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International conference on innovation advances and implementation of flood forecasting technology LONG-TERM ENSEMBLE FORECASTING SPRING RUNOFF VOLUME AND HYDROGRAPH PEAK L. S. Kuchment (1) and A. N. Gelfan (1) (1) Water Problems Institute of Russian Academy of Sciences, 119991 Gubkin 3, Moscow, Russia Abstract A technique for long-term (i.e. two to three months) ensemble forecasting of the spring runoff volumes and the peak discharges has been developed. The technique is based on using physically based model of runoff generation combined with a weather generator. The distributed physically based model includes a description of the snow accumulation and melt, soil freezing and redistribution of soil moisture during the autumn and winter period, and the processes of runoff generation after the beginning of spring snowmelt period. The weather generator, which consists of stochastic models of daily air temperature and precipitation, is used to simulate the meteorological inputs for lead time periods. Long series of possible hydrographs are calculated by the physically based model with Monte Carlo simulated inputs. The probability distributions of the forecast runoff volumes and peak discharges are estimated on the basis of these hydrographs. In addition, the runoff volume and the hydrograph peak are forecast using climatological values of air temperature and precipitation for each chronological day during the lead time period (deterministic forecast). The results of the deterministic forecast of spring runoff volumes, with the help of the physically based model, are compared with the results, which have been obtained on the basis of the regression relationships between the spring runoff volume and the initial river basin indexes under the mean meteorological conditions during the lead time period (the present day procedure of long-term runoff forecasting). The case study has been carried out for the Sosna River basin. This basin covers an area of 16,400 km2. Keywords: long-term ensemble forecast, physically-based model, snowmelt flood, weather generator INTRODUCTION Long-term (i.e. seasonal) forecasts of spring-summer flood volumes are widely used in Russia for water management and for runoff regulation where there are cascades of reservoirs in large river basins. The traditional techniques for such forecasts are based on the application of nonlinear or linear multiple regression relationships between flood volume and the main snowmelt runoff factors, which can include (depending on the physiographic region) the snow water equivalent before melt, the measured autumn soil moisture content (or its calculated index), and the measured depth of a frozen soil (or its calculated index). It is assumed that the precipitation and the air temperature during the lead time period are equal to their mean, climatological values. Opportunities for such forecasts depend on physiographic, climatic conditions and runoff generation mechanism in the river basin. However, in most of Russia these forecasts provide an acceptable level of accuracy. Since the applied regression relationships only account for the integrated characteristics of the hydrometeorological conditions before snowmelt, these forecasting techniques can lead to significant errors if the conditions of snowmelt runoff generation are unusual, (for example, the complicated processes of soil freezing and soil moisture redistribution, the high rate of snow melt, several periods of thaws during a cold season, large liquid precipitation before melt, etc), or the measurements or the indexes of the autumn soil moisture content and the depth of a frozen soil are not representative. It seems that continuous physically based models taking into account snow and soil processes during the winter and spring period give opportunity to improve the forecast. In this paper, we test this approach together with an ensemble form of long-term forecasting of meteorological variables. As a result, we obtain a technique that provides a probabilistic technique of forecasting both snowmelt flood volume and flood peak discharge. The case study has been carried out for the Sosna River basin, which has a catchment area of approximately 16,400 km2. This river is a tributary of the Don River and is located in the forested-steppe zone of the European Russia. 17 to 19 October 2005, Tromsø, Norway 1 ACTIF/FloodMan/FloodRelief International conference on innovation advances and implementation of flood forecasting technology THE USED PHYSICALLY BASED MODEL OF SNOWMELT FLOOD GENERATION The model for runoff generation is based on the finite-element schematization of the river basin shown in Figure 1. This describes the following main processes: snow cover formation and snowmelt, soil freezing and thawing, infiltration into frozen and unfrozen soil, vertical water transfer in an unfrozen soil, evaporation, overland and channel flow. The main aim is to provide a long-term probabilistic forecast. This needs a long series of runoff simulation. As a result we simplified the description of some of these processes in comparison with the previous version of the model (see Kuchment et al., 1986). The bold lines represent the river network The thin lines represent the boundaries of the finite elements Figure 1 Finite-element schematization of the Sosna River watershed Snow cover formation and snowmelt To calculate the characteristics of the snow pack, a system of vertically averaged equations of snow processes has been applied (Kuchment & Gelfan, 1996). The system includes the description of temporal change of the snow depth, content of ice and liquid water, snow density, snowmelt, sublimation, re-freezing melt water, snow metamorphism. This is modelled as follows: dHs dt [ ] = ρw X s ρ0 −1 − ( S + E s )( ρi I s ) −1 − V (1a) d ( ρ i IH ) = ρ w ( X s − S − E s ) + S i (1b) dt d ( ρ w ws H s ) = ρ w ( X l + S − E l − R s ) − S i (1c) dt where Hs is the snow depth; I s and ws are the volumetric content of ice and liquid water in snow, respectively; X s and X l are the snowfall rate and the rainfall rate, respectively (it is assumed that 17 to 19 October 2005, Tromsø, Norway 2 ACTIF/FloodMan/FloodRelief International conference on innovation advances and implementation of flood forecasting technology if the air temperature Ta ≥ 0 oC only rainfall occurs and if Ta < 0 oC only snowfall occurs); S is the snowmelt rate; ρ s is the density of snowpack calculated as ρ s = ρ i I S + ρ w w S ; ρw , ρi , and ρ0 are the density of water, ice, and new snow, respectively; E s is the rate of snow sublimation; E l is the rate of liquid water evaporation from snow; S i is the rate of re-freezing melt water in snow; Rs is the meltwater outflow from snowpack; V is the compression rate. The melting rate S is determined as S = βρ sT a (2) where β is the empirical constant. Soil freezing and redistribution of soil moisture during a cold period The hydrothermal processes in the soil during the cold period are described by the following equations (Kuchment & Gelfan, 1993): ∂T ∂ ⎛ ∂T ⎞ Cf = ⎜λ ⎟, 0 < z < H (t ) (3) ∂t ∂ z ⎝ f ∂z ⎠ ∂T ∂ ⎛ ∂T ⎞ C = ⎜λ ⎟, H (t ) < z < L (4) ∂t ∂z ⎝ ∂z ⎠ T (0, t ) = T0 (t ); T ( H , t ) = 0; T ( L, t ) = TL ; T ( z,0) = T ( z ) ∂θ ∂ ⎛ ∂θ ⎞ = ⎜D − K ⎟, H (t ) < z < L (5) ∂t ∂z ⎝ ∂z ⎠ θ ( L, t ) = θ L ; θ ( H ) = θ 0 ; θ (z,0) = θ (z) ∂T ∂T dH λf z = H −0 = λ z = H + 0 + χρ w (θ − − θ 0 ) (6) ∂z ∂z dt H ( 0) = 0 where H ( t ) is the depth of frozen soil at time t ; T ( z , t ) is the soil temperature at the depth z and time t ; λ f and λ are the thermal conductivities of frozen and unfrozen layers of soil, respectively; C f and C are the heat capacities of frozen and unfrozen layers of soil, respectively; χ is the latent heat of ice fusion; θ ( z , t ) is the volumetric liquid water content in unfrozen layer of soil; θ − is the liquid water content just above the freezing front; θ 0 is the liquid water content at 0oC (assumed to be equal to the moisture content at the wilting point); D is the diffusivity of soil moisture; K is the hydraulic conductivity of soil; L is the depth of the soil where the soil temperature and the volumetric moisture content can be considered as constants equalled TL and θ L , respectively ( L was taken to be equal to 2 m). In this system, the equations (3) and (4) describes heat transfer in the frozen soil layer and in the unfrozen soil layer, respectively. The equation (5) describes soil moisture transfer from the unfrozen layer of soil to the freezing front. According to experimental data, this process plays an important role in the vertical redistribution of soil moisture during the cold period for soils which are typical for forested-steppe zone. The upper boundary condition is formulated as 17 to 19 October 2005, Tromsø, Norway 3 ACTIF/FloodMan/FloodRelief International conference on innovation advances and implementation of flood forecasting technology Ta − T0 ∂T λs = −λ f , Hs > 0 Hs ∂z z = 0 (7) T0 = Ta, Hs = 0 where λ s is the thermal conductivity of snow. The diffusivity, the hydraulic conductivity of unfrozen soil, the heat capacities and the thermal conductivities of frozen and unfrozen soil were calculated by the formulas suggested by Kuchment et al. (1983). Soil thawing Soil thawing is calculated for snow-free areas of the catchment area from the end of snowmelt. The movement of the soil thawing front is described by the equations similar to ones used for soil freezing description excluding equation (5). The description of soil thawing model is presented in (Kuchment, et al., 2000). Meltwater infiltration into frozen soil Saturated hydraulic conductivity of the frozen soil K 0 is calculated as (Kuchment & Gelfan, 1993): f 4 ⎛θ − I − θ0 ⎞ 1 K 0 f = K 0 ⎜ max ⎜ θ ⎟ ⎟ (8) ⎝ max − θ 0 ⎠ (1 + 8 I ) 2 where K 0 is the saturated hydraulic conductivity of an unfrozen soil; θ max is the porosity; I is the ice content of the upper 0.1m-layer of soil. Detention of melt water by basin storage It was assumed that the spatial distribution of the free basin storage capacity before snow melt can be described by exponential probability function. In this case, detention Β of water by the basin storage up to time t after the beginning of melting is determined as (Kuchment et al., 2000): ⎡ ⎛ R ⎞⎤ Β = Β 0 ⎢1 − exp⎜ − ⎜ Β ⎟⎥ ⎟ (9) ⎢ ⎣ ⎝ 0 ⎠⎥⎦ where Β 0 is the mean value of the free storage capacity (or the maximum possible detention); R is the total melt and rainfall water yield on the basin area up to time t. Vertical water transfer in an unfrozen soil and evaporation The changes of the unfrozen soil moisture content and infiltration into the soil during the warm period are calculated by the equation (5). The evaporation rate E is calculated as (Kuchment & Gelfan, 1993): E = k E d aθ u (10) where d a is the air humidity deficit; θ u is the soil moisture content at the upper soil layer; k E is the empirical constant. Overland and channel flow Schematization of the river basin is based on presentation of the overland flow areas by 32 rectangular 17 to 19 October 2005, Tromsø, Norway 4 ACTIF/FloodMan/FloodRelief International conference on innovation advances and implementation of flood forecasting technology strips of different width, length and slope, which are perpendicular to the river channels. The choice of strips is determined by topography, soil types, vegetation, and meteorological data. To calculate the water movement along strips and in the river channels, the kinematic wave equations are applied. The runoff excess is calculated for each strip area taking into account statistical distribution of snow water equivalent and depth of a frozen soil inside of this area. To approximate the distributions, gamma distribution is applied (the mean values are calculated by the model and coefficients of variation are found by the empirical formulas). Calibration and validation of the physically based model The hydraulic parameters of soil in equations (5), (8) and the parameters of the heat flow equation (3), (4) were calculated by the formulas presented in (Kuchment et al., 1983). Soil constants which are necessary for using these formulas was taken from (Reference book of hydrological processes…, 1975). Five parameters (the factor β in formula (2), the mean value of the free storage capacity in formula (9), the saturated hydraulic conductivity K 0 in formula (8), Manning’s roughness coefficients for overland and channel flow) were calibrated against the measured daily discharges at the Sosna river outlet for 15 years (1952-1966). The model validation was carried out using the measured discharges for the next 15 years (1967-1981). THE WEATHER GENERATOR The weather generator includes the stochastic models of daily precipitation and air temperature for the period from 1 March to 30 April (for this period we neglect evaporation). The model of daily precipitation occurrence throughout this period is represented as the first-order Markov chain. Daily precipitation amount is described as a gamma-distributed random value. The air temperature series are simulated by the procedure suggested in (Kuchment et al., 2003). Parameters of the stochastic models were estimated using available meteorological records for 30 year (1952-1981). FORECASTING TECHNIQUES Continuous simulation of runoff generation processes for each spring snowmelt flood began on 1 May of the previous year. Up to 1 March (the date of the forecast issue) the input data for simulation included the observed daily precipitation amount, air temperature and air humidity. After 1 March, the input meteorological data for the lead time period were assigned by one from the following two ways: 1. The daily meteorological data were assigned as the climatological means for each chronological day. In this case, it is possible to obtain the deterministic forecast of the spring flood hydrograph. 2. The daily meteorological inputs were simulated using a weather generator and the Monte Carlo procedure. In this case, we have an opportunity to calculate long series of possible hydrographs and determine probability distribution of the forecasting flood volume and peak discharge (we simulated 1000 hydrographs for each year). Schematic diagrams of the both forecasting techniques are shown in Figures 2 and 3. 17 to 19 October 2005, Tromsø, Norway 5 ACTIF/FloodMan/FloodRelief International conference on innovation advances and implementation of flood forecasting technology Deterministic long-term forecast Characteristics of snow and soil condition on the date of the forecast issue Average temperature and precipitation for the lead-time period (2-3 months ) 10.00 01.03 08.03 15.03 22.03 29.03 05.04 12.04 19.04 5.00 0.000 0.010 0.020 0.00 0.030 0.040 -5.00 0.050 0.060 0.070 -10.00 0.080 0.090 28.02 20.03 09.04 29.04 0.100 Physically based, distributed hydrological model Flood volume and peak discharge Figure 2 Schematic diagram of the deterministic forecast Probabilistic long-term forecast Characteristics of snow and soil condition on the date of the forecast issue Weather generator Monte Carlo generated series of daily temperature and precipitation for the lead-time period (2-3 months) Physically based, distributed hydrological model Probability distributions of flood volume and peak discharge Figure 3 Schematic diagram of the probabilistic forecast Comparison of the deterministic and probabilistic forecasts The results of the deterministic forecast of flood volume and peak discharge for 30 snowmelt floods (1952-1981) as well as the efficiency criterion R2 of Nash & Sutcliffe (1970), which was adopted to estimate the goodness of fit of the forecasted and measured flood characteristics, are shown in Figure 4. The comparison of the observed flood characteristics with their mean forecast values obtained by averaging 1,000 hydrographs calculated for each year using the generated meteorological inputs is given in Figure 5. As can be seen from these Figures, the forecasting techniques used give satisfactory 17 to 19 October 2005, Tromsø, Norway 6 ACTIF/FloodMan/FloodRelief International conference on innovation advances and implementation of flood forecasting technology results for both the flood volume and peak discharge. However, the forecast of the flood volume has appears to be much better. 160 2 R = 0.8149 140 120 100 Ycalc, mm 80 60 40 20 0 0 20 40 60 80 100 120 140 160 Yobs, mm R2 = 0.6142 4000 3000 Qcalc, m /s 3 2000 1000 0 0 1000 2000 3000 4000 5000 6000 3 Qobs, m /s Figure 4 Deterministic forecast of the flood volume (top) and flood peak discharge (bottom) 17 to 19 October 2005, Tromsø, Norway 7 ACTIF/FloodMan/FloodRelief International conference on innovation advances and implementation of flood forecasting technology 160 R2 = 0.8351 140 120 Ycalc, mm 100 80 60 40 20 0 0 20 40 60 80 100 120 140 160 Yobs, mm 4000 3000 Qcalc, m /s 3 2 2000 R = 0.6441 1000 0 0 1000 2000 3000 4000 5000 6000 3 Qobs , m /s Figure 5 Forecast of the flood volume (top) and flood peak discharge (bottom) obtained by the averaging of 1000 simulated hydrographs Comparison of the suggested techniques of the flood volume forecasting with the traditional method For the number of river basins located within the forested-steppe zone of European Russia, the spring snowmelt flood volume is forecast on the basis of the experimental formula suggested by Komarov (1974): ⎡ ⎛ SWE + X ⎞⎤ˆ Y = ( SWE + X ) − P0 ⎢1 − exp⎜ − ˆ ⎜ ⎟⎥ ⎟ (11) ⎢ ⎣ ⎝ P0 ⎠⎥⎦ P0 = a exp[− W (bH + c )] where Y is the flood volume, mm; SWE is the snow water equivalent on the date of the forecast ˆ issue, mm; X is the climatological mean of the precipitation total for the lead time period (equals 27 mm for Sosna basin); P0 is the maximum possible runoff losses depending on the watershed conditions on the date of the forecast issue, mm; W is the dimensionless index of moisture content of 17 to 19 October 2005, Tromsø, Norway 8 ACTIF/FloodMan/FloodRelief International conference on innovation advances and implementation of flood forecasting technology the 1 metre layer of soil; is the freezing depth, cm; а, b, с are the empirical coefficients equal 750 mm, 0.051 and 0.11, respectively. We applied the formula (11) to forecast snowmelt flood volume in the Sosna river for the same 30 years (1952-1981) as used in the previous section. The efficiency criterion of the forecast =0.77, i. e. the forecast is only slightly worse than one obtained with the help of the physically based model (Figures 6, 7). However, formula (11) systematically underestimated the flood volume; mean error is 20 mm. To remove the systematic error, we re-calibrated the coefficients а, b, с in comparison with ones suggested by Komarov (1974) using 15 years of observations (1952-1966). The obtained values of the coefficients а, b, с are 930 mm, 0.040 and 1.85, respectively. The forecast of the flood volume for 30 years by formula (11) with the obtained values of the coefficients is shown in Figure 7. 1969 1972 35 30 30 25 25 Frequency (%) 20 20 15 15 10 10 5 5 0 0 10 20 30 40 50 60 70 80 90 100 0 Flood volume, mm 10 20 30 40 50 60 70 80 90 100 110 120 1973 1977 55 35 50 30 45 40 25 35 20 30 25 15 20 15 10 10 5 5 0 0 10 20 30 40 50 60 70 80 90 60 70 80 90 100 110 120 130 140 150 160 170 180 190 Figure 6 Histograms of the forecasted flood volumes 1965 1966 40 35 35 30 30 Frequency (%) 25 25 20 20 15 15 10 10 5 5 0 0 400 800 1200 1600 2000 2400 2800 3200 3600 4000 3 Flood peak discharge, m /s 0 0 300 600 900 1200 1500 1800 2100 2400 2700 3000 1969 1971 40 45 35 40 30 35 30 25 25 20 20 15 15 10 10 5 5 0 0 0 250 500 750 1000 1250 1500 1750 2000 2250 2500 0 450 900 1350 1800 2250 2700 3150 3600 4050 4500 Figure 7 Histograms of the forecasted flood peak discharge the 1 meter layer of soil; H is the freezing depth, cm; а, b, с are the empirical coefficients equal 750 mm, 0.051 and 0.11, respectively. 17 to 19 October 2005, Tromsø, Norway 9 ACTIF/FloodMan/FloodRelief International conference on innovation advances and implementation of flood forecasting technology 160 140 R2 = 0.8202 120 100 Ycalc, mm 80 60 40 20 0 0 20 40 60 80 100 120 140 160 Yobs, mm Figure 8 Comparison of the flood volumes forecasted by formula (11) with the observed values On average, the forecast accuracy is very close to one obtained with the help of the physically based model. However, in some cases the accuracy differs significantly. For example, for a large flood that occurred in 1970 (the flood volume, 160 mm, was the largest for the period of observations) the forecast error by formula (11) is 52 mm, whereas the deterministic forecast by our model gives the error of 15 mm. Such a difference may be explained by the peculiarities of the runoff losses formation during the spring of 1970, which are accounted by the model but not by formula (11). There were many thaws during the winter of 1969 to 1970 which, in accordance with an upward migration of soil moisture during soil freezing, result in significant decreasing permeability of the upper 10 cm to 30 cm of soil in the beginning of spring melt. The model accounts for such a decreasing, however, the predictor of formula (11) (the water content of the 1 meter layer of soil) was changed only slightly during the winter. CONCLUSION The suggested technique of ensemble forecasting spring runoff volume and hydrograph can be efficiently applied for both deterministic and probabilistic long-term flood forecasts. However, it is necessary to investigate opportunities and reliability of this technique for river basins in different physiographic zones. ACKNOWLEDGEMENT This research was supported by the Russian Foundation of the Basic Research (grant 05-05-64828). REFERENCES Apollov, BA, Kalinin, GP, & Komarov, VD 1974, Hydrological Forecasting, Gidrometeoizdat, Leningrad. (in Russian). Kuchment, LS & Gelfan, AN 1993, Dynamic-stochastic models of river runoff generation, Nauka, Moscow. (In Russian). Kuchment, LS & Gelfan, AN 1996, ‘The determination of the snowmelt rate and meltwater outflow from a snowpack for modelling river runoff generation’, Journal of Hydrology, vol. 179, no. 1/4, pp. 23–36. Kuchment, LS, Demidov, VN & Motovilov, YuG 1983, River runoff formation (physically-based models), Nauka, Moscow. (In Russian) 17 to 19 October 2005, Tromsø, Norway 10 ACTIF/FloodMan/FloodRelief International conference on innovation advances and implementation of flood forecasting technology Kuchment, LS, Demidov, VN & Motovilov, YuG 1986, ‘A physically based model of the formation of snowmelt and rainfall runoff’, in EM Morris (ed). Symposium on the Modeling Snowmelt-Induced Processes, IAHS Publications, no. 155, pp. 27–36. Kuchment, LS, Gelfan, AN & Demidov, VN 2000, ‘A distributed model of runoff generation in the permafrost regions’, Journal of Hydrology, vol. 240, no. 1/2, pp. 1-22 Kuchment, LS, Gelfan, AN & Demidov, VN 2003, ‘Application of dynamic-stochastic models of runoff generation for estimating extreme flood frequency distribution’, in G Blöschl, S Franks, M Kumagai, K Musiake & D Rosbjerg (eds). Water Resources Systems—Hydrological Risk, Management and Development, IAHS Publications, no. 281, pp. 107-114. Nash, JE & Sutcliffe, JV 1970, ‘River flow forecasting through conceptual models’, Journal of Hydrology, vol. 10, no. 3, pp. 282-290. Reference book of the hydrological properties of soils in the Central-Chernozem Region 1975, Hydrometeorological Survey of the Central-Chernozem Regions, Kursk. (In Russian). 17 to 19 October 2005, Tromsø, Norway 11 ACTIF/FloodMan/FloodRelief

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