991

are among the first examples). OI may be viewed as a

nudging technique in which the amount of nudging of the

model solution towards the observations depends on the data

errors, while also permitting error estimates for the solution.

This approach, developed in meteorology for NWP, cannot

improve model parameters or parameterizations, nor can it fit

the entire four-dimensional distribution of observations

simultaneously to the model solution. However, due to OI’s

relatively low computational cost, it remains appropriate for

higher resolution, short-term prediction and state estimation

purposes.

Carrying the least square approach for a time dependent

model to its rigorous limit leads to the “Kalman filter/

smoother” assimilation methodology, which can assimilate

data into a time dependent model while assuring least-square

optimality, full use of a priori error estimates, and calculation of the covariance error matrix for the model outputs.

Apart from the fact that the Kalman filter is formally optimal

in the least-square sense only for linear models, its high
42 Naval Research Reviews

computational cost limits its use at present to simple models

or very coarse OGCMs. Recent efforts are directed at

developing efficient although suboptimal variants of the

Kalman filter/smoother that allow the use of a full nonlinear

OGCM with this method (Fukumori et al., 1993; Fukumori

and Malanotte-Rizzoli, 1995; Menemenlis et al., 1997a,b;

Cane et al., 1998; Verron et al., 1999).

The ultimate goal of combining a formal least-square

optimization approach with a full complexity OGCM

requires simultaneous solution of hundreds of thousands of

coupled nonlinear equations (the model equations at all grid

points and all time steps), and therefore requires an efficient

approach. Such an approach can be found in the “optimal

control” engineering literature. Also known as the “adjoint

method”, this method is capable of model improvement,

parameter estimation and true four-dimensional data assimilation. It is equivalent in principle to the Kalman filter (Ghil

and Malanotte-Rizzoli, 1991), except that it allows us to give

up the use and calculation of full covariance matrices, and

therefore is more computationally feasible for higher

resolution nonlinear OGCMs (Tziperman and Thacker, 1989;

Tziperman et al., 1992a,b; Marotzke, 1992; Marotzke and

Wunsch, 1993; Bergamasco and P. Malanotte-Rizzoli, 1993;

Yu and Malanotte-Rizzoli, 1996; Lee and Marotzke, 1997,

1998; Yu and Malanotte-Rizzoli, 1998). The most recent

application of the methodology involves the evaluation of an

adjoint code for complex OGCM’s through an automatic

compiler (Marotzke et al., 1999).

The development of assimilation methods in physical

oceanography seemed always to trail a few years behind

meteorology. Given that the ocean and atmosphere, even

though characterized by some important differences, are

similar enough that they can be treated with the same

theoretical approaches and methodologies, such a lag can be

surprising. It is therefore important for the ocean modeler to

try to understand why meteorology and oceanography have

seen different rates of development of data assimilation

methodologies in order to isolate potential obstacles to their

future use in oceanography.

Clearly a primary reason for the delayed development of

oceanic data assimilation was the lack of an urgent and

obvious motivation such as generating better and longer

weather forecasts provided meteorology. This situation has

been rapidly changing in recent years, and ample motivation

for ocean data assimilation now exists because of the need

for systematic model improvement and ocean state estimation. The need for ocean prediction is now emerging on

various temporal and spatial scales: from climate change

predictions, through regional forecasts of the large scale

ocean climate variability (of for example the North Atlantic

thermohaline circulation or El Niño in the Pacific Ocean), to

thefew weeks’ regional mesoscale ocean forecasts in frontal

regions like the Gulf Stream system that for example various

Naval applications require.

Want of an obvious motivation aside, however, the most

profound limitation on the development of oceanic data

assimilation may have been the lack of adequate data sets.

The number of available oceanographic observations is far

smaller than the number of meteorological observations,

especially when the different temporal and spatial scales are

considered. It is estimated, in fact, that the number of

presently available oceanographic observations is smaller

than its meteorological counterpart by several orders of

magnitude (Ghil and Malanotte-Rizzoli, 1991; Daley, 1991).

New oceanographic data sets, nearly comparable to the

meteorological one, that is, synopses with with global

coverage, are however becoming available. This oceanographic observational revolution of the 90’s has been made

possible by the advent of satellite oceanography. Already

~40,000 sea surface temperatures are now available daily on

a global scale, measured by the NOAA satellites that have

been flying since the 80’s. Additionally, two satellite

altimeters are now providing observations of the ocean

surface topography that is tightly coupled to ocean currents.

The first of these, TOPEX/POSEIDON, was launched in

1992, and is currently producing global maps of sea surface

height with a horizontal resolution of ~300 km x 300 km at

mid-latitudes every 10 days, and at an impressive accuracy

of 5cm (Stammer and Wunsch, 1994). TOPEX/POSEIDON

altimeter data provide powerful information to inverse

approaches for determination of the large-scale ocean

circulation (Stammer and Wunsch, 1996; Ganachaud et al.,

1997). The European satellite ERS-1 is also measuring sea

surface topography with higher spatial resolution that

resolves the mesoscale eddy field. ERS-1 also measures the

surface wind field on the global scale at a 1 degree resolution, providing thereby information about a crucial driving

force of oceanic circulation. Fu and Fukumori (1996) review

the effects of errors in satellite altimetry for constraining

OGCM’s through data assimilation.

A second major source of worldwide oceanographic observations is the World Ocean Circulation Experiment (WOCE).

Through basin-wide hydrographic sections, both meridional

and zonal, the WOCE should provide a zero-order picture of

the large scale global circulation in the 90’s. Because

hydrographic sections are not synoptic, and are mostly

carried out only once, no data of the time evolution will be

available and very large water bodies between adjacent

sections still remain void of data. Hence the great importance

of numerical models endowed with data assimilation

capability to act as dynamical interpolators and extrapolators

of the oceanic motions. Clearly ocean models and assimilation methods can make better use of the various new and

traditional sources of oceanographic data when reliable error

estimates are available. Particularly important is the possibility of obtaining estimates of the non-diagonal terms of the

error covariance matrices, for which only the diagonal terms,

i.e. the data standard deviations, are usually specified. Hogg

(1996) discusses efforts to obtain estimates of the full error
Volume 51, Number 2 43

covariances of traditional oceanographic datasets (Figure 1

and 2).

It is worthwhile to mention another type of oceanic observation, rather different from traditional point-wise measurements. These are the observations provided by ocean

acoustic tomography that exploits the ocean’s transparency

to sound. As in its more familiar medical application, the

tomographic technique scans the ocean through twodimensional (vertical or horizontal) slices using sound

waves. The difference and novelty of ocean acoustic tomography lies in the integral nature of the tomographic datum

(Munk et al., 1995). The implications and need for the

assimilation of such integral data into OGCM’s are discussed

by Cornuelle and Worcester (1996). A first estimate of the

North Pacific general circulation by combining satellite

altimetry, acoustic tomography and an OGCM was provided

by the ATOC Consortiuim (1998).

This brief discussion of the emerging need for ocean data

assimilation and the new data sets that are becoming available indicates that the limitations imposed by the scarcity

and non-synopticity of oceanic observations are being

overcome. Oceanographic data assimilation can now become

a fully developed, mature field.

Objectives of oceanographic data assimilation

Efforts to combine fully complex OGCMs and oceanographic data may roughly be divided into three main categories: model improvement, model-data synthesis with related

studies of dynamical processes through state estimation, and,

finally, oceanic/climatic forecasting. Let us consider these

objectives in some detail, as well as the assimilation methodologies relevant to each.

Even the highest resolution ocean circulation models cannot

resolve all of the dynamically important physical processes

in the ocean from small scale turbulence to basin scale

currents. There will always be processes that are not represented directly, but are instead parameterized. These

parameterizations are sometimes simple, often complicated,

and always quite uncertain both in form and in the value of

their tunable parameters. Very often the uncertainty in these

parameterizations is accompanied by an extreme sensitivity

of the model results to slight variations in the parameters. An

obvious though not unique example is the parameterization

of small scale vertical mixing in the ocean interior for which

many forms have been proposed. This drastically affects the

strength of the thermohaline circulation and the estimate of

meridional heat flux of OGCMs (Bryan, 1987). Other

examples are the parameterizations of mixed layer dynamics

(Mellor and Yamada, 1982), and of deep water formation

(Visbeck et al., 1996).

The most important example of the need to parameterize the

sub-grid scale motions not resolved by the OGCM resolution

is provided by the parameterization of mesoscale eddies in

coarse OGCM’s used for climate studies. The traditional

horizontal eddy diffusivities have been proven grossly

inadequate, inducing spurious features into the simulations

like the strong artificial upwelling different OGCM’s

produce in the mid-latitude North Atlantic inshore of the

Gulf Stream (Böning et al., 1995). Testing of different

proposed parameterizations, such as those by Green (1970),

Stone (1972), and Gent and McWilliams (1990), has been

extensively discussed in the recent literature, including

notably the work by Böning et al. (1995). For a most recent

review of the assessment of different eddy parameterizations

see Jiang et al. (1999).

Fig. 1 – Space and time scales accessible

by various measurement techniques.

[From Hogg, 1996]

Fig. 2 – A correlation matrix of sea

surface height measured along Topex/

Poseidon descending track no. 202 which

crosses 20°N at about 55°W and 40° N at

about 68° W. filled areas are between -0.2

and zero. [From Hogg, 1996]
44 Naval Research Reviews

Another set of uncertain yet crucial parameters corresponds

to the poorly known surface forcings by wind stress, heat

fluxes and evaporation and precipitation, all of which are

subject to typical uncertainties of 30-50% (Trenberth et al.,

1989; Schmitt et al., 1989; Trenberth and Solomon, 1994).

Finally, a crucial problem that needs to be solved if regional

models are to improve is the specification of open boundary

conditions. The open-boundary condition problem is

mathematically ill-posed and ad hoc boundary conditions,

mostly empirically determined, are prescribed (Chapman,

1985; Robinson et al., 1989; Malanotte-Rizzoli and Young,

1995). Data assimilation approaches can provide a powerful

tool for improving regional ocean models.

The first major objective of oceanographic data assimilation

is to use the available data systematically and quantitatively

in order to test and improve the various uncertainties of

OGCMs. It is important to understand that by model improvement I mean the use of data to determine model

parameters, forcing functions, boundary conditions, etc. in a

way that will yield better performance when the model is

later run without data assimilation. There are typically

thousands of poorly known internal model parameters, such

as viscosity/diffusivity coefficients at each model grid-point,

and many thousands more if the surface forcing functions are

included at every surface grid point (Tziperman and Thacker,

1989). Estimation of these parameters therefore becomes an

extremely complicated nonlinear optimization problem

whosesolution requires efficient methodologies and powerful computers. The assimilation methodology most suited to

deal with these estimation problems is the adjoint method

that calculates the model sensitivity to its

many parameters (Hall and Cacuci, 1983;

Thacker, 1988; Thacker and Long, 1988)

To my knowledge only one application of the

adjoint procedure has been carried out so far

for the optimal estimation of eddy viscosity

parameters. This was done by Tziperman and

Thacker (1989) using simplified model

dynamics and an idealized basin configuration. On the other side, the adjoint approach

has proven very successful in the estimation

of surface forcings (wind stress, surface heat

and moisture fluxes) with OGCMs in fully

realistic configurations. See the study by

Marotzke and Wunsch (1993) and the more recent ones by

Yu and Malanotte-Rizzoli (1996), Lee and Marotzke (1997),

Yu and Malanotte-Rizzoli (1998), and Lee and Marotzke

(1998). Equally successful has been the inclusion of open

boundary conditions as control variables in the adjoint code,

as shown by Gunson and Malanotte-Rizzoli (1996a,b) for

simplified dynamics and idealized model configurations, and

by Zhang and Marotzke (1999) for a fully realistic application of an OGCM to the Indian ocean.

Even though extensive data sets are becoming available

through the new remote sensing methods and the extensive

global observational programs mentioned above, the ocean

remains only sparsely observed. Most of the interior water

mass, and especially the abyssal layers, will continue to

remain unmonitored. Hence the second major objective of

oceanic data assimilation is to have numerical models

constrained to reproduce the available observations act as

dynamical extrapolators and interpolators, propagating

information to times and regions void of data. This approach

is now defined as “model-data synthesis” and has received

tremendous impetus in recent years.

Synthesizing the ocean state from observations may serve

several important goals. On a global scale, unobservable

quantities such as the meridional heat flux and the air-sea

exchanges can be continuously monitored from the assimilation output to infer possible changes due to climate trends.

Knowledge of the natural variability of these quantities is

essential for us to differentiate natural climate variability

from man-induced climate change. On a regional scale, we

see how high resolution, eddy resolving interpolation of

remote sensing or localized data by the models (Mellor and

Ezer, 1991; Capotondi et al., 1995a,b; Malanotte-Rizzoli and

Young, 1995) provides a four dimensional picture of the

eddy field. This picture can then be used to study detailed

dynamical processes of eddy-mean flow interaction, ring

formation and ring/jet interactions in the energetic western

boundary currents.

Global model-data synthesis may be seen in the estimates of

the global circulation by Sirkes and Tziperman (1996) and

those which Stammer et al. (1997) obtained through the

adjoint method. Basin-scale examples, again based on the

adjoint procedure, are found in Marotzke and Wunsch

(1993), Yu and Malanotte-Rizzoli (1996, 1998), and Lee and

Marotzke (1997, 1998). The applications by Menemenlis et

al. (1997a,b) use a suboptimal Kalman filter. In the tropical

ocean, Busalacchi (1996) shows how the unique physics of

the low-latitude oceans and the wealth of observational data

from the Tropical Ocean Global Atmosphere program have

Figure 3 – Contour map of the influence of data from the tide gauge

station at Nauru. In this experiment, data were also assimilated at

Rabaul, Jarvis, Christmas, Santa Crux and Callao. [From Miller and

Cane, 1996]
Volume 51, Number 2 45

catalyzed tropical ocean data assimilation. Among these

tropical ocean assimilations are some of the first applications

of the Kalman filter to actual in situ ocean data, the methodology of which and related theoretical considerations for

model-data synthesis are reviewed by Miller and Cane

(1996) (Figure 3).

The third distinct objective of oceanic data assimilation,

ocean and climate nowcasting and prediction, has not until

recently been a topic of interest to mainstream oceanography.

At present, however, more and more specific oceanographic

applications find prediction not only timely but necessary. It

is convenient to classify the oceanographic prediction

problems by their time scale, as each of them requires

different methodologies of approach and different data.

The problem of climate change is a prediction problem, and

therefore needs to be treated as such. Simulation studies of

climate change due to CO2

 increase and the greenhouse

effect on a time scale of 50 to 100 years, have recently

begun to use coupled atmospheric/ocean general circulation

models (A/OGCM). The first studies that extended such

coupled A/OGCM simulations to a multiple century time

scale were those by Cusbasch et al. (1992) and by Manabe

and Stouffer, (1994). Very recent studies simulating the

coupled ocean/atmosphere system include those by Santer et

al. (1995), Hergerl et al. (1996), Boville et al. (1998). The

use of fully coupled A/OGCMs represents great progress

from the time a few years ago when such studies were based

on atmospheric models alone, were coupled to simple mixedlayer ocean models (as in Wilson and Mitchell, 1987,

Schlesinger and Mitchell, 1987, Wetherald and Manabe,

1988, Washington and Meehl, 1989a), or were coupled to a

model that parameterized heat transport below the mixed

layer as a diffusive process (Hansen et al., 1988). Studies

using fully coupled A/OGCMs have taken one of two routes

to initializing greenhouse warming simulations.

The first approach is to initialize the simulation with steady

state solutions of the separate ocean and atmosphere sub

models obtained by running the two models separately

(Stouffer et al., 1989; Manabe et al., 1991; Cusbasch et al.,

1992; Manabe and Stouffer, 1994; Santer et al., 1995). In this

procedure the atmospheric model is spun up to a statistical

steady state using prescribed SST climatology. The ocean

model is then spun up using boundary conditions that restore

the surface temperature and salinity to a similar climatology.

The difference between the diagnosed heat and fresh water

fluxes and the separate ocean and atmosphere spin-up runs is

used to calculate “flux adjustment” fields. The two models

are then coupled, and the flux correction fields are added to

the ocean surface forcing at every time step during the

subsequent long coupled integration. The flux adjustment,

while clearly artificial and often of undesirably large

amplitude, prevents the quite substantial drifts of the coupled

system from the present climate which occur because the

ocean steady solution is incompatible with the heat and fresh

water fluxes provided by the atmospheric model. The

initialization of coupled models with steady ocean solutions

obtained by restoring the surface model fields of temperature

and salinity to climatological data averaged over the last 40

years or more clearly leaves room for significant improvements. This initialization procedure ignores all the available

data from the ocean interior. In addition, the use of many

year averaged surface data sets results in a very artificial

smoothing—and therefore distortion—of many important

observed features of the oceanic circulation.

The second approach to greenhouse warming simulations is

to initialize the model with the observed ocean climatology

averaged over tens of years, without applying a flux correction to avoid a climate drift of the coupled system (Washington and Meehl, 1989; Boville et al., 1998). This approach,

while it avoids the artificial flux adjustment procedure, also

suffers from a serious drawback. It is well known from

numerical weather prediction that initializing a forecast with

the raw data without any weight given to the model dynamics leads to severe initial “shocks” of the forecast model

while it is adjusting to the initial conditions. Such a violent

response may also be expected in the context of climate

prediction as well, and may severely affect the model’s

response to the greenhouse signal.

What is needed for the climate prediction problem is an

assimilation approach that initializes the prediction simulation using a synthesis of the data and model results. The

initialization should prevent initial shocks, yet constrain the

initial condition using the available four-dimensional oceanic

data base without the artificial smoothing of the temporal

averaging procedure. Such an initialization may also reduce

the climate drift of the coupled system, thus reducing the

need for the artificial flux correction procedure.

Another coupled climate problem where prediction is needed

is the decadal climate variability problem in which the ocean

plays the major role. There are indications, for example, that

variability of the North Atlantic thermohaline circulation

affects the northern European climate on time scales of 10 to

30 years (Kushnir, 1994). The resulting climate and weather

variability has important implications for atmospheric

temperature and precipitation over vast regions. It is mostly

controlled by oceanic processes, and its prediction is of

obvious value. Forecasting decadal climate variability, like

modeling the global greenhouse problem, needs to be done

using coupled A/OGCMs, appropriate data sets, and assimilation methodology. The mechanisms of the thermohaline

variability are still under investigation, with very diverse

explanations offered so far, from strongly nonlinear mechanisms (Weaver et al., 1991) suggesting the use of ocean-only

model studies, to gentler, possibly linear mechanisms, based

on coupled ocean-atmosphere model studies (Delworth et al.,

1993; Griffies and Tziperman, 1995). As the mechanism of

this variability is not yet clear, data assimilation could be

used to interpolate the little data that exist for this phenom-
46 Naval Research Reviews

enon, and perhaps clarify the unresolved dynamical issues.

The physical mechanisms of the decadal climate variability

that results from fluctuations of the thermohaline circulation

may have important implications for predicting this variability, yet practically no work has been carried out so far to

address this issue as an assimilation and prediction problem.

The ocean/climate forecasting problem presenting the most

successful application of data assimilation methods is the

occurrence of El Niño-Southern Oscillations (ENSO) in the

Pacific equatorial band every three to six years. The profound global socio-economic consequences of this phenomenon have attracted considerable attention in terms of pure

modeling, data collection, and assimilation forecasting

studies.

Barnett et al. (1988) discussed three different possible

approaches to predicting the occurrences of ENSO. One

forecasting scheme uses statistical

models that rely on delayed correlations

between various indicators in the

Equatorial Pacific and the occurrence of

ENSO (Barnett, 1984; Graham et al.,

1987). A second scheme uses a linear

dynamical ocean model that is driven by

the observed winds. In the forecast mode,

the winds are assumed to remain constant

beyond the last time for which observations are available, and the ocean model

is integrated ahead for a few months to

produce the forecast (Inoue and O’Brien,

1984). The third ENSO forecast scheme

uses a simple coupled ocean atmosphere

model with linear beta plane dynamics

and a nonlinear equation for the SST

evolution. The model is again initialized

by running it with the observed winds,

and then is integrated further to obtain

the forecast (Cane et al., 1986).

Remarkable progress has been made

since the pioneering work of Barnett

(1984) and Cane et al. (1986) with an

emphasis on applying the most advanced

OGCMs and assimilation schemes to the

ENSO prediction problem. Until recently, in fact, simple coupled oceanatmosphere models seemed to be more

successful in ENSO forecasting, while

fuller primitive equation models had

serious difficulties in simulating, not to

mention forecasting, ENSO events. The

situation has changed. Full threedimensional OGCMs coupled to similar

AGCMs are now catching up with the

simpler models. Miyakoda et al. (1989),

for example, have been using such a

coupled A/OGCM together with an OI assimilation method

to forecast ENSO events. Better performance may be

achieved by using schemes that assimilate all the available

data, including interior ocean data for temperature, salinity

and currents. This has been demonstrated by Ji et al. (1995).

Another direction in which progress has been made is the

development of more advanced assimilation methods such as

Kalman filtering for this application. As in other applications

discussed above, the ENSO prediction problem requires its

own variant of these assimilation methodologies, based on

the apparently chaotic character of ENSO dynamics (Burger

and Cane, 1994; Burger et al., 1995a,b).

Rosati et al. (1996) provide an important example of an

oceanic four-dimensional data assimilation system developed

on the global scale for use in initializing coupled A/OGCMs

and to study interannual variability, with special focus on the

tropical Pacific ocean examining El Niño signature. Leetma

Fig. 4 – Schematic diagram of the North Pacific nowcast/forecast system.

[From Carnes, et al., 1996]
Volume 51, Number 2 47

and Ji (1996) and Ji et al. (1996) also provide an example of

an ocean data assimilation system developed as a component

of a coupled A/OGCM to predict the ENSO phenomenon, but

only for the tropical Pacific domain. The assimilation system

synthesizes various datasets with the ocean model simulation

to obtain analyses used for diagnostics and accurate forecast

initialization. The outstanding success of the climate Prediction Center under the direction of Dr. Leeetma in predicting

the exceptional 1997-1998 El Niño event demonstrates how

essential the assimilation scheme has been for the El Niño

forecast (Climate Prediction Center, National Centers for

Environmental Prediction, 1998).

On a shorter time scale yet lies the problem of extended

seasonal weather prediction, in which again the

ocean plays a crucial role. In many situations a

seasonal forecast of the expected amount of

precipitation, for example, can have a significant impact on agricultural planning, especially

but not exclusively in semi-arid regions. The

application of coupled ocean-atmosphere

GCMs to this problem is at its infancy, and the

obvious need for such work can be expected to

result in more efforts in this direction in the

near future.

It is interesting to note that all the ocean

forecasting problems surveyed so far involve

using a coupled ocean-atmosphere model,

rather than an ocean-only model. There are,

however, situations in which ocean-only

models can be utilized for relevant short-term

assimilation and forecasting studies.

A first example for the ocean component alone

is given by Carnes et al. (1996), who discuss an

ocean modelling, data assimilation monitoring

and prediction system developed for Naval

operational use in the North Pacific ocean

(Figure 4). Three-months long pseudo-operational forecasts are performed in the effort to

address, among other issues, the problem of

extended ocean prediction. A further example

of forecasts on a very short time scale is

provided by Aikman et al. (1996), in which a

quasi-operational East Coast forecast system

has been developed to produce 24-hour

forecasts of water levels, currents, temperature

and salinity in a coastal domain (Figure 5).

A final important example of the use of oceanonly models for the nowcasting and forecasting

of oceanic flows is afforded by those ocean

frontal systems of interest to navies, such as the

prediction of the Gulf Stream front and its

meandering on time scales of two to four

weeks. The operational prediction of such

synoptic oceanic motions is therefore a primary objective per

se and a new profession—that of ocean forecaster—is

rapidly emerging. Ocean forecasting involves real-time

processing and assimilation of remote sensing data, and the

production of timely forecasts of front locations and other

eddy features in the ocean. A significant body of work has

been developed in the last decade for this purpose, and use of

such operational forecasting systems is fairly advanced. See,

for instance, the issue of Oceanography, Vol. 5, no. 1, 1992,

for a review of such operational forecasting systems in the

world ocean, with a general discussion of the Navy Ocean

Modeling and Prediction Program (Peloquin, 1992) and the

interesting DAMEÉ-GSR (Data Assimilation Model Evaluation Experiments – Gulf Stream Region) effort in the Gulf

Fig. 5 – Observed

(upper panel) and

forecast (middle and

lower panels) surface

temperatures on 28

February 1995. The

observed field is

obtained from the

analyzed MCSST

product of NESDIS. The

middle panel SST is

obtained from the

experimental model,

where surface heat and

momentum fluxes are

obtained directly form

the Eta model, and the

lower panel is obtained

from an updated

forecast in which the

heat and momentum

fluxes are calculated

from the lower layer

atmospheric Eta fields.

[From Aikman, et al.,

1996]
48 Naval Research Reviews

Stream System involving the assessment of 4 different

models through prediction evaluation experiments (Leese et

al., 1992; see also Ezer et al., 1992; Ezer et al., 1993;

Willems et al., 1994; Malanotte-Rizzoli and Young, 1997).

The DAMEÉ-GSR effort was successively extended to the

North Atlantic Basin, DAMEÉ–NAB, with similar comparisons of different models in assimilation mode. A special

issue of Deep-Sea Research will be dedicated to DAMEÉNAB.

Robinson (1992) and Robinson et al. (1996) discuss realtime regional forecasting carried out in different areas of the

world-ocean. They illustrate the use and limitations of this

methodology with practical examples using both a primitive

equation and an open ocean quasi-geostrophic model. The

latter constitutes by itself a flexible and logistically portable

open-ocean forecasting system that has been tested in 11

sites of the world ocean comprising frontal systems. All the

tests were real-time forecasts, and for six of them the

forecasts were carried out aboard ships.

Conclusions

Having considered some of the objectives of ocean data

assimilation, it is quite surprising to realize how much work

still remains to meet them. Much of the effort presently

invested in oceanographic data assimilation lies in the

development of appropriate methodologies that would enable

us to approach the objectives discussed above. The diversity

of these objectives clearly indicates that no single assimilation methodology can address all of the needs. It is more

likely that several techniques, such as the Kalman Filter, the

Adjoint Method, and Optimal Interpolation, will be the main

candidates for addressing the future needs of oceanographic

assimilation. Each methodology will be used for the specific

goals to which it is best suited.

With ample motivation for the synthesis of fully complex

OGCMs and oceanic data, and with new observational

techniques and global observational programs being developed, further developments in oceanic data assimilation are

essential. Even though the field has grown impressively in

the last decade, the needs of oceanic data assimilation still

surpass the effort so far invested, and further significant

growth is still necessary.

3. The ATOC Consortium, “The North Pacific general circulation

from altimetry, acoustic tomography and a general circulation

model,” Science, 281, 1327-1332 (1998).

4. T. Barnett, “Prediction of the El Nino of 1982-83,” Monthly

Weather Review, 112, 1403-1407 (1984).

5. T. Barnett, N. Graham, M.A. Cane, S. Zebiak, S. Dolan, J.

O’Brien and D. Legler, “On the prediction of the El Nino of

1986-1987,” Science, 241, 192-196 (1988).

6. C. Bengtsson, M. Ghil and E. Kallen (eds.), Dynamic

Meteorology: Data Assimilation Methods, (Springer-Verlag,

New York, 1981), p. 330.

7. A.F. Bennett, Inverse methods in physical oceanography,

(Cambridge Monographs, Cambridge University Press, 1992),

p. 346.

8. A. Bergamasco and P. Malanotte-Rizzoli, “The seasonal steady

circulation of the Eastern Mediterranean determined with the

adjoint method,” Deep-Sea Research, 40, 1269-1298 (1993).

9. C.W. Böning, W.R. Holland, F.O. Bryan, G. Danabasoglu and

J. McWilliams, “An overlooked problem in the model

simulation of the thermohaline circulation and heat transport in

the Atlantic Ocean,” J. Climatology, 8, 515-523 (1995).

10. B.A. Boville and P.R. Gent, “The NCAR Climate System

model, version one,” J. Climatology, 11, 1115-1130 (1998).

11. K. Bryan, “A numerical method for the study of the circulation

of the world ocean,” J. Computational Physics, 4, 347-376

(1969).

12. F. Bryan, “Parameter sensitivity of primitive equation ocean

general circulation models,” J. Physical Oceanography, 17,

970-985 (1987).

13. G. Burger and M.A. Cane, “Interactive Kalman filtering,” J.

Geophysical Research, 99(C4), 8,015-8,031 (1994).

14. G. Burger, S.E. Zebiak and M.A. Cane, “Quasi-fixed points

and periodic orbits in the Zebiak-Cane ENSO model with

applications in Kalman filtering. Part I: monthly quasi-fixed

points,” Monthly Weather Review, 123, 2,802-2,813 (1995a).

15. G. Burger, S.E. Zebiak and M.A. Cane, “Quasi-fixed points

and periodic orbits in the Zebiak-Cane ENSO model with

applications in Kalman filtering. Part II: periodic orbits,”

Monthly Weather Review, 123, 2,814-2,824 (1995b).

16. A.J. Busalacchi, “Data assimilation in support of tropical

ocean circulation studies,” Modern approaches to data

assimilation in ocean modeling, Elsevier Oceanographic

Series, P. Malanotte-Rizzoli (ed.), (Elsevier, New York, 1996),

61, 235-270.

17. M.A. Cane, S.E. Zebiak and S.C. Dolan, “Experimental

forecast of El Nino,” Nature, 321, 827 (1986).

18. M.A. Cane, A. Kaplan, R.N. Miller, B. Tang, E. Hackert and

A.J. Busalacchi, “Mapping tropical Pacific sea level: data

assimilation via a reduced state space Kalman filter,” J.

Geophysical Research, 101, 22,599-22,617 (1996).

19. A. Capotondi, P. Malanotte-Rizzoli and W.R. Holland,

“Assimilation of altimeter data into a quasi-geostrophic model

References

1. F. Aikman III, G.L. Mellor, T. Ezer, D. Sheinin, P. Chen, L.

Breaker and D.B. Rao, “Towards an operational nowcast/

forecast system for the U.S. East Coast,” Modern Approaches

to Data Assimilation in Ocean Modeling, Elsevier

Oceanography Series, P. Malanotte-Rizzoli (ed.), (Elsevier,

New York, 1996), 61, 374-376.

2. R.A. Anthes, “Data assimilation and initialization of hurricane

prediction models,” J. Atmospheric Sciences, 31, 701-719

(1974).
Volume 51, Number 2 49

of the Gulf Stream system, Part I: dynamical considerations,”

J. Physical Oceanography, 25, 1,130-1,152 (1995a).

20. A. Capotondi, W.R. Holland and P. Malanotte-Rizzoli,

“Assimilation of altimeter data into a quasi-geostrophic model

of the Gulf stream system, Part II. Assimilation results,” J.

Physical Oceanography, 25, 1,153-1,173 (1995b).

21. M.R. Carnes, D.N. Fox, R.C. Rhodes and O.M. Smedstad,

“Data assimilation in the North Pacific Ocean monitoring and

prediction system,” Modern Approaches to Data Assimilation

in Ocean Modeling, Elsevier Oceanography Series, P.

Malanotte-Rizzoli (ed.), (Elsevier, New York, 1996), 61, 319-

346.

22. D.C. Chapman, “Numerical treatment of cross-shelf open

boundaries in a barotropic coastal ocean model,” J. Physical

Oceanography, 15, 1,060-1,075 (1985).

23. Climate Prediction Center, “Activities during the 1997-98 El

Nino/Southern Oscillation Event,” NCEP Report, p. 77 (1998).

24. B.D. Cornuelle and P.F. Worcester, “Ocean Acoustic

Tomography: Integral data and ocean models” Modern

Approaches to data assimilation in ocean modeling, Elsevier

Oceanographic Series, P. Malanotte-Rizzoli, (ed.), (Elsevier,

New York, 1996), 61, 97-118.

25. U. Cusbasch, K. Hasselmann, H. Hock, E. Maier-Reimer, U.

Mikolajewicz, B.D. Santer and R. Sansen, “Time-dependent

greenhouse warming computations with a coupled oceanatmosphere model,” Climate Dynamics, 8, 55-69 (1992).

26. R. Daley, Atmospheric Data Analysis, (Cambridge University

Press, 1991), p. 497.

27. T. Delworth, S. Manabe and R.J. Stouffer, “Interdecadal

variations of the thermohaline circulation in a coupled oceanatmosphere model,” J. Climatology, 12, 1,993-2,011 (1993).

28. J.C. Derber and A. Rosati, “A global ocean data assimilation

system,” J. Physical Oceanography, 19, 1,333-1,347 (1989).

29. T. Ezer, D.S. Ko and G.L. Mellor, “Modeling and forecasting

the Gulf Stream,” Marine Technical Society Journal, 26, 5-14

(1992).

30. T. Ezer, G.L. Mellor, D.S. Ko and Z. Sirkes, “A comparison of

Gulf Stream sea surface height field derived from GEOSAT

altimeter data and those derived from sea surface temperature

data,” J. Atmospheric Oceanic Technology, 10, 76-87 (1993).

31. L.L. Fu and I. Fukumori, “A case study of the effects of errors

in satellite altimetry on data assimilation,” Modern approaches

to data assimilation in ocean modeling, Elsevier

Oceanographic Series, P. Malanotte-Rizzoli (ed.), (Elsevier,

New York, 1996), 61, 77-96.

32. I. Fukumori, J. Benveniste, C.I. Wunsch and D.B. Haidvogel,

“Assimilation of sea surface topography into an ocean

circulation model using a steady state smoother,” J. Physical

Oceanography, 23, 1,831-1,855 (1993).

33. I. Fukumori and P. Malanotte-Rizzoli, “An approximate

Kalman filter for ocean data assimilation: a reduceddimension, static, linearized Kalman filter,” J. Geophysical

Research, 100, 6,777-6,793 (1995).

34. A. Ganachaud, C.I. Wunsch, M.C. Kim and B. Tapley,

“Combination of TOPEX/POSEIDON data with a

hydrographic inversion for the determination of the oceanic

general circulation,” Geophysical Journal International, 128,

708-722 (1997).

35. P.R. Gent and J.C. McWilliams, “Isopycnal mixing in ocean

circulation models,” J. Physical Oceanography, 20, 150-155

(1990).

36. M. Ghil and P. Malanotte-Rizzoli, “Data assimilation in

meteorology and oceanography,” Advances in geophysics, B.

Saltzmann (ed.), 33, 141-266 (1991).

37. N.E. Graham, J. Michaelsen and T.P. Barnett, “An

investigation of the El Nino-Southern Oscillation cycle with

statistical models. I. Predictor field characteristics,” J.

Geophysical Research, 92, 14,251-14,270 (1987).

38. J. Green, “Transfer properties of the large-scale eddies and the

general circulation of the atmosphere,” Royal Meteorological

Society Quarterly Journal, 96, 157-185 (1970).

39. M.S. Griffies and E. Tziperman, “A linear thermohaline

oscillator driven by stochastic atmospheric forcing, J.

Climatology,” 8, 2,440-2,453 (1995).

40. J.R. Gunson and P. Malanotte-Rizzoli, “Assimilation studies of

open-ocean flows. Part I: Estimation of initial and boundary

conditions,” J. Geophysical Research, 101, 28,457-28,472

(1996a).

41. J.R. Gunson and P. Malanotte-Rizzoli, “Assimilation studies of

open-ocean flows. Part II: Error measures with strongly

nonlinear dynamics,” J. Geophysical Research, 101, 28,473-

28,488 (1996b).

42. D.B. Haidvogel and A.R. Robinson (eds.), Dynamics

Atmospheres Oceans, Special Issue on Data Assimilation,

13(3-4), (1989).

43. M.C.B. Hall and D.G. Cacuci, “Physical interpretation of the

adjoint functions for sensitivity analysis of atmospheric

models,” J. Atmospheric Sciences, 40, 2,537-2,546 (1983).

44. J. Hansen, I. Fung, A. Lacis, D. Rind, S. Lebedeff, R. Ruedy,

G. Russell and P. Stone, “Global climate changes as forecast

by Goddard Institute for Space Studies three-dimensional

model,” J. Geophysical Research, 93, 9,341-9,364 (1988).

45. G.C. Hegerl, H. von Storch, K. Hasselmann, B.D. Santer, U.

Cusbasch and P.D. Jones, “Detecting greenhouse-gas induced

climate change with an optimal fingerprint method,” J.

Climatology, 9, 2,281-2,306 (1996).

46. N.G. Hogg, “Oceanographic data for parameter estimation,”

Modern approaches to data assimilation in ocean modeling,

Elsevier Oceanographic Series, P. Malanotte-Rizzoli (ed.),

(Elsevier, New York, 1996), 61, 57-76.

47. W.R. Holland and A. Capotondi, “Recent developments in

prognostic ocean modelling,” Modern approaches to data

assimilation in ocean modeling, Elsevier Oceanographic

Series, P. Malanotte-Rizzoli (ed.), (Elsevier, New York, 1996),

61, 21-56.

48. W.R. Holland and A.D. Hirschman, “A numerical calculation
50 Naval Research Reviews

of the circulation in the North Atlantic Ocean,” J. Physical

Oceanography, 2, 336-354 (1972).

49. W.R. Holland and P. Malanotte-Rizzoli, “Assimilation of

altimeter data into an ocean circulation model: space versus

time resolution studies,” J. Physical Oceanography, 19, 1,507-

1,534 (1989).

50. M. Inoue and J.J. O’Brien, “A forecasting model for the onset

of a major El Nino,” Monthlty Weather Review, 112, 2,326-

2,337 (1984).

51. M. Ji, A. Leetmaa and J. Derber, “An ocean analysis for

seasonal to interannual climate studies,” Monthly Weather

Review, 123, 460-481 (1995).

52. M. Ji, A. Leetmaa and V.E. Kousky, “Coupled model forecasts

of ENSO during the 1980’s and 1990’s at the National

Meteorological Center,” J. Climatology, 9, 3,105-3,120 (1996).

53. S. Jiang, P.H. Stone and P. Malanotte-Rizzoli, “An assessment

of the GFDL ocean model with coarse resolution. Part I:

Annual Mean Climatology,” J. Geophysical Research, in press

(1999).

54. Y. Kushnir, “Interdecadal variations in North Atlantic sea

surface temperature and associated atmospheric conditions,” J.

Climatology, 7, 141-157 (1994).

55. T. Lee and J. Marotzke, “Inferring meridional mass and heat

transports in the Indian Ocean by combining a general

circulation model with climatological data,” J. Geophysical

Research, 102, 10,585-10,602 (1997).

56. T. Lee and J. Marotzke, “Seasonal cycles of meridional

overturning and heat transport of the Indian Ocean,” J.

Physical Oceanography, 28, 923-943 (1998).

57. J.A. Leese, R.C. Willems and L.A. Yeske, “Evaluation

capability for the Navy Ocean Modeling and Prediction

Program,” Oceanography, 1, 55-59 (1992).

58. A. Leetma and M. Ji, “Ocean data assimilation as a component

of a Climate Forecast System,” Modern Approaches to Data

Assimilation in Ocean Modeling, Elsevier Oceanography

Series, P. Malanotte-Rizzoli (ed.), (Elsevier, New York, 1996),

61, 271-296.

59. P. Malanotte-Rizzoli and R.E. Young, “Assimilation of global

versus local datasets into a regional model of the Gulf Stream

system, Part I: Data effectiveness,” J. Geophysical Research,

100, 24,773-24,796 (1995).

60. P. Malanotte-Rizzoli and R.E. Young, “Gulf Stream system

assimilation experiments: a sensitivity study,” J. Atmospheric

Oceanic Technology, 14, 1,392-1,408 (1997).

61. S. Manabe, R.J. Stouffer, M.J. Spelman and K. Bryan,

“Transient responses of a coupled ocean-atmosphere model to

gradual changes of atmospheric CO2

, Part I: annual mean

response,” J. Climatology, 4, 785-818 (1991).

62. S. Manabe and R.J. Stouffer, “Multiple-century response of a

coupled ocean-amosphere model to an increase of atmospheric

carbon dioxide,” J. Climatology, 7, 5-23 (1994).

63. J. Marotzke, “The role of integration time in determining a

steady state through data assimilation,” J. Physical

Oceanography, 22, 1,556-1,567 (1992).

64. J. Marotzke and C. Wunsch, “Finding the steady state of a

general circulation model through data assimilation:

application to the North Atlantic Ocean,” J. Geophysical

Research, 98, 20,149-20,167 (1993).

65. J. Marotzke, R. Giering, Q.K. Zhang, D. Stammer, C. Hill and

T. Lee, “Construction of the adjoint MIT ocean general

circulation model and application to Atlantic heat transport

sensitivity,” J. Geophysical Research, submitted (1999).

66. G.L. Mellor and T. Yamada, “Development of a turbulence

closure model for geophysical fluid problems,” Reviews

Geophysics Space Physics, VOLUME, 20,851-20,875 (1982).

67. G.L. Mellor and T. Ezer, “A Gulf Stream model and an

altimeter assimilation scheme,” J. Geophys. Res., 96, 8,779-

8,795 (1991).

68. D. Menemenlis, A.T. Webb, C.I. Wunsch, U. Send and C. Hill,

“Basin scale ocean circulation from combined altimetry,

tomography and model data,” Nature, 385, 618-621 (1997a).

69. D. Menemenlis, P. Fieguth, C.I. Wunsch and A. Willsky,

“Adaptation of a fast optimal interpolation algorithm to the

mapping of oceanographic data,” J. Geophysical Research,

102, 10,573-10,584 (1997b).

70. W. Menke, Geophysical Data Analysis: Discrete Inverse

Theory, (Academic Press, 1984), p. 284.

71. R.N. Miller and N.A. Cane, “Tropical data assimilation:

theoretical aspects,” Modern Approaches to Data Assimilation

in Ocean Modeling, Elsevier Oceanograhic Series, P.

Malanotte-Rizzoli (ed.), (Elsevier, New York, 1996), 61, 207-

234.

72. K. Miyakoda, J. Sirutis, A. Rosati and R. Gudgel, Proceedings

of Workshop on Japanese coupled ocean-atmosphere response

experiments, A. Sumi (ed.), 23-24 October 1989, p. 93.

73. W.H. Munk, P.F. Worcester and C.I. Wunsch, Ocean Acoustic

Tomography, (Cambridge University Press, 1995), p. 433.

74. Oceanography, 5(1), 80 pages, (1992).

75. R.A. Peloquin, “The navy ocean modeling and prediction

program,” Oceanography, 1, 4-8 (1992).

76. A.R. Robinson, H.G. Arango, A. Warm-Varmas, W. Leslie,

A.J. Miller, P.J. Haley and C.J. Lozano, “Real-time Regional

Forecasting,” Modern Approaches to Data Assimilation in

Ocean Modeling, Elsevier Oceanography Series, P. MalanotteRizzoli (ed.), (Elsevier, New York, 1996), 61, 377-412.

77. A.R. Robinson, “Shipboard prediction with a regional forecast

model,” Oceanography, 1, 42-48 (1992).

78. A.R. Robinson, M.A. Spall, L.F. Walstad and W.G. Leslie,

“Data assimilation and dynamical interpolation in Gulfcast

experiments,” Dynamic Atmospheric Oceans, 13, 269-300

(1989).

79. A. Rosati, R. Gudgel and K. Miyakoda, “Global Ocean Data

Assimilation system,” Modern approaches to data assimilation
Volume 51, Number 2 51

in ocean modeling, Elsevier Oceanographic Series, P.

Malanotte-Rizzoli (ed.), (Elsevier, New York, 1996), 61, 181-

206.

80. B.D. Santer, K. Taylor, T. Wigley, J. Penner, P. Jones and U.

Cusbasch, “Towards the detection and attribution of an

anthropogenic effect on climate,” Climate Dynamics, 12, 77-

100 (1995).

81. J.L. Sarmiento and K. Bryan, “An ocean transport model for

the North Atlantic,” J. Geophysical Research, 93, 10,655-

10,665 (1982).

82. M.E. Schlesinger and J.F.B. Mitchell, “Climate model

simulations of the equilibrium climatic response to increased

carbon dioxide,” Reviews Geophysics, 25, 760-798 (1987).

83. R.W. Schmitt, P.S. Bogden and C.E. Dorman, “Evaporation

minus precipitation and density fluxes for the North Atlantic,”

J. Physical Oceanography, 19, 1,208-1,221 (1989).

84. Z. Sirkes, E. Tziperman and W.C. Thacker, “Combining data

and a Global Primitive Equation Ocean General Circulation

model using the adjoint method,” Modern Approaches to Data

Assimilation in Ocean Modeling, Elsevier Oceanographic

Series, P. Malanotte-Rizzoli (ed.), (Elsevier, New York, 1996),

61, 119-146.

85. D. Stammer and C. Wunsch, “Preliminary assessment of the

accuracy and precision of TOPEX/POSEIDON altimeter data

with respect to the large-scale ocean circulation,” J.

Geophysical Research, 99, 29,584-29,604 (1994).

86. D. Stammer and C. Wunsch, “The determination of the largescale circulation of the Pacific ocean from satellite altimetry

using model Green’s functions,” J. Geophysical Research, 101,

18,409-18,432 (1996).

87. D. Stammer, C.I. Wunsch, R. Goering, Q.K. Zhang, J.

Marotzke, J. Marshall and C.N. Hill, “The global ocean

circulation estimated from TOPEX/POSEIDON altimetry and

the MIT general circulation model,” MIT Center for Global

Change Science, Report No. 49, p. 40 (1997).

88. P.H. Stone, “A simplified radiative-dynamical model for the

static stability of rotating atmospheres,” J. Atmospheric

Sciences, 29, 405-418 (1972).

89. R.J. Stouffer, S. Manabe and K. Bryan, “Interhemispheric

asymmetry in climate response to a gradual increase of

atmospheric CO2

,” Nature, 342, 660-662 (1989).

90. Tarantola, Inverse problems theory, Methods for data fitting

and model parameter estimation, (Elsevier Science Publ.,

1987), p. 613.

91. W.C. Thacker, “Fitting models to data by enforcing spatial and

temporal smoothness,” J. Geophysical Research, 93, 10,655-

10,665 (1988).

92. W.C. Thacker and R.B. Long, “Fitting dynamics to data,” J.

Geophysical Research, 93, 1,227-1,240 (1988).

93. K.E. Trenberth, J.G. Olson and W.G. Large, “A global ocean

wind stress climatology based on ECMWF analysis,” NCAR/

TN-338+STR, p. 93 (1989).

94. R.E. Trenberth and A. Solomon, “The global heat balance: heat

transports in the atmosphere and ocean,” Climate Dynamics, 9,

107-134 (1994).

95. E. Tziperman and W.C. Thacker, “An optimal control/adjoint

equation approach to studying the oceanic general circulation,”

J. Physical Oceanography, 19, 1,471-1,485 (1989).

96. E. Tziperman, W.C. Thacker, R.B. Long and S.M. Hwang,

“Oceanic data analysis using a general circulation model, Part

I: Simulations,” J. Physical Oceanography, 22, 1,434-1,457

(1992a).

97. E. Tziperman, W.C. Thacker, R.B. Long, S.M. Hwang and

S.R. Rintoul, “Oceanic data analysis using a general

circulation model, Part II: A North Atlantic model,” J. Physical

Oceanography, 22, 1,458-1,485 (1992b).

98. J. Verron, L. Gourdeau, D.T. Pham, R. Murtugudde and A.J.

Busalacchi, “An extended Kalman filter to assimilate satellite

altimeter data into a non-linear numerical model of the tropical

Pacific ocean: method and validation,” J. Geophysical

Research, submitted (1999).

99. M. Visbeck, J. Marshall and H. Jones, “Dynamics of Isolated

Convective Regions of the Ocean,” J. Physical Oceanography,

26, 1,721-1,734 (1996).

100. W.M. Washington and G.A. Meehl, “Seasonal cycle

experiments on the climate sensitivity due to a doubling of

CO2

 with an atmospheric general circulation model coupled to

a simple mixed layer ocean model,” J. Geophysical Research,

89, 9,475-9,503 (1989).

101. W.M. Washington, G.A. Meehl, L. VerPlant and T.W. Bettge,

“A world ocean model for greenhouse sensitivity studies:

resolution intercomparison and the role of diagnostic forcing,”

Climate Dynamics, in press (1999).

102. A.J. Weaver, E.S. Sarachik and J. Marotzke, “Freshwater flux

forcing of decadal and interdecadal oceanic variability,”

Nature, 353, 836-838 (1991).

103. R.T. Wetherald and S. Manabe, “Cloud feedback processes in a

general circulation model,” J. Atmospheric Sciences, 45,

1,397-1,415 (1988).

104. R.G. Willems, S.M. Glenn, M.R. Crowley, P. MalanotteRizzoli, R.E. Young, T. Ezer, G. Mellor, H.G. Arango, A.R.

Robinson and C.C.A. Lai, “Experiment evaluates ocean

models and data assimilation in the Gulf Stream,” Earth Ocean

Sciences, Transactions, American Geophysical Union, 75(34),

385-394 (1994).

105. C.A. Wilson and J.F.B. Mitchell, “A doubled CO2

 climate

sensitivity experiment with a global climate model including a

simple ocean,” J. Geophysical Research, 92, 13,315-13,343

(1987).

106. C.I. Wunsch, “The general circulation of the North Atlantic

west of 50 degrees W determined from inverse methods,”

Reviews Geophysics Space Physics, 16, 583-620 (1978).

107. C.I. Wunsch, “Using data with models, ill-posed and timedependent ill-posed problems” Geophysical Tomography, Y.

Desaubies, A. Tarantola and J. Zinn-Justin (eds.), (Elsevier

Publ. Company, 1989a), pp. 3-41.

108. C.I. Wunsch, “Tracer inverse problems,” Oceanic circulation
52 Naval Research Reviews

models: combining data and dynamics, D.L.T. Anderson and J.

Willebrand, (eds.), (Kluwer Academic Publ., 1989b), pp. 1-78.

109. C.I. Wunsch, The Ocean Circulation Inverse Problem,

(Cambridge University Press, 1996), p. 437.

110. C.I. Wunsch and B. Grant, “Towards the general circulation of

the North Atlantic Ocean,” Progress in Oceanography, 11, 1-

59 (1982).

111. L. Yu and P. Malanotte-Rizzoli, “Analysis of the North

Atlantic climatologies using a combined OGCM/adjoint

approach,” J. Marine Research, 54, 867-913 (1996).

112. L. Yu and P. Malanotte-Rizzoli, “Inverse modeling of seasonal

variability in the North Atlantic Ocean,” J. Physical

Oceanography, 28, 902-922 (1998).

113. K.Q. Zhang and J. Marotzke, “The importance of openboundary estimation for an Indian Ocean GCM-data

synthesis,” J. Marine Research, in press (1995).

The Author

Paola Malanotte Rizzoli, formerly of the Istituto

Studio Dinamica Grande Masse in Venice, Italy, is

currently Professor of Oceanography at the

Massachusetts Institute of Technology. She holds a

Ph.D. in physical oceanography from the University of California’s Scripps Institution of Oceanography as well as a Ph.D. in physics from the

University of Padua. Widely known for her

research in physical oceanography and related

fields, she is a member of the American Physical

Society, American Geophysical Union, American

Meteorological Society, Oceanography Society,

Italian Physical Society, and the European

Geophysical Society. Her reputation in oceanographic modeling has led to her appointment to

numerous panels of experts on oceanic and

atmospheric science. She is presently the MIT

director of the MIT/WHOI Joint Program in

Oceanography and Ocean Engineering.
. A practical, objective set of

nalytical solutions, numerical

onal case studies is under

 include massively parallel

memory computers combined

mpling networks using mobile

ient mapping and adaptive

ork simulation and control that

odel input/output is underway.

ecture driven by evolving

s is a design goal.

g and prediction research and

d in universities, the Naval

nis Space Center, Mississippi

other Navy and government

. A principal mission is to

s and prediction tools to the

ate transition of products to

orology and Oceanography

uch as the Fleet Numerical

raphy Center and the Naval

coordinates its research efforts

Warfare Systems Command

METOC Data Acquisition,

ion Program funded by the

 The challenge of advancing

ational ocean modeling and

engineering, interdisciplinary

ration, procurement, training,

lected topics in basic research

nt. The state-of-the-art in data

sampling are reviewed. An

, finite element modeling is

articularly relevant to coastal

geometry. Understanding and

ve research are examined. The

omprehensive, but rather to

important current activities

astal ocean prediction.

Tom Curtin

Office of Naval Research

After an initial career in aerodynamics, George Mellor turned his scientific interests to atmospheric and oceanic turbulent boundary layers. He established the Program in Atmospheric and Oceanic Sciences at Princeton University, which is associated with NOAA’s Geophysical Fluid Dynamics Laboratory (GFDL). Mellor’s research involvesthe study of estuarine and oceanic dynamics through the use of numerical ocean models. Professor Mellor is the author ofmore than one hundred journal articles covering turbulent boundary layers, ocean modeling and other topics in fluid dynamicsand a textbook on Introductory Oceanography. He is a fellow of the American Meteorological Society and the AmericanGeophysical Union. The Princeton Ocean Model (POM), developed by Mellor and Alan Blumberg in the 1970s, is usedwidely by scientists, institutions and industry, including the U.S. Navy, NOAA’s National Environmental Center and theNational Ocean Service.There is an internet users group of over 350 users worldwide. POM includes an imbedded secondmoment turbulence closure sub-model to provide vertical mixing coefficients, a sigma vertical coordinate scaled on waterdepth, orthogonal curvilinear horizontal coordinates and an “Arakawa C” finite differencing scheme. The horizontal griddifferencing is explicit whereas the vertical differencing is implicit. The latter eliminates time constraints for the verticalcoordinate and permits the use of fine vertical resolution in the surface and bottom boundary layers. The model has a freesurface and a split time step. Complete thermodynamics have been implemented. The turbulence closure sub-model is oftencited in the literature as the Mellor-Yamada turbulence closure model, but the model is based on turbulence hypotheses byRotta and Kolmogorov which were extended to stratified flow.

Current users of POM are the beneficiaries of forty years of research. The branch of this evolution at Princeton is

illustrative. In the 1960s, turbulent boundary layer experiments and models were investigated by H.J. Herring and students.In 1969, GFDL was established at Princeton under J. Smagorinsky. In the early 1970s, T.Yamada developed atmosphericboundary layer formulations accounting for turbulence. In the late 1970s based on these advances, the first version of POMwas created by G. Mellor and A. Blumberg. From 1980-83, Dynalysis, a company formed by Blumberg and Herring,applied POM to Gulf of Mexico circulation studies. Simultaneously, L-Y Oey modeled the Hudson/Raritan Estuary. Sincethe mid-80s, improved versions of POM have been developed for Delaware Bay (Galparin), the Arctic Ocean (Kantha,Hakkinen), the Mediterranean Sea (Zavatarelli), the North Atlantic (Ezer) and the coastal zone of the eastern United States(Aikman).

Further information including a list of journal publications can be found in http://www.aos.princeton.edu/wwwpublic/

htdocs.pom/

Dr. George Mellor

Program in Atmospheric and Oceanic Sciences

Princeton University

Princeton, NJ
Volume 51, Number 2/1999

and more . . .

Bringing Life into the Picture p. 2

Where the Waves Are p. 16

Shallow Water, Deep Science p. 26