An operational management system for river flows JR ... - Hydrologie.org

Closing the Gap Between Theory and Practice (Proceedings of the Baltimore Symposium, May 1989) 1AHS Publ. no. ISO, 1989.

An operational management system for river flows

J.R. Moll and J.I. Crebas Rivers, Navigation and Structures Division Delft Hydraulics, P.O. Box 152, 8300 A D Emmeloord, The Netherlands

Abstract The introduction of the Kalman filter in hydrological modelling has started a flow of new developments, particularly in real-time river flow forecasting. These developments have not contributed to the closure of the gap between theory and practice so far. This paper describes an approach to narrow this gap. Two Kalman filter implementations are presented, one in a rainfall-runoff model, and the other in a flow routing model. The models are embedded in a real-time multi-tasking operating system. Three tasks are executed simultaneously: data acquisition, on-line estimation, and forecasting. The operator can evaluate forecasts and analyze management options without interfering with the continuous processes of real-time data acquisition and model update. Applications of the system in two case studies are presented. Introduction The introduction of the Kalman filter in hydrological modelling has started a flow of new developments, particulary in real-time river flow forecasting (O'Connell, 1981; Kraijenhoff and Moll, 1986; Georgakakos, 1986; Szollbsi-Nagy and Mekis, 1988). Existing flood forecasting methods, e.g. empirical statistical methods, conceptual hydrological methods or physically-based hydraulic methods, have been extended with Kalman filters in different ways. In most cases, improvements of forecasting performance of the underlying model have been obtained. In some cases, however, the Kalman filter was reported to be inapplicable. The introduction of the Kalman filter has not contributed to the closure of the gap between theory and practice so far. On the contrary, the larger conceptual and computational burden has impeded practical implementations on a large scale. Research efforts have preferably been aimed at the refinement of already complex models, and not towards the solution of practical problems with perceived commonplace characteristics. In this paper, an approach is described to narrow this gap. The approach is to start from the point of view of a river manager and his information requirements. This leads in a natural way to the specification of a data acquisition system and a set of mathematical models. These models are needed for real-time processing of actual measurement data. Two Kalman filter implementations are presented for this purpose, one in a rainfall-runoff model and the other in a model for open channel flow. Performance of these models has been evaluated on real-world data of the Reiderzijlvest Waterboard drainage network and the River Vecht basin in the Netherlands. Computed results are presented. The paper concludes with a short retrospect on the project, and a few remarks on the limitations and merits of this approach towards bridging the aforementioned gap211

212 J.R. Moll and J.I. Crebas

Operational River Management River management can be considered on a short time scale (several hours up to several days) and a long time scale (several years). Examples of short-term or operational management problems are lock and sluice operation, vessel traffic services and flood forecasting. Examples of long-term or strategic management problems are ecosystem upgrading, river training and fairway capacity expansions. Essential is the possibility to discuss and weight the different future functions of a river system, and to propose infrastructural measures. This paper focuses on the short-term issue of flow forecasting. The data flow in an operational management system is depicted in Fig. 1. The real-world water system is monitored with a measurement system. Data is transferred to a central site, where information processing takes place using mathematical models and site-specific knowledge. Results are displayed to the manager in an easily interprétable format. These results include an overview of the actual situation and short-term forecasts. The manager can interactively simulate operation of structures, compare results of alternatives, and decide on the best course of action. Wherever the number or complexity of the alternatives is impeding the decision-making process, support can be given by a dedicated decision-support system. The actual decision is transmitted to the field and implemented. Effects of control actions are registered by the monitoring system in the next time interval. This closed-loop approach has been selected in developing a real-time system for flow forecasting and flood control. Flow Forecasting Models Three components of the hydrological cycle are of interest in river flow forecasting: quantitative precipitation forecasting, forecasting of runoff from sub-basins, and forecasting of flow propagation through the open channel network. In a real-time setting, forecasts are confronted with actual measurements of the variables of interest every time a measurement is collected. Data assimilation techniques can be used to combine these two sources of information, taking into account their respective accuracy, and resulting in an estimate of the actual state (see Fig. 2). This estimate is used as the initial state in forthcoming model computations. Preferably this state is represented in such a way that not only mathematical purposes are served, but also a physical interpretation can be attached to it. It is possible to consider a rainfall-runoff process as an input-output process and describe it by linear systems theory (Dooge, 1973), ARMAX models (Ljung and Soderstrbm, 1983) or threshold models (Tong, 1983). These basically black-box approaches do not allow a physical interpretation of states or parameters. The rainfall-runoff model described in this section is a derivative of the well-known Sacramento watershed model. A tentative interpretation of state variable values is possible. The model for open channel flow is based on the full St. Venant equations, allowing detailed interpretations. Rainfall-mnoff model. The land phase of the hydrological cycle is approached by an explicit soil moisture accounting lumped parameter model. The basin is divided into one or more segments, all of them discharging to the main channel system. Within every segment, areal

An operational management system for river flows 213

control

water

system

system

measurement system

A

e

w information system :

decision support

models

system

objectives

• knowledge

presentation

strategies

system

Fig. 1. An operational management system.

homogeneity with respect to rainfall and basin characteristics is assumed. A schematic layout of the model is given in Fig. 3. The drainage system of the pervious part of the basin is divided into an upper zone, representing the basin surface system, and a lower zone representing the basin groundwater reservoir system. Both zones have a tension and a free water storage element. The lower zone free water is stored in two reservoirs, representing the slow and fast groundwater flow component. To represent the periods when all tension water reservoirs are full and an increasing fraction of the basin assumes impervious characteristics, an additional impervious area is defined. The water levels in six reservoirs represent the actual state of the basin:


rneteo model

W

estimate of actual state data assimilation

rainfallrunoff model

V. P

rainfall measurements

estimate of actual state

data assimilation flow routing \ model P

runoff measurements

estimate of actual state

1

data

flow, water levels — > {

water level measurements

. assimilation

Fig. 2. Data assimulation in mathematical models.

tmttt E T

imittitiu

DEMAND

PRECIPITATION INPUT

*

,. IMPERVIOU * 5

PERVIOUS AREA

DIRECT RUNOFF

I

E T

UPPER TENSION WATER E T

^ ^ ~"

^ ^ ^

SURFACE RUNOFF

'

FREE WATER INTERFLOW

1

PERCOLATION

/ -

P

CHANNEL

\ Pr

f

LOWER

ZONE

\

1

j

1 free Iwatcr E T L

TENSION -WATER J

*3

1

x

'

X.

BASE FLOW

!

Fig. 3. Sacramento model.


Xi =

level in upper zone tension water reservoir

X9 =

level in upper zone free water reservoir

X3 =

level in lower zone tension water reservoir

XA =

level in lower zone primary free water reservoir

Xr =

level in lower zone secondary free water reservoir

Xg =

level in additional impervious area reservoir

The threshold response of the reservoirs is approximated by a nonlinear continuous function (Georgakakos, 1986). The following constraints determine the definition domain of the variables x-: 0 < x± < x 1 (max)

i - 1,...,5

(1)

System dynamics are given by: X - f(X,P,e)

(2)

q = h(X)

(3)

with: X p e q

= state vector = precipitation = évapotranspiration = basin outflow

By linearizing locally around state trajectories and adding system noise to the equations, an Extended Kalman Filter can be formulated to perform state estimation (Jazwinsky, 1970): x(t+l)|t)

=

f [ x ( t | t ) , u(t)]

(4)

X(t+l|t+l) =

X(t+l|t) + K(t+1) [Y(t+1) - h((X(t+l|t))]

(5)

P(t+l)|t)

F t P(t|t) F^ + Q

«=

P(t+l|t+l) =

(6)

P(t+l|t) - P(t+l|t) H^ +1 [H t+1 P(t+l|t) H^+]_ + R ] " H t + 1 P(t+l|t)

K(t+1)

=

P(t+l|t) H^ +1 [H t+1 P(t+l|t) H^ +1 + R ] "

with: U K P Y Q R

= input vector = Kalman Gain vector = state covariance matrix = observation vector = system noise covariance matrix = measurement noise covariance matrix

1

(7) 1

(8)


The input vector U contains precipitation p and évapotranspiration e; observation vector Y is the basin outflow q. Sometimes q is not measured directly, but can be derived from rating curves or estimated from the open channel model. The system noise covariance matrix Q is diagonal. Its values can be calibrated with the results of preliminary model runs. Flow routing model. The open channel network is schematized in a number of branches and structures. The differential equations for a branch are (St. Venant):

(9)

| f + S - q(h) - 0 32 + a_ (av s!J}

at

3x

As

+T gB A

|£

s 3x

+T

g& 4^L

-

C2R A

K

do)

li _ o

s p

s

where: B h Q A A q a C R g rs p The «quation

= = = = = = = = = = = = for a

FCh-L, h 2 ,

width of the flow area A s water level discharge in flow area A& total area, including storage area flow area lateral discharge per unit length into the channel coefficient for distribution of velocity Chezy coefficient for bottom roughness hydraulic radius acceleration of gravity wind shear stress density of water structure is:

Q, t ) - 0

(11)

The differential equations are discretized on a staggered computational grid, and linearized together with the structure equations, leading to linear equations of the following statespace form: A[X(t)] X(t+1) - B[X(t), U(t+1)]

(12)

with: A,B U X

= = =

transition rnatrices boundary conditions state vector

The following state vector is selected: X(t) = [Q1(t)

Qn(t), hx(t)

hm(t), f 1 ( t ) , . . . , f

(t),

fw(t)]


with: number of h-points

m

number of Q-points

n

number of bottom stress factors f

bottom stress factor i; i = l,...,p

i

wind stress factor Note that state augmentation has been performed by inclusion of the parameter vector = [fi (t),...,f' (t), L / t ) ] . This feature allows the adaptive real-time estimation of bottom stress in specified branches and of global wind stress. An f- parameter is a factor inserted in the bottom-stress term of the momentum equation for the specified branch j : Q-lQ-l .V .V f.

(13)

C. R. A 1

J

J

S.

The f parameter is a factor inserted in the wind-stress term of the momentum equation for alibranches: B s.

P

S.

(14)

The state transition equations consist of equation (12) and the following equation for the evolution of the parameters: 0(t+l) =

6(t)

(15)

System noise is added to the state transition equations: noise intensity of equation of continuity noise intensity of equation of momentum %

noise intensity of water level boundary condition noise intensity of discharge boundary condition

% 1w

noise intensity of bottom stress factor noise intensity of wind stress factor

The system noise covariance matrix is diagonal. Spatial relationships in the system noise are generated by the implicit way of solving the equation for the state covariance matrix P(t+l|t).


The observation equations have a very simple structure: Y ( t ) = H-X(t) + V(t)

(16)

with: Y H V

= = =

vector of observed water levels observation matrix, with as rows unity vectors measurement noise vector

The Extended Kalman Filter algorithm, Equations (4) through (8), is applied. Observing the implicit structure of Equation (12), Equations (4) and (6) are modified: A(Xt) X ( t + l | t ) A-P(t+l|t)

= B ( X t , U t + ] _)

• AT -

(||

- | |

A " 1 B) P ( t | t )

(4') {§§ - | |

A"1 B)T + Q

(6')

Information Processing Various observation data are sent from the field to the central computer at the request of the latter (every model time step). The time interval is initially set and can be changed. After receiving the data a filtering step is performed; from its results a selection is stored in the data base. After an automatic filtering step, one or more simulation runs are activated, retrieving their input data from scenario and strategy files. Scenario files contain forecasts of hydrological boundary conditions, for instance rainfall, tides and evaporation. Strategy files contain forecasts of parameters under human control, for instance gate settings and pumping station schedules. When the requested simulation runs are finished, "ready to display" time-series plots of the presentation stations are generated and stored. The screen of the central computer consists of four windows: two upper, one lower, and a main central window. The upper left one shows messages concerning the communication with the field and, if not active, the activation time. The upper right one shows the current time in hours and minutes. The lower window shows messages concerning the filtering and simulation runs. The only window the user has access to is the central window, the userinterface. When not in use, this window shows the network and, at every presentation station, the safety signals for the last filter step, and the forecast value for the end of the simulation period (see Fig. 4). The user can choose from menus a.o. the following options (see Fig. 5): add/change simulation scenarios add/change simulation strategies change system parameters such as time intervals, etc. refresh plot of network display of time-series plot of a presentation station (recent history plus forecast) generate and display time-series plot (water level or flow) at any location

An opcrationai management system for river flows 219

Case Studies Reiderzijlvest Waterboard. The drainage area of Reiderzijlvest is situated in the northeast of the Netherlands, and covers 149 km . The runoff is collected in a main channel system that spills during low tide at the sluice of Nieuwe Statenzijl in the Dollard estuary. The open channel network contains a storage area of 1.8 km only. A few small polders serve as additional storage area. This limited open water storage capacity causes large fluctuations of water levels in the channels, resulting in damage to channel banks. The Reiderzijlvest Waterboard is about to build a new spilling sluice, having four gates, and equipped with an automatic control system. Once in every tidal cycle of 12.4 hours, a control decision is made on the number of gates to be used for spilling, and on their opening period. Such a decision can be based on the volume spilled during the last cycle and on measurements of local water levels, but also on flow forecasts. In the latter case, a form of anticipatory control is chosen, and telemetered measurement data on rainfall and water levels at different sites is required. Delft Hydraulics has been asked to advise in the selection of the control system by evaluating expected reduction in water level fluctuations with costs of the different alternatives. A Sacramento rainfall-runoff model and a WAFLOW open channel model have been calibrated using available measurement data. Real-time use of the models extended with Kalman filters has been simulated. Fig. 6 gives an example of 1-day forecasts. The preliminary results with the models are promising, and a substantial reduction of water level fluctuations seems feasible. Vecht River. The Vecht River has a length of 180 km and the river basin has an area of 3800 km 2 (2100 km 7 in the Netherlands and 1700 km1 in West Germany) (see Fig. 7). The Dutch part of the river has a length of 60 km and is canalized. Six weirs are used for operational water management, particulary during medium and low flow periods. Floods occur frequently, and high flow velocities cause damage to bank protection works. The travel time of floods through the lower 60 km is 14 hours; flood duration can exceed five days regularly. As the dynamic storage in the system is marginal, flood regulation by operation of the weirs is not possible at the moment. During the winter of 1986-1987, overtopping of river banks was imminent. Rijkswaterstaat Directorate of Overijssel is developing an integral water management plan for the River Vecht, and has asked Delft Hydraulics to assist with flow computations and a flood forecasting system. A NETFIL model has been calibrated for the lower Vecht. The schematization consists of 26 computational grid-points (h-points). Fig. 8 contains a length profile of the model. Computed water levels with confidence levels are included. The NETFIL model in combination with a rainfall-runoff model will serve in operational as well as in strategic water management of the Vecht River. Fig. 9 contains results of the NETFIL calibration. Closing the Gap Between Theory and Practice In this paper, an approach is described to offer new methods and techniques for practical river management. A key feature in the approach is a user-oriented form: starting from the information requirements of the user, a dedicated flow forecasting system is developed.

220 J.R. Moll and J.I. Crcbas

COMMUNICATION:

SLEEP UNTIL

13:00

12:10

Niouwa Slatenzljl

REIDERZIJLVEST

HIT ANY KEY TO ACTIVATE USER INTERFACE

START OF

SIMULATION

Fig. 4. User interface: display. COMMUNICATION : SLEEP UNTIL

USER

13:00

OPTIONS: • SCENARIOS • STRATEGIES • SIMULATIONS • PLOTS

NOTHING

LEFT TO DO

Fig. 5. User interface: options.

12:15

An operational management system for river flows 221 20.0

I X

18.0

— forecast x observation

/ E 16.0 5 o

8—x

/( \ x

o 14.0 A x V 12.0 X

N.

10.0

^ 7

;

15

9 12 •> time in days

REIDERZIJLVEST SAMFIL rainfall - runoff

18

Fig. 6. Sacramento model: one day runoff forecasts versus measurements.

ê Mordenberg

^

J

;i jkl_ing*n.

T •

)\.

^u\' - TjHE NETHERLANDS

• ^

GERMANYj

}\-~^

K,

\L

Fig. 7. River Vecht drainage basin.

-

T


VECHT

7 6 5 4 De Haandrik 3 Hardenberg 2 Marienberg 1

RIVER

Junnc

0 -1

ZWARTE WATER

Vilsteren

-2

Vechterweerd

-3

10

20

30

40

60

50

> distance in k m

Fig. 8. Length of profile of the Vecht.

4.50

>

A

20

STATION

50 60 70 80 —> t i m e in h o u r s

VILSTEREN

UPSTREAM

OF

WEIR

Fig. 9. NETFIL calibration.

90

100

110

120


The actual development took place along the following stages: (a)

Based on contacts with clients, specifications for a general real-time flow forecasting and flood control software package have been drawn up.

(b)

Development of models, data structures, user dialogue, graphics and real-time control system has followed, resulting in a prototype for demonstration.

(c)

This prototype has been presented to a group of invited potential clients, and the different concepts and modules have been discussed and criticized.

(d)

Specifications for the system have been adjusted accordingly.

(e)

Within one month after the demonstration, three requests for the development of dedicated systems were received already.

The prototype has been implemented on a personal computer. This implementation forms a particularly attractive solution for management of river basins of moderate size. Personal computers are introduced into management practice on a large scale, and are therefore easily accepted in this case. Other attractive features are that the system can be implemented in-house and operate as a stand-alone machine. Drawbacks, however, are that available memory capacity (640K) prohibits applications on large network schematizations at the moment, and also computations with the Extended Kalman filters tend to be very time-consuming. The rapid developments in microcomputer technology will solve these problems soon. The approach outlined has enabled the introduction of new methods in hydrological practice, and has thus contributed to bridging the gap. It can be envisaged that a similar course of action could be successful in other situations. Conclusions The introduction of new scientific technologies into the practice of water management is, and will continue to be, a challenging issue. A challenge for the scientist, who must try to think as a river basin manager and recognize those actual problems that might be solved by scientific efforts or the introduction of new technologies. A challenge, too, for the water manager, who must be aware of scientific developments and their relevance for his daily responsibilities. The major challenge, however, is the former one: the rapid developments in theory pose a responsibility primarily with the scientists to keep open communication with the practice and, better still, bridge the existing gap. References Dooge, J.C.I. (1973). Washington, DC.

Linear theory of hydrologie systems.

USDA Tech. Bull. 1468,

Georgakakos, K. (1986). A generalized stochastic hydrometeorological model for flood and flash-flood forecasting 1. Formulation; and 2. Case studies. Water Resour. Res., 22(13), 2083-2106.


Jazwinsky, A.H. (1970). Stochastic Processes and Filtering Theory. Academic Press, New York, NY. Kraijenhoff, D.A. and J.R. Moll (eds.) (1986). Rivers, Modelling and Forecasting. Reidel P., Dordrecht, The Netherlands. Ljung, L. and T. Soderstrom (1983). Theory and Practice of Recursive Identification. MIT Press, Cambridge, MA. O'Connell, P.E. (1981). Adaptive hydrological forecasting -- a review. Hydrol. Sci. Bull, 26(2), 179-205. Szollôsi-Nagy, A. and E. Mekis (1988). Comparative analysis of three recursive real time river flow forecasting models: deterministic, stochastic and coupled deterministic-stochastic. Stoch. Hydrol. and Hydraul, 2(1), 17-33. Tong, H. (1983). Threshold models in non-linear time series analysis. Lecture Notes in Statistics, Springer Verlag, Berlin, W. Germany.