with a water budget model

Transcription

1 Daily and seasonal runoff forecasting with a water budget model M.C. Quick and A. Pipes Department of Civil Engineering, University of British CoZumbia, Vancouver, British Columbia ABSTRACT: The paper describes a computer model for forecasting daily values and seasonal volumes of streamflow which arise from snowmelt and rain. The model carries out a total water balance budget and identifies the contributions to runoff, soil moisture, and evaporation by area-elevation bands in the mountainous catchment. The model coefficients are held constant both throughout the season and from year to year, a modelling criterion which is considered essential for forecasting. Short-term forecasts are made from preceding meteorological data and weather forecasts for the next few days. Long-term forecasts of seasonal volume inflows are made by using snowpack measurements and antecedent conditions together with recorded weather patterns from previous years. Weather patterns are selected which can be classified as average, extreme-high, and extreme-low, so that the most probable volume together with upper and lower bounds can be forecast. RESUME: On décrit un modèle pour ordinateur permettant de prévoir l'importance quotidienne et saisonnière des eaux qui surgissent par suite de pluies et de la fonte des neiges. Ce modèle donne un bilan total des eaux de ruissellement, de l'humidité du terrain et de l'évaporation selon des bandes en fonction de l'altitude dans les régions montagneuses. Les coefficients sont considérés comme constants d'un bout 2 l'autre de la saison et d'année en année, ce qui est essentiel pour les prgvisions. Les prévisions de courte durée sont faites 'a partir de données et de prévisions météorologiques. Celles de longue durée, pour le débit saisonnier, sont faites en tenant compte des mesures de neiges tassées, de données passées et de données statistiques des années précédentes. Des configurations de temps sont classées comme moyennes, extrêmement élevées, extrêmement basses, de façon que l'on puisse avoir des probabilités de débit et des valeurs limites intérieures et supérieures. PURPOSE OF THE STUDY AND OUTLINE OF THE METHOD A method is described for the calculation of streamflow runoff arising from both snowmelt and rainfall. The method is so designed that a complete water balance is maintained between input, outflow, and evapotranspiration, as well as accounting for soil moisture and groundwater. For the size of catchment currently being studied, namely, the Okanagan Lake watershed with an area of some 3,770 km2, the calculations are carried out on a daily basis. The purposes for developing the calculation method are twofold. The first is to develop an understanding of the hydrological behaviour of the Okanagan watershed, particularly to identify the areas that do and those that do not contribute to runoff under given input conditions. The second purpose is to use the fully developed method as a forecasting tool so that the several lake storages can 1017

2 be operated to minimize flood risks and to assist in the operation of lake outflows and levels. With the help of such forecasts better use may be made of the available runoff for such competitive uses as irrigation, fisheries, and domestic, industrial, and recreational requirements. The method is developed so that all identifiable components of the hydrologic process are represented in a physically realistic manner. All coefficients used in the calculations are maintained as true constants and are not varied either during a given calculation year or from year to year. This constancy of coefficients is considered essential for the method to be useful in the forecasting mode, as well as being desirable in the simulator mode. Great effort has been made to keep the method simple, with the minimum of coefficients necessary to adequately describe the total runoff process. Results are presented to illustrate the use of the model to explain the recorded runoff that has occurred in the last eight years for which adequate data is available. A few years of extreme flows which have occurred in the last 25 years have also been studied. The forecasting method is then illustrated using some of the historical data and estimates are given of forecast reliability for forecasting volume inflows. The study shows that, by March Ist, only part of the seasonal runoff can be explained, and therefore forecast, by the information available at that time. The remaining runoff is a function of precipitation and temperature sequence during the melt season. The resulting forecast developed takes this uncertainty into account and gives an average forecast together with upper and lower bounds. These bounds can be narrowed considerably as the season progresses. THE OKANAGAN SYSTEM: FACTORS INFLUENCING CONCEPTION OF METHOD Okanagan Lake is situated in a deep valley in the interior of British Columbia. The valley bottom is extremely dry, very warm in summer, and subject to subzero weather in winter. The thriving agriculture depends on irrigation water derived from the surrounding mountains and lakes. Much of the water comes from the melting of winter snowpacks, although summer rain, particularly during snowmelt, is significant in some years. The location of the basin is given in Figure 1. The total water resource system is limited in various respects. The below average runoff years have produced concern for survival of the fruit trees and vines of the orchard industry. The limited outflows to Okanagan Lake and the constraints of possible downstream flooding in Osoyoos Lake requires that the Okanagan Lake level is reduced adequately to receive some of the higher inflows. This is seen to be a fairly severe limitation in that at present the lake is only operated through four feet, whereas the summer inflows have historically raised the lake by some six feet, despite maximum discharge. Even at high discharge and with no inflow it takes some 25 days to reduce the lake level by just one foot. When it is realized that the majority of the lake inflows occur during a four month period, it will be appreciated that a good forecast is essential to operating the system for the conflicting constraints of flood control as opposed to irrigation storage. An important feature of the Okanagan system is the upland storage, which is made up of a number of small lakes, most of which have been dammed to increase storage. These lakes are operated by the 1018

3 local Irrigation Districts and are a major source of irrigation water. An improved understanding of the areal distribution of runoff can assist in the planning of such storage, while any improvement in forecast accuracy will assist in the operation of these lakes, particularly in dry years when irrigation may have to be minimized and scheduling may be critical. THE COMPUTER MODEL OUTLINE The watershed is represented on an area-elevation basis. It has been found adequate to use 150 m elevation increments for the Okanagan Valley elevation range of 350 to 2,150 m, and, because of sparseness of meteorological data, the area within each elevation band has not been subdivided. The areal distribution of snowcover is derived from the snowcourse data and can be upgraded during the progress of the runoff season. Precipitation is calculated from five stations and areal and elevation distribution factors have been derived from historical data and reconstitution of historical runoff. Daily snowmelt is calculated for each elevation band using average daily temperatures and an average lapse rate. The use of average daily temperatures for calculating snowmelt has been found to be an excellent index in good agreement with snowpillow and meltcatchbasin studies made on Mount Seymour [l]. Precipitation during the snowmelt season is partitioned between rain and snow by using a temperature index for each elevation band. Rain is added to the melt to yield a total daily precipitation plus melt input. A percentage of the watershed is considered to be impermeable, with all the precipitation in this area running off. This impermeable area is considered to increase as a function of the soil moisture status of the watershed and can reach a maximum of 30 per cent of each band area as the rainfall and snowmelt input reduces the soil moisture deficit to zero. The remainder of the catchment is subject to a water balance analysis involving allowance for soil moisture deficit, evapotranspiration, and percolation to groundwater. The residual precipitation from the water balance calculation contributes to fast runoff. The impermeable area runoff and the net water balance runoff is then routed to the stream system using a unit hydrograph method. Allowance is made for the upland lake storage which controls about 20 per cent of the runoff above 1,200 m. A running total of water flowing to storage indicates when the upland storages are filled. This lake storage provides much of the consumption during the latter part of the irrigation season. A total water balance accounting procedure is carried out in the model so that the total snowmelt and rain is partitioned between the soil moisture, evapotranspiration, and runoff. If the initial snowpack is known, an account of residual snowpack in each elevation band can be made and areal depletion of snowcover is calculated in the model. This is an important feature of the model because snowmelt is very much a function of snow-covered area. In this manner, the model checks itself by calculating a total water balance continuously. Arising from this total water balance, it is possible to show how much of the runcff is coming from each elevation band and how much is being lost to soil moisture, and hence to evapotranspiration. Further corrections are made to the calculated stream runoff to allow for evaporation from Okanagan Lake and direct precipitation 1019

4 to the lake. This final corrected value, referred to as net lake inflow, is combined with data on the controlled lake outflows to predict the Okanagan Lake level. Some comment should be made on the method for calculating daily lake evaporation and evapotranspiration from each elevation band. The only immediately useful data was monthly pan evaporation corrected to lake values. These monthly values are redistributed using the ratio of maximum daily temperature to monthly cumulative maximum temperature. The daily values for Okanagan Lake are treated as a reasonable measure of potential evapotranspiration at lake level. From data published by Blaney [Z] and, more recently, by Ferguson [3], these values of evapotranspiration are decreased at an average lapse rate of about 25 per cent per 1,000 m. In addition, the evapotranspiration rate is assumed to diminish exponentially as a function of the soil moisture deficit. It is interesting to note that by lapsing the potential evapotranspiration proportionally with maximum daily temperatures above a base of O0C, a seasonal effect similar to that suggested by Ferguson is produced. ASSESSMENT OF THE COMPUTER MODEL: RECONSTITUTION OF HISTORICAL RECORDS A general description of the computer model was given in the previous section. The final form of the model resulted from experience and experimentation with various preliminary forms. Throughout the development two basic rules were observed: firstly, the model must be kept as simple as possible, yet physically as realistic as possible, and secondly, any coefficients used must be constant throughout the season and even from year to year. The model was fitted by first making logical 'guestimates' of the coefficients. These first estimates were refined by using graphical presentation and visual comparison of computed and actual outputs. This visual-graphic approach is surprisingly powerful because it enables the mind to handle much complex data at a glance. Other approaches, such as residual variance and other statistical measures do not reveal the location of the misfit: they cannot easily distinguish between a rather general error as opposed to a large local error, although this is easily seen by visual inspection. The basic data supplied to the model consists of: 1. Snowpack data for March Ist and later updatings. 2. Daily maximum and minimum temperatures from five meteorological stations. 3. Daily precipitation for the same station. 4. Monthly lake or pan evaporation data. 5. Daily lake discharges for Okanagan Lake at Penticton and daily lake levels for Okanagan Lake. It should be noted that Okanagan Lake levels are susceptible to error from wind Set-up, but such errors tend to average out even over two or three days. 6. Upland reservoir storage for March 1. The lake data is used to compute a net lake inflow which is considered to be the output of the computer model. The remaining data is used to calculate snowmelt and rain input and to partition this total input into evaporation, groundwater, and runoff. The resulting reconstitution of historical years of runoff is shown plotted in Figures 2, 3, and 4. The one factor that must be 1020

5 estimated each year is the soil moisture deficit which describes the state of the catchment at the commencement of runoff. This factor can be partially estimated from melt occurring before March 1st and to a lesser extent, from rain during the previous fall. Precise definition of this important factor can only be achieved, at present, after analysis of the first part of the melt season, and therefore it currently represents an inherent basic error in any forecast. It may prove possible to achieve a better definition of this factor after further study and analysis. The other problem area at present is a systematic over-production from late melt-season rain. This error may be due to overestimates of rain by the meteorological stations currently used. Such an error may be either in amount or in areal distribution and can be corrected by a fairly constant decrease of rain, either in amount or in contributing area. The reconstitutions illustrated show a small error for seasonal volumes because the seasonal volumes are brought more into line by adjusting the initial soil moisture deficit, the average adjustment being 125Mm3. Therefore a better estimate of volume error is given by the unexplained variation in the initial soil moisture deficit. The computer simulation indicates the distribution of the total input for each elevation band between evapotranspiration, soil moisture, contribution to groundwater, and residual to fast runoff. The analysis also shows what percentage of effective runoff arises from winter snowpack (March Ist) as opposed to spring snow and rain. For an average year 87 per cent of the total runoff arises from the catchment areas above 1,200 m. Of the total precipitation only some 30 per cent eventually becomes fast runoff, and a further 14 per cent emerges as long-term groundwater base flow. The remaining 56 per cent is lost as evaporation. Furthermore, it appears that 50 per cent of the runoff can be accounted for by March 1st data, whereas the remaining 50 per cent on average arises from later events. For an extreme year these values can be as low as 35 per cent for March 1st data, leaving 65 per cent from later events. The land surface runoff is further controlled by upland reservoir storage and the Okanagan Lake water balance to yield the model output, that is, the net inflow quantity to Okanagan Lake. The detailed water budget is given in Figure 5. The detailed information contained in the water balance account is difficult to grasp and consequently an attempt has been made to illustrate the major features of the budget in graphical form. Figures 6, 7, and 8 show the variation in total snowpack from March Ist onwards plotted against cumulative net lake inflow. Such a diagram goes a long way towards defining the likely precision of forecast. Figure 8 has been drawn as an idealized and simplified version of this type of diagram. Suppose that actual records are plotted like the idealized diagram, then the March 1st snowpack will give an excellent index of the final lake inflow. In practice the lines for various years cross over as shown on Figure 7. The forecast error increases with the number of cross-overs, although some errors tend to be self-cancelling. These diagrams show that the number of cross-overs decreases markedly as the season progresses, so that by May 1st the final outcome is far more deterministic. When forecasting for the current year it would probably be of considerable help to the forecaster to superimpose the latest data for the current season on Figure 6. Such a plot will show the possible routes that the season may yet follow. From the theoretical view- 1021

6 point the figures might be considered to represent a series of stages and states in a dynamic programming regime. The various routes from one state to a range of future states would each have a statistical probability, so that there would be a most probable outcome as well as various more extreme outcomes. USE OF THE COMPUTER MODEL TO ILLUSTRATE THE EXTREME RANGE AND UNCERTAINTY OF THE SEASONAL RUNOFF FORECAST The computer model has the ability to continuously monitor the hydrologic state of the watershed over extended periods of time; as well it maintains a consistently favourable relationship between the meteorological input and the recorded basin runoff; both these abilities tend to substantiate the parametric interrelationships used in the model. The model can therefore be used to test different weather sequences during the runoff period and to determine the hydrologic impact that they would have at any given time and from any given state of the watershed during the runoff period. An operational forecasting method can then be used which will give three levels of forecast-an average or most probable volume, an extreme high volume, and an extreme low volume of lake inflow. Three example forecasts are summarized below. The first example (see Fig. 9), an average year is based on 1964 when the March 1st snowpack was 874Mm and the runoff volume, March 1st to July Ist, was 430Mm3. To give an upper bound for this year, the 1964 pack was subjected to 1948 summer temperature and precipitation. The 1948 summer was moderately warm and very wet. Switching to the 1948 summer on April 1st gave a March 1st to July 1st runoff volume of 934 Mm3 which is more than twice the actual 1964 runoff. Switching to 1948 one month later on May 1st gave a March 1st to July 1st runoff volume of 645Mm3, so that the month of April alone could account for an additional 284Mm3. On the other hand, giving 1964 the 1970 summer from April 1st yields only 381Mm3 from March 1st to July 1st. Switching a month later, on May Ist, to 1970 summer, further reduces the runoff to 325Mm3. The second example is considered to be a "high bound" year. The maximum recorded snowpack probably occurred in 1946 although snowcourse data were sparse. The actual March 1st to July 1st runoff was 695Mm3. Applying 1948 summer from April 1st gave a runoff of 1,083Mm3 whereas if 1946 summer continued to May 1st and then the 1948 summer was applied, the runoff was only 832Mm3. Again the large contribution due to April is seen, a difference of more than 250Mm3. By subjecting 1946 to the 1970 summer might indicate a minimum expected runoff for the year. Switching to 1946 on April 1st gave 533Mm3 for the March 1st to July 1st volume, whereas delaying the switch to May 1st gave 495Mm3. The upper extreme of 878 KAF shows much more variability than does the lower extreme of 533Mm3. The forecast precision improves considerably as the season progresses, as has been illustrated for an average year in Figure 9. The third example is a "low bound" year based on 1963 which had the minimum March 1st snowpack on record. The actual 1963 runoff volume, March 1st to July Ist, was 232Mm3. Giving 1963 the 1948 summer from April 1st increased the runoff volume to 598Mm3, whereas delaying the 1948 summer to May 1st gave a runoff volume of 421Mn3. Again the significance of April's weather is apparent. To produce a low extreme, 1963 is given 1970 summer from April 1st and May Ist which gave runoff volumes of 16OMm3 and 195~m~, respectively. The 1022

7 low value of 160Mm3 might be compared with the worst low flow sequence of record, namely 1929, 1930 and 1931 when the inflows were 160, 186, and 154Mm3, respectively, for March 1st to July Ist. SUMMARY AND CONCLUSIONS The forecasting study demonstrates that any forecast of volume inflow for Okanagan Lake will necessarily be uncertain due to the unknown pattern of melt and precipitation during the melt season. The study has tried to determine the magnitude of the uncertainty, or inherent error of forecast, I based on certain probabilities of extreme events, although the exact possibilities are not considered to be well defined as yet. The study reveals that there is a large inherent error of forecast for seasonal volume inflows to Okanagan Lake if the forecast is based on March 1st data. The weather pattern after March Ist can, in extreme conditions, increase the runoff by more than 100 per cent or decrease the runoff by some 30 to 40 per cent. These extremes have a recurrence interval of about 1 in 100 years. These large inherent forecast errors can be given bounds and can be recognized as the true uncertainties under which the system is being operated. The uncertainty of forecast decreases appreciably as.che melt season progresses and the outcome of the operation of the system can be more certain. The forecasts can be used in conjunction with some such lake operating scheme as proposed by Russell [4] to minimize flood or drought risks. Presumably the early season operation will involve flood control whereas droughts later in the season will be the major concern. The system may well have to be operated conservatively because of this inherent forecast error and the limited outflow capacity of Okanagan Lake. The computer model achieves a total water balance throughout the season and indicates how much water is going to fast runoff, groundwater base flow, soil moisture and eventual evapotranspiration, and lake storage. The calculations show that the runoff from summer rain is very much a function of the residual snowpack. Rain on snow is very effective for runoff, whereas rain on soil usually gives a small or zero runoff contribution. The initial soil moisture deficit bears some relationship to winter melt and antecedent conditions but so far has defied accurate definition. At present this soil moisture deficit can only be accurately defined after the first few weeks if data are available. The variability of soil moisture deficit is from 50Mm3 to 270Mm3 for the region above 1,200 m. Below 1,200 m there is a huge deficit which is generally never satisfied. Certainly the catchment below 1,200 m contributes only small amounts to basin runoff and this contribution appears to come from areas which are effectively impervious and not subject to a water balance. For forecasting, Figures 7 and 8 showing snowpack depletion versus cumulative lake inflow, are valuable aids. As previously stated the reliability of forecast depends partly on the number of times the various yearly lines cross each other. In a perfectly deterministic situation the lines would never cross, as in Figure 8. In practice the crossing of lines is most frequent in the early part of the season and the number of crossings decreases considerably even after 60Mm3 has flowed into the lake. Superimposing the current year s forecast on such a diagram gives a good visual indication of the range of outcomes. 1023

8 ACKNOWLEDGMENTS Data used in this study were provided by Environment Canada, Water Survey Division, Inland Waters Directorate and Atmospheric Sciences Division, Atmospheric Environment Service, and also by the British Columbia Water Resources Services. The help and cooperation of these agencies is gratefully acknowledged. The funding for the study was provided by the British Columbia Disaster Relief Fund. RE FE RENCE S [Il E21 [31 [41 QUICK, M.C. (1972). Experimental studies on Mount Seymour. Dept. of Civil Eng., University of British Columbia. BLANEY, H.E. (1956). Evaporation from free water surfaces at high altitudes. Proc. Am. Soc. Civil Engrs., J. Irrigation Div., Vol. 82, IR3, Paper 1104, November. FERGUSON, H.L. (1971). Some preliminary notes on the variation of evaporation with elevation. Okanagan Study Report. RUSSELL, S.O., and CASELTON, W.F. (1971). Reservoir operation with imperfect flow forecasts. Proc. Am. Soc. Civil Engrs., J. Hydraulics Div., Vol. 97, HY2, February. SELECTED SOURCES : HYDROLOGIC MODELS r31 [ CRAWFORD, N.B., and LINSLEY, R.K. Digital simulation in hydrology. Stanford Watershed Model IV, Tech. Report No. 39, Dept. Civil Eng., Stanford University, Stanford, California, O'CONNELL, NASH and FARRELL. River flow forecasting through conceptual models II. J. Hydrology, 1970, p QUICK, M.C., and PIPES, A. UBC Fraser runoff model for forecasting and planning studies. Dept. of Civil Eng., Water Resource Series, Ilniversity of British Columbia, ROCKWOOD, D.M. Columbia basin streamflow routing by computer. Proc. Am. Soc. Civil Engrs., J. Waterways and Harbours Div., Vol. 84, Part 1, Paper No. 1874, December SCHEWERHORN, V.P., and KUEHL, D.W. Operational streamflow forecasting with the SSARR model. The Use of Analog and I Divital Computers in Hydrology, Vol. 1, Int. Assoc. Sci. I-lydrol.,

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17 I nnn --I Lower 1970 Bound /7 \ June 15 O I I Recorded Nef Lake Inflow (Mm ) Fig. 9. Illustrative forecasts of the future net lake inflows plotted against recorded net lake inflow. (Extreme values and actual values are shown for 1964) DISCUSSION K.S. Davar (Canada) - The results you presented, and those given in other presentations, demonstrate the difficulty of approximating watershed response by routing procedures using constant parameters. The problem of initiating and routing in a watershed model depends to a large extent on correct evaluation of the storage and transmissibility characteristics of the basin. This is best accomplished by actual field measurements, particularly of soil moisture and groundwater, even if they are used only as indices. lvould you comment on the absence of such parameters in your model? 1033

18 M.C. Quick (Canada) - In response to your question I would like to explain the nature of the Okanagan basin model in greater detail. The initial input to the model includes a term to include the initial soil moisture deficit which must be satisfied by meltwater and rain. In addition, a groundwater abstraction rate, infiltration if you prefer, must be met before generation by the model. The impervious portion of the basin is meanwhile assumed to produce direct runoff. Initially the groundwater abstraction rate is unknown, but it is assumed that there is a maximum value which cannot be exceeded and that the groundwater storage is large. Groundwater excess is included, if necessary, when the simulated output and measured lake inflow are compared. The nature of the model produces the non-linear behaviour observed in real catchments, and yet we are still able to use constant coefficients. 1034