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Water for the Future: Hydrology in Perspective (Proceedings of the Rome Symposium, April 1987). IAHS Publ. no. 164, 1987.

Parameter determination and input estimation in rainfall-runoff modelling based on remote sensing techniques

GERT A. SCHULTZ Ruhr University Bochum, 4630 Bochum, FR Germany

ABSTRACT In rainfall-runoff modelling three consecutive steps have usually to be taken: choice of an adequate model structure, estimation of the model parameters, selection of the model input data. The paper discusses the potential use of remote sensing (RS) data for parameter determination and input estimation, along with relevant model structures for RS data use. First RS platforms and sensors are discussed which may be used for hydrological applications. After a brief discussion of model structures, two different ways of model parameter estimation are presented using RS information. An example of Landsat imagery use for parameter estimation is given. It is emphasized that the resolution in space of the model structure, the parameters and the input data must be in good agreement. The estimation of model input data from RS sources is considered for three types of problem: (a) rainfall estimation with the aid of weather radar for flood forecasting, (b) rainfall estimation for runoff computation from geostationary satellites, (c) runoff estimation (monthly values) for design purposes using imagery from polar orbiting satellites. A discussion of model performance utilizing RS information is followed by some conclusions.

Determination des paramètres et estimation des données d'entrée dans un modèle pluies-débits basé sur les techniques de télédétection RESUME Dans la mise en modèle pluies-debits on doit passer habituellement par trois étapes consécutives: choix d'une structure adéquate de modèle, estimation des paramètres du modèle, selection des données d'entrées du modèle. Cette communication traite des possibilités de la télédétection pour la détermination des paramètres et l'estimation des données d'entrée en même temps que de la structure convenable du modèle pour l'utilisation des données de la télédétection. Tout d'abord les plates-formes de télédétection et les capteurs qui peuvent être utilisés pour les applications hydrologiques sont étudiés. Après une brève discussion sur les structures du modèle, on présente deux approches différentes pour l'estimation des paramètres à partir de l'information fournie par la télédétection. On donne un exemple de l'emploi de l'imagerie Landsat pour l'estimation des paramètres. On insiste sur le fait que la résolution spatiale, les paramètres et les données d'entrées doivent être en bon accord. Cette estimation des données d'entrée provenant de la télédétection présentée pour trois types

426 Gert A.Schultz

de problèmes: (a) estimation des hauteurs de précipitation avec l'aide de radar météorologiques pour la prévision des crues, (b) estimation des hauteurs de précipitation pour le calcul de l'écoulement à partir de satellites géostation-naires, (c) estimation de l'écoulement (valeurs mensuelles) pour la mise au point des projets sur la base de l'imagerie fournie par les satellites à orbite polaire. Une discussion sur les performances du modèle qui utilise les données de la télédétection suit avec des conclusions.

INTRODUCTION

If the behaviour of a hydrological system is to be represented by a mathematical model, three consecutive steps have usually to be taken:

(a) specification of the mathematical structure of the model -deterministic or stochastic, lumped system or distributed system type, linear or nonlinear etc.,

(b) model calibration, i.e. system identification by computing the model parameters for the system under consideration,

(c) specification of the model input to be used for the simulation of the hydrological process in the hydrological system, with the aid of the mathematical model and the model parameters identified under (a) and (b) above.

The choice of the mathematical model (and thus its structure) is dependent on :

- scale of prototype system depending on time and space, - knowledge of the system structure and the hydrological process, - the objective of modelling, - the available hydrometeorological data.

HYDROLOGICALLY RELEVANT REMOTE SENSING DATA

For hydrological purposes various RS platforms can be used, e.g. aeroplanes (for air photography), boats (containing eTg. multifrequency echo sounders), ground based radar as well as satellites and spacecraft.

Sensors relevant for hydrological applications are photographic cameras (recording scenes in various spectral bands), scanning radiometers (depending upon rotation or oscillation of part of the instrument or its platform), "push broom" sensors, spectrometers and microwave radars.

Among the many different spectral bands in which data can be acquired by the various sensors, the visible (VIS), infrared (IR), water vapour (WV) as well as passive and active microwave channels are of particular importance. Different frequencies (or wave lengths) of the electromagnetic spectrum give different information relevant for different hydrological variables. Also combinations of the information from various spectral bands can be used in order to identify hydrological variables.

Table 1 gives some information on potential uses of certain RS signals relevant for various hydrological and water management problems.

Since all information obtained from RS sources is not in the form

Parameter determination and input estimation 427

TABLE 1 Information on remote sensing platforms

No.

1

2

3

4

5

RS platform

Air photography

Radar

SATELLITES : (a) Landsat

(b) GOES Meteosat

(c) NOAA series TIROS N

Resolution in: Time Space

(pixel size)

can be adapted to the

few minutes less than 1 km x 1 km

MSS 18 days 54 x 76 m

TM*

30 x 30 m

30 minutes 5 x 5 km (SSP)

12 h 900 x 900 m

Spectral channels

hydrological

X band (3 cm)

C band (5 cm) S band (10 cm wave length)

Vis: 0.5-0.6 0.6-0.7 0.7-0.8 IR: 0.8-1.1

Vis, IR,

Vis, IR

\im

]im \im

\im

WV

Remarks

problem

Ground based

In orbit

Polar orbiting

Geo-syn-chronous

Polar orbiting

Vis = visible; IR = infrared; WV = water vapour. *Highest resolution in space by the SPOT satellite (10 x 10 m) started 1986.

of hydrological data (like water level, discharge etc.) but exists only as electromagnetic signals, the first task consists in evaluating which type of signal gives relevant information for which type of hydrological parameter or variable. Sometimes the signal is highly relevant for the hydrological phenomenon, sometimes, however, it gives only partial information. Here a danger of misinterpretation exists. This fact also requires that a calibration procedure with the aid of ground truth is always necessary!

Another feature which has to be carefully observed is the resolution in time and space available from the various RS sources (Table 1). Highly dynamic processes in small areas require high resolution information in both time and space. This is seldom available. However, ground based radar measurements yield rainfall data with a high resolution in time and space. Air photography and some types of satellites (e.g. Landsat or SPOT) produce data with high resolution in space but low resolution in time. Other platforms (e.g. GOES, GMS or Meteosat satellites) produce high

428 Gert A.Schultz

resolution data in time (4 hour repetition rate) but low resolution in space (5 km x 5 km pixels in the infrared band).

The main advantage of RS data lies in the fact that it always produces areal information instead of the point measurements which are still predominant in hydrology. RS measurements of major importance in hydrology are the following:

- multlspectral air photography (from aeroplanes or balloons), - echo sounders for sediment measurements (on boats), - ultrasonic velocity measurements in rivers, - laser techniques for various measurements (e.g. velocity in

open channels or pipes), - ground based weather radar for quantitative rainfall

measurements as basis for runoff computations (in real time), - satellite measurements from polar orbiting or geo-synchronous

satellites in various spectral bands, - space shuttle measurements.

MODEL STRUCTURES SUITABLE FOR RS DATA

In the classical age of hydrology almost all models were lumped but when modern hydrology started the distributed type of model came into being (Fleming, 1975; Schultz, 1968) . Since the available input data did not usually meet the requirements of distributed type models, lumped models prevailed, particularly in their more refined versions (Fleming, 1975). With the advent of radar and satellites (such as Landsat), extremely high resolution data became available. Thus in hydrological modelling the question arose: how much data are really needed?

No matter whether a lumped or distributed model is used, there is always one or more transfer functions which compute the model output with the aid of the input data. Usually in hydrological models both input and output data are hydrometeorological variables. Thus the transfer function has some physical meaning.

If RS data are used, the output is also a hydrometeorological variable (e.g. rainfall or runoff). The model input, however, is electromagnetic information obtained from some sensors in some spectral band. This information has no meteorological or hydrological meaning. The transfer function transforms an electromagnetic input into a hydrometeorological output. Furthermore, the input cannot be taken from the sensor directly: it has to be manipulated before it can be used as an input to the model.

An extension of the input information, but a further complication of the model structure, is the fact that several RS platforms offer information on more than one spectral band (e.g. GOES: 2, Meteosat: 3, Landsat: up to 8 spectral bands). Thus the model input may be formed by data from, say the infrared, visible and water vapour channel and it can be classed as a truly multivariate model. At present, almost all models are still based on an input from one electromagnetic band only. Attempts are presently being made to use more than one channel, thus there is a requirement to have more than one transfer function within the model. Difficulties arise from the questions of which spectral data are relevant for the model and how


they should be incorporated. As far as the input-output transformation part of the model is

concerned, one can state that it would be possible, in theory, to construct a model which contains a transfer function for input from each spectral band for each pixel. Although this would be possible, there is the question of whether this is necessary and reasonable. At present there is not enough information available on how such a model should be structured concerning:

- resolution in space, - relevance of spectral bands, - manipulation of spectral data in order to make them usable as

the model input, - the mathematical structure of the transfer functions for each

spectral band and each pixel. From this discussion it can be concluded that at present it is by

no means clear what is the best structure for hydrological models to utilize RS data. The full potential of RS data can, however, be exploited only by use of distributed models, taking advantage of the high resolution of RS data in space. On the other hand there are problems which can be solved with the aid of lumped models using RS data in a form adapted to such problems. Examples are now given of the use of both types of model, i.e. lumped and distributed system models, distinguishing between the use of RS data for model parameter estimation on the one hand and for model input on the other hand. Examples for both uses of RS data will be given in the following chapters.

MODEL PARAMETERS ESTIMATED FROM RS DATA

In some cases RS data are used only to estimate model parameters, while the model input stems from other sources (usually, if distributed models are applied); in other cases the same type of RS data is used for both parameter estimation and model input determination.

Parameter estimation with the aid of RS data

Recently several new models have been developed - or existing models adapted - so that they can use RS data for an accurate estimation of model parameters. In this field Landsat imagery is of great importance due to its extremely high resolution in space (Abbott et al., 1981; Cermak et al., Rango et al., 1983). Besides these efforts which mainly help to determine model parameters like soil cover, soil type, snow/ice cover, drainage density etc. for each pixel in the catchment, other investigations show how to determine for each pixel soil moisture (e.g. as antecedant precipitation index) allowing excess rain to be distinguished from the infiltration rate (Jackson et al., 1981). The new SPOT satellite (space resolution 10 x 10 m) looks downwards and also sideways making it possible to estimate the hydrologically important parameter "slope" in catchments (from pixel to pixel) and in river channels.

These techniques for estimation of model parameters take advantage of the high resolution in space of air photography,

430 Gert A.Schultz

Landsat or SPOT data. The corresponding low resolution in time is not relevant for this purpose.

Figure 1 shows an example of a land use classification of a part of the Ruhr catchment in the FR Germany based on a Landsat 2 (MSS) image of 1975. The classification uses maximum likelihood estimators based on three spectral bands. From this information various hydrologically relevant parameters can be determined for each pixel (80 x 80 m).

Since most catchments in developed areas change characteristics rapidly over the years and between seasons, the hydrologically relevant parameters depending e.g. on land use also vary with time. Such changes can be specified with the aid of RS data. As an example

FIG.l Supervised classification map of Landsat 2 image from 16 September 1975 (maximum likelihood classification) geometrically registrated to the UTM coordinate system, without 6-line striping, 256 x 256 pixels area.


for the determination of land use changes the Landsat image of Fig.l (in 1975) is compared to the same scene 10 years later, i.e. 1985 (Landsat 4 MSS). All pixels showing changes are printed in black in Fig.2, which presents the result of the comparison of the two scenes. Thus an artifical lake (Kemnade), constructed in the Ruhr River valley in 1979, is shown in black, since it did not exist in 1975 (Fig.l).

Model parameters estimated from RS data which also serve as model input

In some cases, particularly if lumped models are used, the model parameters are determined with the aid of simultaneous input and output data - analogous to the unit hydrograph principle. The main difference, however, lies in the fact that the model input consists of electromagnetic signals instead of e.g. rainfall. From this RS information is derived in a first step the model input and then the system's behaviour is identified by a transfer function transforming

1 Lake Kemnade

FIG.2 Comparison between the 1975 image of Fig.l and the same scene (Landsat 4, MSS) on 4 April 1985. Black pixels are those of different classification, e.g. Lake Kemnade (bottom centre).

432 Gert A.Schultz

the RS based input into a hydrologieal output, e.g. river runoff. This procedure for parameter estimation is next explained with an example given.

MODEL INPUT DERIVED FROM RS DATA AND MODEL PERFORMANCE

RS information obtained from many platforms and sensors can be used for many different hydrological purposes (Farnsworth et al., 1984; Herschy et al., 1985). In the context of this paper on rainfall-runoff modelling only three types of relevant RS input are briefly discussed:

- radar rainfall measurements for flood forecasting, - infrared data from geostationary satellites for rainfall

estimation as a basis for runoff computation, - infrared data from polar orbiting satellites for the estimation

of monthly runoff values for design purposes.

Radar rainfall measurements as basis for flood forecasts

For flood forecasting purposes it is necessary to have the forecast available as early as possible. The lead time of the forecast can be shortened if the flood forecast is issued while it is still raining. For this purpose, radar rainfall measurements are highly suitable since they have a high resolution in time and space and since all the input information is collected at one point (radar). In such cases, a distributed model with high resolution in space and time is of advantage.

For this study a C-band weather radar was used giving rainfall data in polar coordinates of 1 km in radius of 1° of angle. Thus the pixel size is about 1 km2 and the time interval was chosen to be 15 minutes. Figure 3 shows isohyets based on radar measurements constructed by the computer for the Gunz River catchment, a Danube tributary. The mathematical model consists of two components:

- the first transforms the electromagnetic signal (radar echo) into the rainfall (model input),

- the second takes this distributed input and employs it in a rainfall-runoff model. Figure 4 shows the performance of the model for real time flood forecasting. More details on the technique are published elsewhere (Klatt & Schultz, 1985; Schultz, 1986).

Rainfall estimation with the aid of satellite data

Another method of rainfall estimation for runoff computation from RS data is the use of infrared imagery (IR) from geostationary satellites (Table 1). There are several techniques available which use the imagery from GOES, Meteosat or GMS satellites (Barrett & Martin, 1981; Scofield, 1984). The resolution in time (| h intervals) is for most purposes good enough, but the resolution in space is only 5 x 5 km pixels.

Figure 5 shows a comparison between IR information obtained from Meteosat (Fig.5(a)) and simultaneously but completely independent ground truth (Fig.5(b)), i.e. isohyets constructed with the aid of


FIG.3 Isohyets from radar rainfall measurements, Gunz River catchment; grid of polar coordinates (7 August 1978, 14.45-15.00 h).

conventional raingauge measurements in southern Germany (Kruger et al., 1985). Although Fig.5 shows some correspondence between IR data and ground truth, the mathematical relationship between the two is not simple. Hydrological models transforming satellite data into a flood hydrograph consist of two consecutive partial models:

(a) a rainfall model transforming the satellite information into rainfall data,

(b) a runoff model transforming this rainfall into a flow hydrograph.

For (a) various models are in use (Barrett & Martin, 1981) such as cloud indexing methods, life history methods, bi-spectral cloud model and microwave methods. The accuracy of these models is still to be improved.

For (b) classical hydrological black-box models can be used (e.g. the unit hydrograph) or - if the rainfall is estimated with high resolution in space - distributed type models can be applied.

Runoff estimation with the aid of satellite data

The design of a water supply system (e.g. based on a large dam) requires a long time series of river flow data in order to evaluate reliability. These data are very often not available. An observation network is usually installed for a short period yielding hydrological data but not allowing a reliability evaluation.

The short time series of observed (ground) data can be extended with the aid of satellite data which are available for some years

434 Gert A.Schultz

4 Mean rainfo!! (mm)

Time 1 hours )

0 16 32 i8 64 -f— 07 08. \—08.08. f— 09.08.

'—Time of forecast

80 96 112 -10.08.—+— 11.08.78

80-

64-

•

48 -

32 -

16 -

0 -

Runoff <m3 é

' 1

y

/ / (

"

(""-

"'

Y-observed

Y-V-forecast

^0,

\ ^

. — • -

, -V-. ' *

Time Ihours) i r" ' i r *•

0 16 -|—07.08. f -

32 -08.08-

48 64 -\—09.08.— -10.08.

96 116 -+—11.08.78

- Time of forecast

FIG.4 Flood forecast (Gunz River) based on radar rainfall measurements (at the end of the storm).

(e.g. NOAA for 12 years). Since long-term data series are required, NOAA/TIROS N, data

seem appropriate although these polar orbiting satellites produce only two images per day. Only information from the infrared channel was chosen. These infrared (IR) data had to be manipulated in order to become usable as the model input. Therefore an input variable B(T) was developed (T being cloud top temperature) which uses the two IR images per day and the three coldest "grey steps" of the grey scale contained in the images.

B(T) =0.5 Z2k=l Z ^ B C T i ) ^

where B(T±)

k,l = fractional cloud cover index of IR density range

i (i = 1,2,3) on image k (k = 1,2) of day 1 (NOAA produces two images per day) valid for the river catchment area,

= number of day, = weighting coefficient of the i-th density range

(i = 1,2,3); this parameter is seasonally changing.


Temperature ranges of cloud surface

| H = -30--40°C ! ! l l = -«)--5u°C IH=<: -S0°C

FIG.5 Comparison between IR satellite information and simultaneous isohyets (ground truth) in southern Germany. (a) Convective cell derived from Meteosat IR image, 16.55 h GMT, 6 August 1978; (b) isohyetal map based on raingauges, 16.45-17.15 h GMT, 6 August 1978.

B(T) can be interpreted as a mean daily temperature weighted cloud cover index computed for the whole river catchment area. B(T) serves as input data to the hydrological model.

The model applies a transfer function hk which transforms the input B(T) into an output q-̂ (representing a daily indicator of runoff) . The required monthly runoff is then just the sum of q^ for all days of the month. The transformation of model input into output is done with the aid of the well known convolution integral containing B(T) as input and hk as transfer function (Striibing & Schultz, 1985; Schultz, 1987). The model was applied for river catchments in southern France. Figure 6 shows an example of the model performance for 1977 data.

In the context of the previous discussion about parameter estimation, it should be noted that the model parameters are the ordinates of the transfer function hk.

Analogous to the unit hydrograph principle these ordinates of hk

are determined with the aid of simultaneous input and output data. Input data here are the B(T) values obtained from RS information while output data are the runoff values.

436 Gert A.Schultz

35,0-

30.0-

25,0-

20,0

15,0

10,0

5,0

~| ^ ' ' ' ' ' -̂i—i—i i i i i—i—r—i—i—i—i—i—i—i — Monm 10 12 2 4 6 8 10 12 2 4 6 8 10

\ 1975 1 1977

FIG.6 Monthly runoff values based on IR satellite imagery (Save River / France) .

CONCLUSIONS

The following conclusions may be drawn: (1) The information obtained from some RS platforms allows

parameters of distributed models to be determined with an extremely high resolution in space (which is not always required).

(2) The full potential of some RS data can be exploited only with the aid of distributed hydrological models which will become more important due to new RS systems.

(3) Hydrological models working on the basis of transfer functions have to transform input obtained from several electromagnetic spectral bands into hydrological variables. Here the understanding of the physical processes involved is still to be developed.

(4) Since several RS data acquisition systems provide simultaneous information on various spectral bands, models have to be developed which can make efficient use of the information obtained from all relevant spectral channels.

(5) Obviously some data do not permit a deterministic relationship between spectral input and hydrological output to be established but may be suitable for developing a stochastic model.

(6) The hydrological models developed so far for computation of hydrological variables on the basis of RS data are still in their infancy. We have to learn how to transform the available RS information - which with future RS systems will become even more comprehensive - into hydrological variables. Models on the lines of regression, translation and retention, transfer functions etc. will certainly not be sufficient in the future.

i Mean monthly runoff (m-3 s1 - f Calibration period -If-


(7) The development of newly structured hydrological models on using RS data should be a great challenge for today's hydrologists.

(8) The agencies manufacturing and operating RS systems are in the process of producing promising new platforms and sensors. With the advent of new satellite types (e.g. NASA's EOS or ESA's ERS-1 and polar platform) it can be expected that the potential of RS in hydrology will dramatically increase during the next two decades.

REFERENCES

Abbott, M.B., Clarke, R. & Preissmann, A. (1981) Logistics and benefits of the European Hydrologie System (SHE). In: Logistics and Benefits of Using Mathematical Models of Hydrologie and Water Resources Systems (ed. by A.Askew, F.Greco & J.Kindler). IIASA Proceedings Series, vol.13, Pergamon Press, Oxford.

Barrett, E.C. & Martin, D.W. (1981) The Use of Satellite Data in Rainfall Monitoring. Academic Press, London.

Cermak, R.J., Feldman, A. & Webb, R.P. (1981) Hydrologie Land Use Classification Using Land sat, in Satellite Hydrology (ed. by M.Deutsch, J.Wiesnet & A.Rango). American Water Resources Association.

Farnsworth, R.K., Barrett, E.C. & Dhanju, M.S. (1984) Application of Remote Sensing to Hydrology Including Ground Water. UNESCO, Technical Documents in Hydrology, Paris.

Fleming, G. (1975) Computer Simulation Techniques in Hydrology. Elsevier, New York.

Herschy, R.W., Barrett, E.C. & Roozekrans, J.N. (1985) Remote Sensing in Hydrology and Water Management. ESA Contract no.5769/A84/D/JS (SC), Strasbourg.

Jackson, T.J., Schmugge, T.J., Nicks, A.D., Colemann, G.A. & Engman, E.T. (1981) Soil moisture updating and microwave remote sensing for hydrological simulation. Hydrol. Sci. Bull. 26(3), 305-319.

Klatt, P. & Schultz, G.A. (1985) Flood forecasting on the basis of radar rainfall measurement and rainfall forecasting. In: Hydrological Applications of Remote Sensing and Remote Data Transmission (Proc. Hamburg Symp., August 1983), 307-315. IAHS Publ. no.145.

Kriiger, L.-R., Harboe, R. & Schultz, G.A. (1985) Estimation of convective rainfall volumes with the aid of satellite data. In: Hydrological Applications of Remote Sensing and Remote Data Transmission (Proc. Hamburg Symp., August 1983), 273-380. IAHS Publ. no.145.

Rango, A., Feldman, A., George III, T.S. & Ragan, R.M. (1983) Effective use of Landsat data in hydrologie models. Wat. Resour. Bull. 19(2).

Schultz, G.A. (1968) Digital computer solutions for flood hydrograph prediction from rainfall data. Proceedings of UNESCO Symposium on the Use of Analog and Digital Computers in Hydrology, Tucson, Arizona.

Schultz, G.A. (1986) How does remote sensing information influence the structure of hydrologie models? Proceedings of the IVth International Hydrology Symposium, Fort Collins, USA, 1985. To

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be published by Water Resources Publications, Littleton, Colorado, USA.

Schultz, G.A. (1987) Flood forecasting based on rainfall radar measurement and stochastic rainfall forecasting in the Fed. Republic of Germany. In: Weather Radar and Flood Forecasting (ed. by C.Kirby & V.Collinge). John Wiley, Chichester, UK.

Scofield, R.A. (1984) The NESDIS operational convective precipitation estimation technique. Proceedings, 10th Weather Forecasting and Analysis Conference (June 1984). American Meteorological Society.

Striibing, G. & Schultz, G.A. (1985) Estimation of monthly river runoff data on the basis of satellite imagery. In: Hydrological Applications of Remote Sensing and Remote Data Transmission (Proc. Hamburg Symp., August 1983), 491-498. IAHS Publ. no. 145.