The simulation of runoff from a Himalayan Glacier basin using an Artificial Neural Network (ANN) is presented. The performance of the ANN model is found to be superior to the Energy Balance Model and the Multiple Regression model. The RMS Error is used as the figure of merit for judging the performance of the three models, and the RMS Error for the ANN model is the latest of the three models. The ANN is faster in learning and exhibits excellent system generalization characteristics

Buch, A. M.

Narain, A.

Pandey, P. C.

English

NASA Technical Reports Server

N94-35061
Application of Artificial Neural Networks in
Hydrological Modeling : A Case Study of
Runoff Simulation of a Himalayan Glacier Basin
A.M. Buch A. Narain
E-Mall : ambuchesac.erneLln
P.C. Pandey
Remote Sensing Applications Qroup
Space Appllcatlonl Centre (ISRO)
Ahmedabad 380-053 (INDIA)
Abstract
The simulation of runoff from a
Himalayan Glacier basin using
an Artificial Neural Network
(ANN) is presented. The
performance of the ANN model is
found to be superior to the
Energy Balance Model and the
Multiple Regression model. The
RMS Error is used as the figure
of merit for judging the
performance of the three
models, and the RMS Error for
the ANN model is the least of
the three models. The ANN is
faster in learning and exhibits
excellent system generalization
characteristics.
Introduction
Central Asia, the main regime
of mountain glaciation in the
Himalayas, is notable for its
diversity of hydrological and
meteorological conditions. As
the largest ice-sheet outside
the polar regions, it nourishes
some of the largest river
systems, like the Indus, the
Ganges, etc. These mountain
rivers have as their source
the liquid run-off from melting
snow and ice as well as liquid
precipitation into their
drainage basins. However, for
most of the river systems in
the Central Asia, the water
from melting is the main source
of nourishment.
The study of the glaciated
mountainous areas presents many
difficulties, due to both lack
of information on the water
balance elements and the
great variety and complexity of
natural conditions of these
areas. The structure of natural
zones of ablation ( and
consequently the water balance)
is determined by geographical
position and the peculiarities
of orography, the absolute and
relative height of mountains,
the circulation processes and
radiation regime, the
exposition of slopes, the
geological structure, etc. [7]
There exist many empirical
methods of simulating and
predicting glacier melt runoff,
223
https://ntrs.nasa.gov/search.jsp?R=19940030555 2020-06-16T12:57:58+00:00Z
including time series modeling
and actual physical parametric
modeling. One of the most
widely studied and viable
method is the Energy-Balance
Model. This method has been
advocated by various
researchers for operational
runoff forecastiDg from
glacierized basins. [3], [4],
[zo]
The Study Area
The Chhota Shigri glacier is a
medium size valley glacier
situated in the Lahaul and
Spitti District of Himachal
Pradesh (India). The glacier
lies between latitudes 77-29N
and 77-33N and longitudes 32-
lIE to 32-18E, covering an
area of about 19.39 sq. km.
Geologically this area is
confined to the Rohtang
gneissic complex of the Central
Crystalline of the higher
Himalaya. Fig. 1 (a) shows
various features of the glacier
and Figure 1 (b) shows relevant
hydrogeomorphological
parameters. [i]
The Energy Balance Model
Marks and Dozier (1992) have
carefully analyzed the various
types of heat fluxes and their
relative influence over the
snow melt run-off process in a
small alpine basin. They have
clearly demonstrated the
dominance of solar radiation
heat flux and two other
important fluxes, viz. the
sensible heat flux, and the
latent heat flux in the runoff
calculations. This logic can be
applied to other glaciated
areas as well. Since the solar
radiation is easily measured
and the heat flux is easily
?¢30'
3_'
20'
- Chholru K..azo Ro.O._o.._'_'m.,=i"
32",r o • /,4 °.F
"IW_ I__//--eniesses
_'+_",.',_J_ .,Y (Pre combr-
_L,,"_,- ""_" " ion )
_,' %_
SARA UMGA / L ["
PASS Sl00m 0 1 2. 34Kr 
32t
-4- 4--
10
Figure 1 (a). Glacier Location Map
Total Area of the Glacier
Accumulation Area
Average Height of Acc. Area
Ablation Area
Average Height of Abl. Area
Accumulation Area Ratio
Maximum Glacier Height
Snout Height
Orientation
Average Gradient
Length of Glacier
19.89 sq. km.
18.15 sq. km.
5010 Mts.
1.24 sq. km.
4188 Mrs.
0.91
5595 Mts.
:3840 Mts.
NNE
176 Mts./km.
10.00 km.
(adopted from Dhanju and Buch, 1989)
Figure 1 (b). Hydrogeomorphological Parameters
224
Run-off in Cusec.
11
S
6 t I I I I
6 9 13 17 21
Number of days since July 15, 1988
26
Figure 2.
"-_ Observed Runoff
Hydrograph of Chhota 8higri Stream
modeled for a given topography,
it should be possible to
reliably model the runoff from
glaciated areas.
The energy budget for a melting
glacier can be expressed as
Qm = Qn + Qh + Qe + Qr --- (1)
Where
Qm = Energy flux actually
available for melting the ice.
Qn = Net radiation flux
Watts / Sq. Meter )
( in
Qh = Sensible heat flux (
Watts / Sq. Meter )
in
Qe = Latent heat flux
Watts / Sq. Meter )
( in
Qr = Sensible heat flux from
rain. ( This term is negligible
in our case as no rain was
observed during the period
this study.)
of
The net radiation flux is
calculated as
Qn = Qsw + Qlw (2)
Where
Qsw = Shortwave radiation
balance measured at the
observatory, by net radiometer.
Qlw = Long wave
budget at the surface,
using the algorithm
by [13].
radiation
modeled
suggested
The turbulent fluxes, viz. The
Qh and Qe were determined using
the standard aerodynamic
formulae and the roughness
length was assumed to be
constant at 5mm for this
experiment.
225
Ono Output Unit
Thirty
Hidden Units
Three Input Unite
Figure 3. Neural Network Architecture
used |o_ Glacier FIun-ot| Simulation
The hydrometeorological data
and the net radiation flux
data, along with corresponding
runoff, were collected in situ
during the Chhota shigri
Glacier Expedition in July -
August, 1988. The approach to
this glacier is possible only
during the ablation season, as
the high mountain passes remain
snow-covered for the rest of
the period. This is the major
bottle-neck in collecting
long-term melt-discharge
records for these areas. The
Hydrograph of the Chhota
shigri melt-stream is shown in
Figure 2.
The data are sparse and call
for a technique that can
generalize the latent system
configuration to improve their
applicability to runoff
calculations. One such recent
technique that possesses
excellent generalization
characteristics in addition to
very good learning capability
is the Artificial Neural
Network technique.
Modeling Physical Systems and
Processes using Artificial
Neural Networks
Many of our research efforts in
the field of Remote Sensing
remain directed towards
understanding and developing
mathematical models that can
simulate dynamic physical
processes in oceans,
atomosphere and the environment
in general. The spacecrft-based
sensors provide much-needed
details about various
parameters
processes.
limited
physical
environment,
that govern these
However, due to
knowledge of the
processes in the
and the inherent
noise in many geophysical data,
environmental systems often
cannot be accurately
represented through numeric
values describing their
physical properties and
interactions, but rather are
subjected to categorisation
into broad classes. [9]
The modelers have been
investigating many different
techniques to exactly simulate
the processes from the previous
knowledge, available in terms
of historic data (very good
survey of recent tachniques is
provided by Tsonis and Elsner,
1989). Many efforts to model
dynamic systems have been
undermined by the system's
inherent chaoticity in the
data. One solution is to model
the temporal variability of a
parameter rather than the
parameter per se. [2]
Neural Network Architecture
used for Runoff simulation
Recently, there has been a
great surge in the application
of multi-layer-feed-forward
Artificial Neural Networks to
diverse system identification
problems [2], [ii], [5]. In
226
Modeled Run-off (Cusec)
13
12
11
10
9
8
7
6
6
6
.......' "
A X'"
_1_ "_' _
zl
_ f I I 1 ] 1 1
6 7 8 9 10 11 12 13
Observed Run-off (Cusec)
I ".-.g-Energy B-,lanoe Model Multiple-regression × ANN Model
Figure 4. Comparative Model Performance
this study, the
Fast-Back-Error-Propagation
algorithm has been used. [6]
The network for run-off
prediction comprises 3 layers,
viz. the input layer, the
hidden layer and the output
layer. The input layer consists
three input neurons
corresponding to three heat
fluxes viz. the Solar Radiation
Heat Flux, the Sensible Heat
Flux and the Latent Heat Flux.
The hidden layer has 30
nodes, and the output layer
consists of one neuron
corresponding to the modeled
run-off value. The schematic
diagram .is shown in Figure 3.
Generalisation Performance of
ANN Model
Generalisation is a measure of
how well the network performs
on the actual problem once the
training is complete.
The standard method for
measuring the generalisation
characteristics of a given
model is called the method of
'Cross Validation' The method
splits the data set into two
subsets, viz. the training data
set and the testing data set.
The learning is performed using
the training data set and the
network performance is
evaluated using the test data
set. Unless the training set
is large enough, the
performance of the network on
training data is not likely to
be an accurate measure of its
performance on future or
unknown data.
To achieve a statistically
significant result, several
independent splits are required
and the average of the results
is accepted as the overall
227
Model RMS Error
Energy Balance Model
Multiple Regression Model
ANN Model ( 1391 Iterations )
1.46
1.54
0.06
Figure 5, Table Showing Modeling Errors
performance of the network.
While the cross validation
method is a widely accepted
method, it is extremely time-
consuming in the case of ANN as
lenghty training times are
required for each independent
partition of the data set.
In the case of the Himalayan
glacier basins, the
hydrometeorological data
collected in situ are sparce,
as the mountain passes leading
to the glacier snout remain
open for a very short
period towards the end of
summer. Hence, all of the data
sets have to be used for
meaningful training. Thus there
is a need for alternate
reliable methods for
predicting the generalisation
performance of the network
without having a test data set.
An alternative technique which
requires far fewer computations
is called the 'Predicted
Squared Error' technique. This
technique relies on statistical
methods to derive an expression
for the generalisation
performance of a system as a
function of its performance on
the training data set, the
number of free parameters in
the system and the size of the
training data set. [5]
PSE = MSE+(2*Nw/Np)*(r2) (3)
Where
PSE = Pridicted Squared
( For Future )
Error.
MSE = Mean Squared Error of the
training data set.
Nw = Number of free parametres
in the model (120 in our
case ).
Np = Number of training
patterns for the model (24 in
our case ).
(r2) = Variance of the noise
determined by the formula :
(r2) = abs[ (p/(p-Nw))*MSE] (4)
Where
p = Number of patterns used for
training the network.
The MSE in the ANN model for
the Chhota Shigri Runoff Model
is estimated at 0.0036. Hence
by substituting the values in
eq. 4 and eq. 3 we get the PSE
as 0.0126, which is quite
acceptable as model error
considering the paucity of
data.
Conclusions
Figure 4 depicts the resultant
calculated runoff from the
energy balance model against
two other models, viz. the
Multiple-Regression Model, the
Energy Balance Model and the
ANN model. (See Figure 5)
It can be clearly seen from the
228
comparative performance of the
three different models that the
trained ANN model assumes the
flow values that are closest to
in situ measured values.
(The Correlation Coefficient
between the measured runoff and
the runoff simulated by ANN
model is of the order of
0.9998) Currently, we are
investigating the application
of different ANN models to
diverse hydrological and
meteorological simulation and
forecasting problems.
The technique of system
modeling with ANN holds very
good promise. However, it
requires rigorous research and
simulations before any
operational model can be
developed.
Acknowledgements
The authors are grateful to Mr.
N.D. Sen, School of
Environmental Sciences,
Jawaharlal Nehru Univesity, New
Delhi, for providing
Hydrometeorological Data and
Energy Balance Model output for
the Chhota Shigri Glacier.
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Application of artificial neural networks in hydrological modeling: A case study of runoff simulation of a Himalayan glacier basin

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