modelling and forecasting snowmelt floods for operational...

Modelling Snowmelt-Induced Processes (Proceedings of the Budapest Symposium July 1986). IAHS Publ. no. 155,1986.

Modelling and forecasting snowmelt floods for operational forecasting in Finland

BERTEL VEHVILAINEN Hydrological Office, PO Box 436, SF-00101 Helsinki 10, Finland

ABSTRACT A modified version of HBV-3 model is in operational use on nine river basins ranging from 300 to 30 000 km2 in Finland. The snowmelt model used is a modified degree-day method with temperature and precipitation as input data. For one experimental area (21 km2) different types of snowmelt models are tested including degree-day models, energy balance models and mixed degree-day and energy balance models. From these models one cannot clearly determine the best, but a modified degree-day model with solar radiation and wind as extra term gave slightly better results than other model versions. For updating of model two different methods are used. When an unstable degree-day factor caused slight errors in the start of snowmelt this is corrected by changing observed temperatures. During flood peak and recession an autoregressive error model is used to correct the forecast on the basis of previous errors.

Modélisation et prévision des crues des eaux de fonte dans un but opérationnel en Finlande RESUME Une version modifiée du modèle HBV-3 se trouve à l'état opérationnel dans neuf bassins hydrographiques de 300 à 30 000 km2 en Finlande. Le modèle de fonte des neiges utilisé est une méthode degré-jour modifiée, avec la température et la précipitation comme intrants. Pour l'une des zones expérimentales (21 km ), différents modèles de fonte des neiges ont été testés, y compris des modèles degré-jour, des modèles à bilans d'énergie et des modèles mixtes degré-jour et bilan d'énergie. Parmi ces modèles, il est difficile de dire avec certitude quel est le meilleur, mais un modèle modifié degré-jour avec rayonnement solaire et vélocité du vent comme un terme supplémentaire, a donnée des résultats légèrement supérieurs aux autres versions du modèle. Pour actualiser le modèle, deux méthodes différentes sont utilisées. Quand des facteurs degré-jour instables provoquent de légères erreurs dans le début de la fonte des neiges, cela est corrigé en changant les températures observées. Pendant la pointe de la crue et le retrait un modèle d'erreur autorégressif, basé sur les erreurs précédentes, est utilisé pour corriger le prognostic.

245

246 B. Vehvilainen

INTRODUCTION

In this study the research area is a small experimental basin Tujuoja) in western Finland about 100 km from the coast (64 N, 25 E). The area is 20.6 km of which 82% is forest, (canopy density 30%), 12% field, 4% bog and 2% urban area. There are no lakes in the area and the mean slope is 2.3%.

The data available for study are daily values of runoff, precipitation, mean, maximum and minimum temperatures, shortwave radiation, cloudiness, vapour pressure and wind speed. The measuring height for meteorological data is 2 m. The data are divided into two parts: 1976-1981 for calibration and 1970-1976 for verification.

The criterion for the efficiency of the model is:

R2 = (F2 - F2)/F2 (1) o o

where F is the variance of observations and FQ is the sum of squares of residuals. The value of R will range from -°° to +1. Model efficiency +1 means complete agreement between observed and simulated values.

For initial calibration a parameter grid method has been used: the best value of a parameter is searched within a given range with a given increment. For final calibration the optimization method of Rosenbrock (Rosenbrock, 1960) has been used.

Some results from Loimijoki, a larger basin (61°N 23°E, area 1980 km2) in southern Finland, are also presented. The Loimijoki basin is also flat (altitude range 50-100 m) with 55% open areas (mainly field and marshland) and 45% forest. In the study area there are practically no lakes; the lake percentage is 0.5%.

DEGREE-DAY METHOD

In the basic degree-day snowmelt model used in this study the following processes are simulated:

(a) Snowmelt

MELT = KM (T - T ) (2) o

where KM = degree-day factor (mm °C - 1day - 1), T = mean temperature (°C), and T 0 = threshold temperature for melt (°C).

(b) Liquid water storage in the snowpack. (c) Freezing of liquid water in the snowpack. This is simulated

with a similar procedure to that used for snowmelt. (d) Computation of snow covered area as a function of cumulative

melt. With this snowmelt model included in the HBV-3 runoff model

(Figs 1 and 2) (Bergstrom, 1976) the following values of model efficiency R have been obtained:

Forecasting snowmelt floods in Finland 247

Calibration Tujuoja 0.82 Loimijoki 0.86

Verification 0.64 0.74

FIG.l The structure of HBV-3 model with degree-day snowmelt model.

The required input data are daily mean temperature and precipitation.

MODIFIED DEGREE-DAY METHOD USED IN FORECASTING MODELS

As snowmelt proceeds the structure of snow and the snowpack changes. Increasing grain size and development of vertical and horizontal drains in snowpack diminish liquid water retention capacity. Larger grain size, water in snow and shallower snow cover decrease the albedo of snow and enhance radiation melt. In order to take these two phenomena into account, decreasing water holding capacity and increasing degree-day factor with cumulative melt have been used in the model. The following values of model efficiency are then obtained:

Tujuoja Loimijoki

Calibration 0.86 0.86

Verification 0.74 0.77

In both cases the modified version gave better results than the

248 B.Vehviïàinen

270

I s km mm TUJUOJA

1981

Simulated

/ V \ \ v

V - ^ \

i 1 ! \

~ > 5 cr <u Q)

5

A 11

11

\ \

i

h \ \

•H \ \

\ \ \ \ \ \ \ \ \ \ \ \\ \ \ \ \ \ \

^ \ \ \ \ ^

•- o

-3

-6

-9

FIG. 2 model

20.V 30.\

Simulation of runoff with degree-day snowmelt in spring 1981 with mean temperatures as input data.

basic degree-day model in the verification period. The initial and final values of degree-day factor and retention

capacity were:

Tujuoja Loimijoki

Degree-day factor (mm C day ) : initial final 1.0 4.0 3.5 4.5

Retention capacity (% by weight) : initial final 60 3 42 6

The initial retention capacity is greater than the measured values of 5-10% by volume or approximately 15-30% by weight given by different sources (Kuusisto, 1984). The reason is that in a large scale model the retention capacity simulates both retention of liquid water in snow and in temporary water storages behind and between snowpacks.


With the basic degree-day method the model often created small flood peaks during short warm periods, before the snowmelt runoff started in reality. With increasing degree-day factor and decreasing retention capacity this error vanished from simulations.

OTHER MODIFICATIONS

Without increasing input data (temperature and precipitation) there are still some possible ways to try to improve the degree-day model.

We can add an extra term to take into account the effect of precipitation by

MELT = (KM + PKM P)(T - T ) (3) o

where P = precipitation (mm), and PKM = parameter. The value of parameter PKM should be 0.0125°C-1day-1 given a specific heat of 4.2 J g- °C~ . The inclusion of precipitation gave only very modest improvement at these two study areas, which is to be expected given the small value of the parameter PKM.

The degree-day factor for open areas (bog, field) is larger than for forest (Vehvilàinen & Kuusisto, 1984). A modified form of the model taking this into account was also tested at the Tujuoja basin with the following results:

Calibration Verification Model efficiency 0.84 0.65

The values of the degree-day factor in this modification for open and forested areas were:

Open areas (18%) .- Forest (72%) : initial final initial final

Degree-day factor 3.0 7.2 3.0 4.2

At Tujuoja basin the inclusion of different degree-day factors for open areas and forest did not give better results. One reason for this rather unexpected result may be that with more parameters the possibility of over-fitting becomes greater.

Popov (Kuzmin, 1972) has presented a temperature index model, which is related to the energy balance approach. According to Popov, incoming shortwave radiation (RS), effective longwave radiation (RL) and vapour pressure (e) can be expressed as a function of temperature:

RS = 238 J cm_2day~l0C_1(T max

RL = 92 J cm-2day_1°C-1(T mean

e = 0.35 mb°C-1 T . + 4.11 mb

- T ) - 50 J cm~2day X (4) mean

- T . ) (5) m m

(6)

Using these equations and the energy balance approach, snowmelt (mm) is calculated with the formulae:

250 B.Vehvilainen

MELT(DAY) = 6.2 (1 - A) (T - T ) + 0.65 U (T - 0.5) -max mean mean

1.4 (T - T . ) (7) mean m m

MELT(NIGHT) = 0.65 U (T - 0.5) - 1.4 (T - T . ) (8) mean mean m m

where A = albedo, calculated as a function of cumulative melt, and U = wind speed (m s~ ).

This model gave a model efficiency for the Tujuoja basin of 0.25, which means that it was not at all suitable. With a modification in the advective part and with optimization a model efficiency of 0.82 was obtained by the formulae:

MELT(DAY) = 0.67 (1 - A) (T - T ) + max mean

1.89 (1 + 0.05 U) (T - 1.3) - 0.25 (T - T . ) (9) mean mean m m

MELT(NIGHT) = 1.89 (1 + 0.05 U) (T - 1.3) -mean

0.25 (T - T . ) (10) mean m m

This model is quite near the degree-day model. The best model efficiency (R2=0.83) was obtained with the model:

MELT(DAY) =2.2 (1 + 0.04 U) (T - 2.7) (11) mean

MELT(NIGHT) = 2.2 (1 + 0.04 U) (T - 2.7) (12) mean

This is just the basic degree-day model with wind as an extra term. It seems that Popov's model is not valid for forested conditions at Tujuoja basin.

ENERGY BALANCE MODEL

The use of an energy balance approach inevitably increases the required input data, which limits its use in operational forecasting. If daily values of shortwave radiation, mean temperature, wind, vapour pressure and precipitation are available the following energy balance model may be used:

RTOT = RSN + RLN + RSEN + RLAT + RP (13)

where RTOT = energy balance on snow cover, RSN = net solar radiation, RLN = net longwave radiation, RSEN = sensible heat, RLAT = latent heat of evaporation/condensation, and RP = heat from liquid precipitation.

RSN = RS (1-A) CF (14)

where RS = measured solar radiation, A = albedo and CF = forest


transmission coefficient CM).3). The difficulties with these formulae lie in calculating the snow

cover albedo. In this work albedo was taken to be a function of cumulative snowmelt and the forest transmission coefficient is a function of canopy density (Eagleson, 1970).

In the longwave radiation calculations it is assumed that the forest radiates as a blackbody at the ambient air temperature:

RLN = F T \ + (1 - F) UE T1*. - aï"* (15) air air snow

where F = forest canopy density CU).3); a = Stefan-Boltzman coefficient; UE = humidity function = a + b /e~; T a i r = air temperature (K); T s n o w = snow temperature (K); a, b = constants, a ̂ 0.6, b 'V 0.05; and e = vapour pressure (mb).

The following equations for turbulent transfer of sensible and latent heat at the snow surface are used:

RSEN = CS U (T . - T ) (16) air snow

RLAT = CL U (e . - e ) (17) air snow

where CS, CL = parameters and U = wind velocity (m s~ ). The parameters CS and CL can also be calculated from meteorological measurements, but this increases the need for input data and therefore the above equations are preferable for operational purposes.

The heat from liquid precipitation is

RP = CP P (T - T ) (18) p snow

where CP = specific heat of water, P = precipitation, and Tp = temperature of precipitation ̂ air-

Before snow can melt, the cumulated energy input to the snow has to overcome the cold content of the snowpack. This process is also included in the model. After the snow has reached the melting point the melt rate is

MELT = RTOT/CM (19)

where CM = latent heat of fusion. With this model the results at Tujuoja basin (Fig.3) were as

follows:

Calibration Verification Model efficiency 0.84 0.65

Over the calibration period the model efficiency was as good as with the best degree-day model but for the verification period the modified degree-day model gave better results. When inspecting individual melt periods it was found that energy balance model was better in situations when mean temperature was near or below 0°C and snowmelt was going on due to intensive shortwave radiation.

Table 1 shows the values of the energy balance components during

252 B.Vehvilainen 2 7 0 r

I s'krti2

FIG.3 Simulation of runoff with energy balance model at spring 1981. Energy balance model functioned better at the beginning of snowmelt during a cold clear-sky period with abundant solar radiation during the day time.

the April and May snowmelt April shortwave radiation longwave radiation also be shortwave radiation. Sens in May of shortwave radiât at the beginning of the me latent heat is negative. and condensation condition

periods calculated by the model. In dominates the energy flux. In May comes positive and is about half the net ible heat is about 10% in April and 20% ion. Snow evaporation conditions prevail It period which means that the flux of In May the division between evaporation s is more even and the latent heat flux is


TABLE 1 The values of simulated energy balance components (J cm month ) on snow cover during April and Mag at Tujuoja basin

April

-71 -72

-73

-74

-75

-76

-77

-78

-79 -80

-81

Mean

RSN

6450 3750 2950 6360 5280 5780 3640 4310 4730 4100 6070

4860

RLN

-2910 -1130 -1350 -1610 - 450 -1990 -1220 -2530 -1690 + 260 -2630

-1570

RSEN

380

620

560

230

870

380

930

350

540

590 390

530

RLAT

- 960 - 490 - 380 - 730 - 590 -1040 - 510 - 740 - 320 - 420 -1290

- 680

RP

10

20

40

0

20

10

30 10

40

10

10

20

RTOT

2970 2770 1820 4250 5130 3140 2870 1400 3300 4540 2540

3160

May

-71 -72

-73

-74

-75

-76

-77 -78

-79 -80

-81

Mean

RSN

2410 530

410

230

800 1080 1590 1670

330

230 1380

970

RLN

930 520

370

150

780

440 1180

120

250

120 570

490

RSEN

480 180 200

120

580 180

270 210

260

60

560

280

RLAT

-160 60 30

- 40 60

20 - 40 -310 - 20 - 20 -140

- 50

RP

10

10 10

0

10

10

20 0

10

0

0

10

RTOT

3660 1320 1030

460

2240 1730 3010 1690

830

390

2360

1700

near zero. Melt due to liquid precipitation is negligible.

COMBINED DEGREE-DAY AND ENERGY BALANCE METHODS

According to the results from the energy balance model at Tujuoja basin, shortwave radiation dominates snowmelt, especially during the first part of the melt period. So the inclusion of shortwave radiation into degree-day model may give some improvement, especially in cases when temperature is near of under 0°C and the degree-day model is incapable of simulating snowmelt. Also the addition of sensible and latent heat terms may give some improvement. With the best modified degree-day model the following extra terms in snowmelt calculations have been tested: C RS (shortwave term), C U (f - T0) (sensible heat term), C U (e - e0) (latent heat term), C P (T - T0) (precipitation term), where C = parameter, T = mean

254 B.Vehvilainen

temperature (°C), and TQ, e 0 = threshold values for T and e. The results for the Tujuoja basin are as follows:

R2 R2

(calibration) (verification) Best degree-day model 0.83 0.72 With shortwave term 0.85 0.73 With sensible heat term 0.84 0.74 With latent heat term 0.84 0.70 With precipitation term 0.84 0.72

Incorporation of the shortwave term and sensible heat term gave a small improvement in the model efficiency. Use of these two terms in an operational model means that two more observations must be made every day i.e. shortwave radiation and wind speed. Given the small improvements in R2 it is not reasonable to do the extra work in order to use these terms in operational snowmelt models.

AUTOREGRESSIVE ERROR MODEL IN FORECASTING

One way of improving hydrological forecasts is to use an autore-gressive error model together with the hydrological model (Lundberg, 1982). The parameters of the error model are estimated from the time series of residuals during the calibration period. For the Loimijoki basin an autoregressive AR(l)-model has been tested:

Z. = *, Z. + a. (20) l 1 l-l l

where z^ = current value of error, (f)̂ = coefficient, and a = current shock from a random process with zero mean and variance <Ja. With this model the following results have been obtained for different lags.

Model efficiency, R2

Basic hydrological model 0.864 With AR(1)-model, lag = 1 0.916

2 0.875 3 0.869 4 0.866 5 0.866

In this test lag means how old in days the error in use is i.e. how many days ahead the "forecast" is made in the calibration period.

The error model improves results considerably (Fig.4) for one to two days ahead; after that the effect diminishes very quickly. The use of the AR-model also required accurate and quickly transported data. Without daily observations of the forecasted component (discharge or water level) the AR-model is useless.

MODEL UPDATING

The use of the AR-model presented in the previous section is one way to update or correct forecasts. The other possibility is to


change temperature values so that the observed and calculated discharges are made equal (Fig.5). This is done especially at the beginning of snowmelt when unstable degree-day factors causes errors in snowmelt simulation, for example, during a clear and rather cold period when temperatures are near or under 0°C but solar radiation melts snow during the day time. By equating observed and calculated discharges we conserve the water balance and do not move errors to the end of the snowmelt period. Another situation when temperature modification is often used is at the start of intensive snowmelt. Updating the model at this stage usually gives good predictions of the timing of the flood peak.

During the flood peak and in the recession period it is preferable to use the autoregressive AR-model to correct the forecast, especially when the reason for incorrect simulation is not clear.

LOIMIJOKI, Maurialankosk „

21.1V M I N c / / V

/ / ' //241V

/ ' M I N -120 / /

mrnNf

- 8 0 | ^ V _ i/itf

-4o/18- IV

1985 ^ ^

- Observed /

Forecast ' /

Ik \\ J'\ \./L \ * if \ \ x s /

'— V8>* \ y 9 \ M \ O ^ s ^ _ ^

! W

\ \ "^o

1 1 I I " . !

18.1V 22.IV 26.IV 30.IV 6.V 10.V 14.V 18.V

FIG.4 The use of autoregressive error model with hydrological model in forecasting. Forecasts of 28 April and 1 May are made without the AR-model and the forecast of 5 May is made with the AR-model.

256 B .Vehviïàinen

ULJUA RESERVOIR Spr ing 1982

Observed Forecast

Hi 1 IV 5.1V 10.1V 15.1V 20.1V 25.1 V 30.1V 5V 10V 15 V

FIG.5 The updating of the model by changing temperature values during intensive snowmelt (29 April) in order to get better forecast for the timing of flood peak.

REFERENCES

Bergstrom, S. (1976) Development and application of a conceptual runoff model for Scandinavian catchments. SMHI, RHO 7, Norrko-ping, Sweden.

Eagleson, P.S. (1970) Dynamic Hydrology. McGraw-Hill, New York. Kuusisto, E. (1984) Snow accumulation and snowmelt in Finland.

Publ. Wat. Res. Inst. 55. Kuzmin, P.P. (1972) Melting of snow cover. Israel Program for

Scientific Translations. Lundberg, A. (1982) Combination of a conceptual model and an

autoregressive error model for improving short time forecasting. Rosenbrock, H.H. (1960) An automatic method for finding the

greatest or least value of a function. Computer J. 3, Vehvilalnen, B. & Kuusisto, E. (1984) The application of simple

snowmelt models in three different terrain types. Proc. 5th Northern Research Basins Symp. (Vierumaki, Finland),

modelling and forecasting snowmelt floods for operational...

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