Estimation of monthly river runoff data on the basis of satellite imagery

Hydrological Applications of Remote Sensing and Remote Data Transmission (Proceedings of the Hamburg Symposium, August 1983). IAHS Publ. no. 145. Estimation of monthly river runoff data on the basis of satellite imagery INTRODUCTION G, STRÛBING & G. A. SCHULTZ Ruhr-Universitat Bochum, 4630 Bochum, Federal Republic of Germany ABSTRACT For the generation of long time series of hydrological design data, e.g. monthly runoff values, a method is presented using information obtained from the NOAA Polar Orbiting Satellite System. This method consists of four consecutive steps, namely: (a) satellite remote sensing data processing, (b) development and calibration of a mathematical model, which correlates measured runoff values (ground truth) with satellite data, (c) generation of long monthly runoff time series on the basis of satellite data alone, and (d) by means of a stochastic model and the time series computed under (c): simulation of synthetic runoff time series, which are long enough to meet the requirements of a potential application. First results of the application of this method in a basin in southwestern France are described. Estimation des écoulements mensuels à l'aide données de satellite RESUME Dans ce rapport une méthode est présentée pour le calcul d'une série chronologique d'écoulements mensuels d'un bassin versant à partir de la série de longue durée des données d'un satellite météorologique à orbite polaire. La méthode comporte quatre parties essentielles: (a) le traitement et l'analyse des données de la télédétection, (b) la mise au point d'un modèle mathématique et la détermination des paramètres de ce modèle à partir des séries simultanément observées et de courte durée d'écoulement et d'information par satellite, (c) le calcul d'une série chronologique des écoulements mensuels à l'aide du modèle mis au point en (b) et en utilisant seulement les données de la télédétection du satellite, et (d) la simulation d'une série d'écoulement d'une durée suffisante en ce qui concerne une application potentielle avec un modèle stochastique se basant sur la série calculée en (c). L'application de la méthode et les premiers résultats pour un bassin versant au sudouest de la France sont décrits. The planning and design of water resources systems is often based on only short or inadequate time series of hydrometric data, particularly in developing countries. In modern hydrology, stochastic methods have been developed in order to generate long term time series of 491

492 G.Str'ûbing & G.A.Schultz hydrological data with shorter observed time series having a higher uncertainty in the generated data. In order to overcome this problem a method is presented using remote sensing data obtained from satellites for the generation of long time series of hydrological design data, e.g. monthly runoff values. In recent years extensive research programmes were devoted to the use of remote sensing techniques for the acquisition of hydrological data, particularly for rainfall (Barrett & Martin, 1981), soil moisture and snow cover, but less for the estimation of runoff data (Amorocho, 1975). The method presented consists of four consecutive steps, namely: (a) processing of the satellite data; (b) development of a mathematical model, which correlates measured runoff values with satellite data and calibration of this model with simultaneous data, available at least for a short period of time for both ground truth and satellite data; (c) generation of long monthly runoff time series on the basis of the observed long term satellite data by means of the mathematical model calibrated under (b). For more than 10 years remote sensing data have existed for large parts of the world and thus runoff time series can be computed for the same space of time; (d) depending on the objectives of a potential water project, it may become necessary to generate longer time series on the basis of the data obtained in item (c) by means of a stochastic data generation model. The first three steps of this method are described in this paper. For test purposes the technique was verified in the basin of the River Baise (southern France, tributary to the River Garonne), which covers an area of about 1000 km. ANALYSIS OF THE SATELLITE IMAGE INFORMATION Choice of the satellite system Basically the information from both geostationary and polar orbiting weather satellite systems are suitable for the analysis. For the choice of system the following criteria have been used: (a) Rate of image production: the information from geostationary satellites has a repetition rate of once very 30 minutes, whereas the repetition rate of polar orbiting satellites is considerably smaller (two images per day). (b) Spatial resolution: the spatial resolution of the imagery obtained from polar orbiting satellites is usually more favourable (e.g. NOAA 5: -0.8 km ) than that of geostationary satellites (e.g. METEOSAT: ~6 km 2 ). (c) Spectral range: there is no significant difference between the two systems as both transmit images to the earth in the visible and in the thermal infrared range of the "atmospheric window". Whilst the above-mentioned criteria depend on the satellite system the following one is independent of the system, but regarding the objectives of this study, namely the generation of long term runoff time series, it is of particular importance: (d) Availability of the satellite information: this means the

Monthly river runoff estimated by satellite 493 availability of a long uninterrupted time series of satellite imagery and furthermore the easy access to these data. After evaluation of all these criteria the NOAA Polar Orbiting Satellite System, which has been operated and maintained by NOAA- NESS (USA) since the late 1980's, was chosen. The spatial resolution and the availability of a long series of satellite imagery led to this decision despite the disadvantage of the rather low resolution in time. As the results show, the number of available images is sufficient for the estimation of monthly runoff values. Image processing The NOAA satellites follow a sun-synchronous, polar orbit with an altitude of about 1500 km (NOAA 1-5) and now 830-870 km (NOAA 6-7). They are equipped with a very high resolution radiometer, which transmits images to the earth, both in the visible range of the electromagnetic spectrum (0.6-0.7 nm) and in the infrared range (10.5-12.5 um). These images have a spatial resolution of about 0.8 km at the nadir of the satellite and a repetition rate of 12 h (0900 h and 2100 h local solar time), i.e. at each point of the earth there are two images every day. Due to the low rate of image production a "life-history approach" to the variability in time of the cloud size and cloud surface temperature cannot be applied in this study. Accordingly a simple indexing technique (Barrett, 1970) has been adopted which identifies the size of cloud coverage over the observed area as well as the cloud surface temperatures by analysis of the relevant infrared imagery. Different from the commonly used indexing technique, the cloud type is not identified in this study. Therefore an interpretation of the information of the visible channel is not necessary. The indexing technique presented in this paper is based on the following physical principles (Mason, 1971): (a) the lower the surface temperature of a cloud, the higher is the probability of rainfall below; (b) the lower the cloud surface temperature, the more intense the rainfall (if it rains at all). The actual analysis of the information obtained from the infrared channel can be divided into three steps: Pre-processing of the imagery Due to the large number of images, a pre-selection of all images with no clouds visible over the area was carried out. Only those images exposing cloud cover over the area considered were transposed on fine grain positive film such that parts with low density (i.e. cold temperature) would be developed showing high film contrast. In order to facilitate the identification of the basin the images were enlarged approximately four times, thus yielding a scale of about 1:13 000 000 at the nadir of the satellite. Navigation By means of a mathematical model simulating the motion of the satellite and scanner, the position of the test area on the image was identified. This model uses the geocentric system of longitudes and latitudes as terrestrial reference system. Input data are the coordinates of landmarks visible on the images, the

494 G.Str'ùbing & G.A.Schultz coordinates of the area and of the satellite's ground track, which can be computed by prediction of the satellite's orbit. As a result of the simulation the position of the test area is identified using the chosen landmarks as reference points. In this way, it was possible to specify the border of the test area in the images. Quantitative approach Since the satellite information is available on film in analogous form and its interpretation is based on simple enhancement with subsequent area determination, the images are evaluated using an integrated false colour TV device. The whole film density (from base density to maximum) is divided into six density ranges. Thus each density value of the six-step calibration scale visible on the image is the mean value of one density range. This calibration technique based on the image grey scale is necessary, because within the photo-technical process small brightness deviations from image to image cannot be excluded and in this way the values of the images become comparable. Within the next step of image processing, partial areas (within the test area) covered by each density range are determined. Since only infrared images are used, each density range can be considered as certain temperature ranges. The analysis revealed that the partial areas of only the three coldest temperature ranges represent cloud surfaces. Thus the sum of these values forms the cloud coverage over the test area at the time the image was taken. The remaining density ranges can be interpreted as the emission of the earth's surface, including vegetation, etc. THE HYDROLÛGICAL MODEL The purpose of the model is to compute mean monthly runoff values for a river basin as the basis for the design of water resources projects. A linear black-box model is applied (somewhat analogous to the unit-hydrograph concept) which computes indicators of daily runoff values by convoluting the satellite image information as an input with a specified system function. From these indicators mean monthly runoff values are determined. Although the model itself is time invariant, a time variance over the year is introduced by subdividing the year into seasons. Input data Given the values of the partial areas of the three low density ranges per image and the two images per day, a "mean daily temperature-weighted cloud cover index" B(T) is calculated as input : B(T), = 0.5 Y 2 V 3 B(T. )f i 1 (1) 1 L k=l i=l i k. 1 where B(TJ), : fractional cloud cover index of density range i (i = 1,2,3) on image k (k = 1,2) of day 1 1 : number of day a i : weighting coefficient of the i-th density range (i = 1,2,3). Since only two images per day are available, no statement about the potential within-day variation of the cloud coverage is possible.

Monthly river runoff estimated by satellite 495 Therefore, the information gap between two images is bridged by a linear approach. The weighting coefficients, a-^, are determined by a simple direct search method. The objective function used for this optimization technique is the minimization of the sum of squares of differences between estimated and recorded mean monthly runoff values. The constraints are specified by the aforementioned physical principles, i.e. the smaller the density range (= colder temperature) the higher the value of the coefficient a^. The mathematical model The transformation of the (satellite derived) cloud cover index B(T) into runoff values is based on a linear transfer model of the form: where 3 1 Q m (m,j) : mean monthly runoff value of month m, year j (m s ) tb(m,j) : number of the first day of month m, year j te(m,j) : number of the last day of month m, year j S : memory of the system in days hjj : discrete value of the response function h(t) of the system (m 3 s -1 ), k = 1,...,S. B(T) : mean cloud cover index of day 1 - k + 1 1 : number of day n : number of days in month m, year j The time length S of the memory is defined as the duration (in days) during which the response of the system to an input shows a significant difference from zero. It is equal to the length of the response function of the system. This length is determined by the autocovariance function of the recorded runoff values. Since these runoff time series are short (according to the purpose of this study), the estimation of the autocovariance function is rather uncertain. Therefore the influence of the length of the memory should be estimated by means of a sensitivity analysis. The discrete values h^ (k = 1,...,S) of the response function are estimated by a least square procedure in order to minimize the sum of squares of the differences between recorded daily flows and computed daily indicators of the runoff. These indicators can be computed with the aid of the following expression in equation (2): «I = i i h k B < T >i- k+ i where 3 1 q-, : indicator of the runoff of day 1 (m s ) The reduction of time resolution from daily indicators (input) to monthly values (output) acts as a low-pass filter by which the negative effect of the small rate of image production and thus large (within day) information gaps of the input data is reduced. (3> APPLICATION OF THE METHOD IN THE BAISE RIVER BASIN The model was calibrated and tested with data from the Baise River

496 G.Strubing & G.A.Schultz t Coefficient 0j 1. Season, 2. Season ; 3. Season : U. Season 4,0-3,5-3,0- i 2.5-2,0-1,5- I: I; f I: : V. - a i 2 1,0- a 3 0,5- Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov FIG.l Seasonal variation of the weighting coefficients a^ of the fractional cloud cover index of density range i; i = - 1,2,3. &- basin, an area of about 1000 km. Mean daily discharge has been recorded for 17 years. For calibration and verification purposes the period of October 1975 to October 1977 was chosen, because these two years deviate significantly from average conditions in both 12,0 10,0' " Mean daily temperature weighted cloud cover index [%] 8,0 6.0 4.0 2.0 0,0 Oct Nov 1975 I Ll I 1. lu JJL L\ Apr Jun Jul 1976 Aug Sep Mean daily temperature weighted cloud cover index [%! 6.0' 0.0-12,0-10.0-8,0-4.0-2.0-0.0- Li li,.i JJ4_ J_J_JL L_JL Hr FIG.2 Input data: mean daily temperature weighted cloud cover index in per cent of the maximum possible value (total cloud coverage of the first density range). Nov Dec Jan Feb Mar Apr May Jun Aug Sep

Monthly river runoff estimated by satellite 497 directions. In this manner the performance of the method is tested even for extreme events. The time period between November 1975 and October 1976 was chosen for model calibration, the period November 1976 to October 1977 for independent model verification. The subdivision of the year into seasons (see Fig.l) was based on climate diagrams from surrounding climate stations. The best agreement between computed mean monthly runoff values and measured data was obtained from those coefficients a^ (for the calculation of the mean daily temperature-weighted cloud cover index) presented in Fig.l. The cloud cover indices, B(T), computed with the aid of equation (1) and the coefficients, a i( are shown in Fig.2. A comparison between computed and recorded mean monthly runoff values for the River Baise is presented in Fig.3. The computed values are based on a seasonal, varying response function with memory of seven days. The deviation between computed and recorded values " Mean monthly runoff [mvs] recorded computed I U Calibrations period I 25,0-5,0 4,0 3,0-2,0 1,0 0,0 10 11 12 1 2 3 4 5 5 7 i«- 19 75-4" 1976 9 10 11 12 1 2 3 4 5 6 7 4«1977 - FIG.3 Comparison between computed and recorded mean monthly runoff values for the River Baise.

498 G.Strïïbing S G.A.Schultz lies between +65% (9.77) and -148% (10.77); the mean deviation, however, amounts to +9%. For the extreme events in December 1976 and July 1977, the adaption of the computed runoffs to the measured data can be considered as reasonably good. Definite statements about the quality of the described method for very long time series cannot be given, since results for only two years are available. For greater assurance, it is normally advisable to have more than one year for calibration and verification, respectively. However, given the good results obtained so far, the method seems suitable to reduce the problems occurring in the planning of water resources projects based only on short time series of hydrological data. REFERENCES Amorocho, J. (1975) An application of satellite imagery to hydrologie modelling the upper Sinu River Basin, Columbia. Proc. International Symposium and Workshop on the Application of Mathematical Models in Hydrology and Water Resources Systems, Bratislava. Barrett, E.C. (1970) The estimation of monthly rainfall from satellite data. Mon. Weath. Rev. 98, 322-327. Barrett, E.C. & Martin, D.W. (1981) The Use of Satellite Data in Rainfall Monitoring. Academic Press, London. Mason, B.J. (1971) The Physics of Clouds. Clarendon Press, Oxford, UK.