The preliminary Japanese snowmelt runoff model was modified so that all the input variables arc of the antecedent days and the inflow of the previous day is taken into account. A few LANDSAT images obtained in the past were effectively used to verify and modify the depletion curve induced from the snow water equivalent distribution at maximum stage and the accumulated degree days at one representative point selected in the basin. Together with the depletion curve, the relationship between the basin ide daily snowmelt amount and the air temperature at the point above are exhibited homograph form for the convenience of the model user. The runoff forecasting procedure is summarized

Ishihara, K.

Nishimura, Y.

Takeda, K.

English

NASA Technical Reports Server

SNOWMELT RUNOFF MODEL IN JAPAN
Kenji Ishihara and Yoshiaki Nishimura
Environmental Research & Technology Institute
Kaname Takeda
National Institute of Resources
Science and Technology Agency
INTRODUCTION
Preliminary results [1] of Japanese snowmelt runoff modelling were proposed at First Japan/US
Snow and Evapotranspiration Workshop held in Tokyo on March, 1982. Aim!ng at the daily
snowmelt runoff forecasting, the preliminary model was designed through multiple regression
analyses based on the hydrological conception. However, it involved several operational defects as
follows:
i) containing three input variables of mean air temperature, precipitation and snow cover area at the
day of which the inflow ought to be forecast.
ii) insufficient concordance between the hydrological conception and the parameters which resulted
from the multiple regression analyses.
In the present study the model was, then, so modified that all the input variables are of the
antecedent days. The inflow of the previous day is also taken into account. The new model was
developed in use of the 1980 data in the Okutadami River Basin, chosen again as the test basin, and
was adapted to the other years for its operative efficiency.
The optimum contribution of the Satellite imagery to the snowmelt runoff forecasting is the
extraction of the snow coverage. Japan is, unfortunately, covered with much cloud in snowmelt
season. Only in a fortunate season, one can obtain only one or two useful imagery. Unlike US it is,
therefore, impossible in Japan to draw the depletion curve of snow coverage based on the imageries.
However, a few imageries obtained in the past were effectively utilized for the verification and
modification of the depletion curve induced from the snow water equivalent distribution at maximum
stage and the accumulated degree-days at one representative point selected in the basin. This point is
equipped with data collection facilities and is expected to fully function as DCP.
Together with the depletion curve, the relationship between the basin-wide daily snowmelt
amount and the air temperature at the point above were exhibited in form of nomograph for the con-
venience of the model user.
The Japanese model proposed inthe present study is, thus, the practical model of the snow melt
runoff forecasting.
TEST BASIN
The Okutadami River basin (area 414 km2) chosen as the test basin for this analysis is situated
in Central Japan shown in Figure 1.. The highest and lowest altitudes of the basin are 2346 m and
782 m respectively. The altitude difference is, therefore, 1564 m. This basin is one of the heaviest
29
https://ntrs.nasa.gov/search.jsp?R=19850014916 2020-03-22T18:39:23+00:00Z
snowfall area in Japan; the maximum snow depth recorded in recent 20 years was 598cm at
Okutadami Meteorological Observing Station located at the dam site in the basin. The station runs
the measurement of snow water equivalent and inflow into the reservoir as well as the general
meteorological observation. Located slightly outside the basin is the Hinoemata meteorological
observing station of air temperature and precipitation. Two stations above and the representative
point (mentioned later), Maruyama, provide all the necessary input data of the model. Those loca-
tions are shown in Figure 2.
The snow depth measurements by helicopter at ten to twenty points scattered in the basin are
carried out at the maximum stage of snow depth at about the end of every winter season by the
Electric Power Development Company. The measurement points by helicopter are shown in
Figure 3.
CONCEPT OF SNOWMELT RUNOFF MODEL
Two forms of multiple regression models were considered. First model is as follows;
Rn = c + alXn_ 1 + a2Xn_2 + a3Xn_3 (1)
+ blYn_ l + b2Yn_2 + b3Yn_3
Xn_ i = (Mn_ i "1- Pn_i)S'n_ i (2)
Yn-i = Pn-i s "n-i (3)
where
R_ : daily direct inflow (m3/sec) into reservoir on the day, n
c : constant
al,a2,a3,bl,b2,b3 : partial regression coefficient
Mn_ i : mean snowmelt amount on the day n-i (m3*sec-lokm -2)
P,-i : mean rainfall amount on the day n-i (m3osec-l.km -2)
S'_ i : area where daily mean air temperature is above 0°C within snow cover area
on the day n-i (km2)
S"_ i : area where daily mean air temperatureis above0°C withinnon-snowcover
area on the day n-i (km2)
The secondmodel, in whichthe direct inflowof the previousday, Rn_1, is addedto the
variablesof the first model,is as follows;
Rn = c + dRn_ 1 + alXn_ 1 + a2Xn_2 + a3Xn- 3 (4)
+ blYn_ 1 + b2Yn_ 2 -t-"b3Yn_ 3
30
where
d : partial regression coefficient
DEPENDENT VARIABLE
Direct Inflow
The dependent variable of the model is the daily direct inflow, R_, into the reservoir. The base
flow which should be subtracted from the daily inflow to obtain the direct inflow, R,, is expressed
by
rt = ro (1.0+0.001240 (5)
where
rt : base flow after t days from the day when first discharge occurs due to snowmelting in the
season (ma/sec)
r0 : inflow before the snowmelt season starts (m3/sec)
The equation (5) was empirically determined by the inflow data recorded at the beginning and end of
the several snowmelt seasons
INDEPENDENT VARIABLES
Snow Cover Area and Its Related Areas, Sn_l, S'n_ I and S"n_ I
The snow coverage information from Landsat MSS is scarcely obtainable in Japan. Then, the
snow line during snowmelt season was considered to appear when snow water equivalent in a mesh
(shown in Figure 2) became equal to the snowmelt amount which can be calculated by the degree-
day method (mentioned later). In order to extract the snow line, the computation of the snow water
equivalent in each mesh at the maximum stage is required. Then, the computation was made by
following three methods; the tbp'o_raphic method [3] in use of the extensive snow survey data in
1980, the degree-day method [4] in effective use of two Landsat MSS data fortunately obtained in
1979 and the comparison method [5] in use of the regional snow depth data obtained for several
years with helicopter. Next, the date when all the snow deposits disappear was calculated for each
mesh, applying the degree-day method. The snow cover area and its related areas, Sn_i,s',_i and
s",_i were then counted for every day during each snowmelt season.
Total Snowmelt Amount, Mn.i.S'n_I
The degree-day method was adopted for the snowmelt calculation, expressed by
M = K_T (6)
31
where
M : snowmelt amount (g/cm2)
leT : accumulated daily mean air temperature above 0°C (°C.day)
k : degree-day factor (0.45; average value in preceding studies)
The daily mean air temperature at the Okutadami Meteorological Observing Station was adopted
as the standard for the estimation of the air temperature at all meshes assuming the lapse-rate as -0.6
°C/100 m.
Applying the equation (6), the calculation of the daily snowmelt amount was made for each
mesh within the area, S'n_i, during each snowmelt season. By summing up them, the total snowmelt
amount in whole basin, Mn_i'S'n_i was then obtained.
Total Rainfall Amount, Pn_i°S'n_i and Pn_i°S"n_i
The Okutadami Station is the only one rainfall observation station within the basin running
throughout snowmelt season. However, located at the lowest elevation and the northern edge of the
basin, it does not give the mean rainfall of the basin. Then, the Hinoemata Station was adopted for
this purpose, although it is located at slightly outside the basin. After careful meteorological inspec-
tion, it was assumed that the precipitation at Hinoemata is equal to the rainfall amount in each mesh
where the daily mean air temperature is above 0 °C both in snow cover and non-snow cover area.
The total rainfall amount, Pn_i"S'n_i and Pn_i°S"n_i were then obtained.
CONSTRUCTION OF SNOWMELT RUNOFF MODEL
Now, all the input data were prepared for the determination of the constant and partial regres-
sion coefficients of the equations (4) and (5). The multiple regression analyses were, then, carried
out in use of data in 1980. The resultant constructed two models are presented in Table 1.
The comparison between the observed and calculated inflow, exhibited in Figures 4 and 5,
shows that the models would stand the practical use the snowmelt runoff forecasting.
NOMOGRAPHS FOR PRACTICAL USE OF MODELS
In course of the model construction, the input variable values were obtained through the com-
plex calculation procedure relating to the mesh. Necessary for the convenience of the practical use of
the models is an easy acquisition of the input variable data. Following nomographs were, then,
devised.
Nomograph (I) for Basin-Wide Snow Amount at Maximum Stage
The Maruyama shown in Figure 2 was selected among several tens proposed sites in the basin
as the best representative site, whose snow water equivalent has a linear correlation with the basin-
wide snow amount throughout both snowfall and snowmelt seasons. Based on the six years data is
32
Figure 6 (nomograph (I)), which exhibits a relationship between the basin-wide snow amount and
Maruyama's snow water equivalent at the maximum stage.
The Maruyama is situated at roughly mean altitude of the whole basin and is at present equipped
with DCP.
Nomograph (11)for Snow Cover Area
The depletion curve of snow cover area with increasing degree-day at the Maruyama was
obtained for four snowmelt seasons, and is exhibited in Figure 7. The curves seem to depend on the
snow amount at the maximum stage. Then, the relation was investigated between the snow amount
above and the Maruyama's degree-day accumulated up to the first day when the bare ground appears
somewhere in the basin, namely, Sn_i/A< 1. A is the basin area. A linear correlation was found as
shown in Figure 8. Based on this correlation, the depletion curve was standardized. The resultant
curve shown in Figure 9 is the nomograph (II).
Nomograph (111)for Basin-Wide Snowmelt Amount
A clear relation was found between the basin-wide daily snowmelt amount and the daily mean
air temperature at the Maruyama through the medium of the ratio (Sn_i/A). This relation shown in
Figure 10 is the nomograph (III) for Mn_i-S'n_ i.
Nomograph (IV, V) for Basin-Wide Rainfall
In the models, two kinds of basin-wide rainfall amount are taken into account; one in the snow
cover area (Sn_i) and another in the non-snow cover area (A-Sn_i).
Regarding the snow cover area, the extraction of the area (S'n_in-i) where the daily mean air
temperature is above 0 °C is necessary. For simplicity, the relation was obtained between the total
rainfall amount (Pn_i,S 'n-i) and the Hinoemata precipitation (Pn-i) through the medium of the pro-
duct of the Okutadami daily mean air temperature and the ratio (Sn_i/A). The relation shown in
Figure 11 is the nomograph (IV) for Pn_i'S'n_i.
As for the non-snow cover area, this area is usually above 0 °C during a snowmelt season, so
that S"n_in-i - A - S__i. Exhibited in Figure 12 is the nomograph (V) for Pn_i°S"n_i .
VERIFICATION OF SNOWMELT RUNOFF MODELS
In order t6 verify the models (Table 1 constructed for the 1980 data, the models were applied to
the other two years, 1979 and 1982. All the input values were obtained in use of the nomographs
(I)-(V). The results are shown in Figures 13-16. A good agreement can be seen except May 26-28,
1979. A large difference in this period may be caused by heavy rainfall unusually in a snowmelt
season which occurred on May 26 and 27. In Japan the rainy season starts at the beginning of June,
and often heavy rainfall occurs. The fact above shows that the models should not be applied in case
the heavy rainfall happened near the end of snowmelt season when the snow cover area shrinks up
to the top of the high mountains.
33
CONCLUSION
In the present study scarce Landsat MSS data obliged the limited but efficient utilization for the
verification of the depletion curve of the snow cover area. In order to construct the models, the
complex topographic mesh analyses were carried out. However, the data of final necessity become
only the mean air temperature and precipitation for the daily use of the models.
The runoff forecasting procedure is summarized in Figure 17.
REFERENCES
1. Ishihara K., M. Matsuda, Y. Nishimura and K. Takeda (1982): Snowmelt runoff model in Japan.
Proc. of First Japan/US Snow and Evapotranspiration Workshop, Mar. 1982, Tokyo, p. 1-24.
2. Martinec, J., A. Rango and E. Major (1983). The Snowmelt-Runoff Model (SRM) User's
Manual. NASA Reference Publication 1100, P. 1-110.
3. Ishihara, K. (1956): Estimation of Snow Depth at Ungauged Point Using Regression Analysis of
Topographic Effects. Journal of the Japanese Society of Snow and Ice, Vol. 33, No. 3, p.
134-138, (in Japanese).
4. Takeda, K. and Y,. Takahashi (1981): Estimation of Basin-wide Snow Water Equivalent Using
Landsat-derived Snow Line and Degree-day Method. Proceedings of the Japan Society of Civil
Engineers, No. 311, p. 81-92 (in Japanese).
5. Electric Power Development Company (1980): Data Report of Snow, Weather and Discharge in
Okutadami Region (1957-1959). p. 1-424.
34
138° E 146°E
o
44°N
Figure1. Locationof TheTestBasin
35
i- i (f(L:i;[4i- .,i.;J[AF_V[-- PC)J. IJI )
, . , , - :1_ i-_ i-,-_:'--P_i ,;_._;l..',i;,',:.Ir_ N
....................... _..............
k i i T---I-r--,i-_--T-I.......I--¢--i-I-i-/'q'--
__--T-_-]---!-F-] .......-I--]--T-T-_--' "-:'__u''_-.',f---t-.J,-- 4-. --4 .......... -4....
• t,._eteoPol, obsepvinfl !-_---_ -- f--;--4---¢--d ..... --_---_j--f---_H
_q • I I : I / I I
oration (pun thl'ouqh FI!--T .... i--y-i-t .... [----q---F--]-_
_-44---d-_...... --_ --4........ _--_,......
p_ ye,'.[r ) [___. : . : i._.] _[__!_ i ....z/]
_-'__ l.I--4-_i-
!tl-fi-f-tq-t......4
Figure 2. Location of Two Meteorological Observing Stations
(Okutadami, Hinoemata) and Representative Point (Maruyama)
36
N\
Figure 3. Locations of Points Where Snow Depth and Its Water Equivalent
were Measured by Electric Power Development Co.
37
Table 1
Snowmelt Runoff Model
MODEL- I
Rn= 14.0+ 0.491X_-l+0.106 Xn-_.0.044 Xo-'
+ 0.121¥o-'+0.120 ¥_-_
m.c.c. • O.9 21 s.d. • 17.2
MODEL-II
R_= 7.33 + 0.549 R_-,+0.392 Xn-1"- 0.110 X_-_
- 0,.05 7 Yo-1
m.c.c. • 0.943 s.d." 14.7
20o m.c.c. 0.921
s.d. "17.2
!
I; I
i ,
-') II I I
[L Ill I I
_ ' ,_,,
_ ,
._ I00
1.1-
' Jli'
•--_1., [,,,.,, /_ '
',,
V
0
3/1 10 20 /./1 10 20 5/1 10 20 6/1 10 20 310
DATE
Figure 4. Comparison Between Observed (Solid Line) and Calculated
(Broken Line) Inflow in Use of MODEL-I for 1980 Snowmelt Season
39
2oo m.c.c. 0.943
,! s.d. • 14.6
ill Id',I:ll
OBSERVED ,_
;I
,!i
" S !,_ ', I ''
"i i/"jo ioo ',u_ r ,,z , ,,,
'! 7I;,
l| I
II
I'\
o
311 10 20 t,/1 10 20 5/1 10 20 6/1 10 20 30
DATE
Figure 5. Comparison between observed (Solid Line) and Calculated
(Broken Line) Inflow in Use of MODEL-II for 1980 Snowmelt Season
4O
.!..)
78/
r_
t_J 200 19
c.:}
•t 1ow 9811/8_
}-.--
d')
---)
x
2.<_- _ 1982
,-< / 1977
zD 100
o
Z
<
2-
0
Z
_r_ 50
[L]
LD
z
_.
, I i I
< 0 50 100 150 200
SNOW WATER _:QU[ AT _dt,__ gi/cm 3.... •,,,-,U YAMA ( )
Figure 6. NOMOGRAPH(I) for Basin-Wide Snow Amount at Maximum
Stage in Use of Snow Water Equivalent at Maruyama
41
1.0
0.3 '79
_o
0.2
98 158 184cm
0.!
0.0 m,
I00 200 300 400 500 600 700
ACCUMULATED DEGREE-DAYS AT MARUYAMA ('C day)
Figure 7. Relationship Between Depletion of Snow Cover Area and Accumulated Degree Days at
Maruyama (Parameter: Basin-Wide Snow Amount at Maximum Stage)
>,
©
o
--._100 1982
cc •
9 • 1980
:_--
U")
>...
< •1978<3
I
W
w 197
c)
uJ 50
a
DJ
,<
.J
-J
,.2_
.q_b
(_.)
U
i I ! I
0 50 100 150 200
BASIN WIDE SNOW AMOUNT AT MAXIMUM STAGE (g/cm_)
Figure 8. Relationship Between Basin-Wide Snow Amount and Accumulated
Degree-Days at Maruyama Before Snow Cover Area Depletion Starts
43
010
100 200 300 zOO 500 600 ?00
ACCUMULATED DEGREE-DAYS AT MARUYAMA ("C.day)
Figure 9. Nomograph(ll) for Snow Cover Area. (Parameter: Basin-Wide Snow Amount at Maximum
Stage.)
3OO
0 5 10 15 20 0 KUTADAM!
! 1 I ! I
0 5 10 15 20 MARUYAMA
DALLY MEAN AIR TEMR (°C)
Figure 10. Nomograph(lll) for Basin-Wide Snow-Melt in Use of Daily Mean Air Temperature at
Maruyama. (Parameter: Relative Snow Cover Area, Sn_i/A)
45
I00
80
/ 70
I i , I • i * I
0 5 10 15 20 25
DALLY RA[NF'ALL AMOUNT AT HINOEMATA(mm)
Figure 11. Nomograph(IV) for Total Daily Rainfall Amount in Snow Cover Area in Use of Daily
Rainfall at Hinoemata (Parameter: Daily Mean Air Temperature x Relative Snow Cover Area)
46
Figure 12. Nomograph(V) for Total Daily Rainfall Amount in Non-Snow Cover Area in Use of Daily
Rainfall at Hinoemata Station. (Parameter: Relative Non-Snow Cover Area, 1-Sn_i/A)
47
230
m.c.c. 0.835
s.d. • 17.0
0 --
311 10 20 I./'1 10 20 511 10 20 611 10 20 30
DATE
Figure 13. Comparison Between Observed (Solid Line) and Calculated
(Broken Line) Inflow in Use of MODEL-I for 1979 Snowmelt Season
48
o
3/1 10 20 c./1 10 20 5/1 10 20 6/1 10 20 30
DATE
Figure 14. Comparison Between Observed (Solid Line) and Calculated
(Broken Line) Inflow in Use of MODEL-I for 1982 Snowmelt Season
49
2oo m.c.c. • 0 8 91
s.d. • 13.8
OBSERVED
CALCULATED
100
LL
z
2
o
3/1 10 20 f./1 10 20 5/1 10 20 6/I 10 20 30
DATE
Figure 15. Comparison Between Observed (Solid Line) and Calculated
(Broke Line) Inflow in Use of MODEL-II for 1979 Snowmelt Season
50
0
311 10 20 t_ll I0 20 511 10 20 611 10 20 30
DATE
Figure 16. Comparison Between Observed (Solid Line) and Calculated(BrokenLine) Inflowin Use of MODEL-IIfor 1982SnowmeltSeason
51
Water Dairy mean IDaity mean Dairy IInftow of
equivalent air temperature lair temperature precipitation iprevlous day
snow depth at Okutadami St. lat Maruyama at Hinoemata
at Maruyama 1
INomograph(1)I INomograph(_)liNomogre.Ph(V)I
L
,r,
I N°m°graph(II) I
I
Nomograph(E[)
I
Ixo-,l I 1
! I
Modet-II IModet-XI
Figure 17. Procedure of the Snowmelt Runoff Forecasting


Snowmelt Runoff Model in Japan

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server