# How to deal with non-stationary conditions in hydrology using neural networks

AI and Robotics

Oct 19, 2013 (4 years and 6 months ago)

108 views

How to deal with non
-
stationary conditions in
hydrology using neural networks

Virgile TAVER
1, 2

Anne JOHANNET
2

Valérie BORRELL ESTUPINA
1

Séverin PISTRE
1

(1) HSM, HydroSciences Montpellier, UMR5569,
Université de Montpellier

2,
France

(2) Ecole des Mines d’Alès
, France

IAHS General Assembly in Göteborg
-

July 2013

Session : Testing simulation and forecasting models in non
-
stationary conditions

1

Neural Networks (NN)

The Neural Networks are increasingly used in hydrology:

o
For prediction

o
For forecasting floods

o
For modelling unknown relations

The Neural Networks learn their behavior by training, nevertheless:

o
They are sensible to overfitting (bias
-
variance dilemma)

o
Model complexity must be chosen as simple as possible

o
Regularization methods must be used

Neural Networks

Methods Results Conclusion

2

Neural Networks

Neuron definition:

o
Weighted sum

o
Non
-
linear function (
f
)

Neural Network architecture:

o
Multilayer perceptron

Universal approximation

Parsimony (for statistical models)

Neural Networks

Methods Results Conclusion

3

Neural Network: design methodology

Minimization of the quadratic error during training by Levenberg
-
Marquardt rule

Data base utilization:

o
One (sub)
-
set for training (
P
i
,
i
=1,5)

o
One (sub)
-
set for stopping (early stopping with records ≠(
P
i
,
i
=1,5))

o
One (sub)
-
set for test (in level 3), different from training and stop sets

Complexity selection

o
Definition of architecture using cross
-
validation (included inside the training period) :

Input variables (
u
i
)

Number of hidden layers and hidden neurons

o
Selection using Nash criterion

Neural Networks

Methods Results Conclusion

4

3 ways of modelling

3 models can be investigated regarding the
postulated model

For example let us consider an
analogy

: calculate the price of a

baguette”
, 3 methods can used to estimate such a price :

1.
Take into account the
price of primary ingredients

(flour, water …), energy, and
compute the price for a specific recipe

2.
If the state measurement is good: take into account the
measured price
yesterday
, and anticipate a one
-
day evolution

3.
If the state measurement isn't good: take into account the
estimated price
yesterday
, and anticipate evolution

Neural Networks
Methods

Results Conclusion

5

3 ways of modelling

3 models can be investigated regarding the
postulated model:

1.
Computing discharge from

rainfall and physics

2.
Computing discharge from

the state measurement

3.
Computing discharge from

the state estimation

Neural Networks
Methods

Results Conclusion

6

Static
system
modelling

Dynamic
system
modelling

=> Non
-
directed NN model

=> Static NN model

=> Directed NN model

1 NN model for each postulated model

Un
-
directed

NN model

Static

NN model

Directed

NN model

Postulated model 1

Postulated model 2: noise on the state

Postulated model 3 : noise on the measurement

φ

q
-
1

u

(
k
)

y
p

(
k
)

b

(
k
+1)

y
p
(
k
+1)

φ
RN

u

(
k
)

y
p

(
k
)

g
(
k
+1)

y
p
:

observed

output

of

the

physical

process

u

(
k
)
:

observed

input

of

the

physical

process

(
rain
)

b

(
k
)
:

noise

φ

q
-
1

u

(
k
)

x
p

(
k
)

b

(
k
+1)

y
p
(
k
+1)

x
p

(
k
+1)

φ

u

(
k
)

y
p
(
k
+1)

φ
RN

u

(
k
)

g
(
k
+1)

φ
RN

q
-
1

u

(
k
)

g

(
k
)

g

(
k
+1)

Neural Networks
Methods

Results Conclusion

7

1 NN model for each postulated model

Un
-
directed

NN model

Static

NN model

Directed

NN model

Postulated model 1

Postulated model 2: noise on the state

Postulated model 3 : noise on the measurement

φ

q
-
1

u

(
k
)

y
p

(
k
)

b

(
k
+1)

y
p
(
k
+1)

φ
RN

u

(
k
)

y
p

(
k
)

g
(
k
+1)

y
p
:

observed

output

of

the

physical

process

u

(
k
)
:

observed

input

of

the

physical

process

(
rain
)

b

(
k
)
:

noise

φ

q
-
1

u

(
k
)

x
p

(
k
)

b

(
k
+1)

y
p
(
k
+1)

x
p

(
k
+1)

φ

u

(
k
)

y
p
(
k
+1)

φ
RN

u

(
k
)

g
(
k
+1)

φ
RN

q
-
1

u

(
k
)

g

(
k
)

g

(
k
+1)

Neural Networks
Methods

Results Conclusion

8

1 NN model for each postulated model

Non
-
directed

NN model

Static

NN model

Directed

NN model

Postulated model 1

Postulated model 2: noise on the state

Postulated model 3 : noise on the measurement

φ

q
-
1

u

(
k
)

y
p

(
k
)

b

(
k
+1)

y
p
(
k
+1)

φ
RN

u

(
k
)

y
p

(
k
)

g
(
k
+1)

y
p
:

observed

output

of

the

physical

process

u

(
k
)
:

observed

input

of

the

physical

process

(
rain
)

b

(
k
)
:

noise

φ

q
-
1

u

(
k
)

x
p

(
k
)

b

(
k
+1)

y
p
(
k
+1)

x
p

(
k
+1)

φ

u

(
k
)

y
p
(
k
+1)

φ
RN

u

(
k
)

g
(
k
+1)

φ
RN

q
-
1

u

(
k
)

g

(
k
)

g

(
k
+1)

Neural Networks
Methods

Results Conclusion

9

1 NN model for each postulated model

Non
-
directed

NN model

Static

NN model

Directed

NN model

Postulated model 1

Postulated model 2: noise on the state

Postulated model 3 : noise on the measurement

φ

q
-
1

u

(
k
)

y
p

(
k
)

b

(
k
+1)

y
p
(
k
+1)

φ
RN

u

(
k
)

y
p

(
k
)

g
(
k
+1)

y
p
:

observed

output

of

the

physical

process

u

(
k
)
:

observed

input

of

the

physical

process

(
rain
)

b

(
k
)
:

noise

φ

q
-
1

u

(
k
)

x
p

(
k
)

b

(
k
+1)

y
p
(
k
+1)

x
p

(
k
+1)

φ

u

(
k
)

y
p
(
k
+1)

φ
RN

u

(
k
)

g
(
k
+1)

φ
RN

q
-
1

u

(
k
)

g

(
k
)

g

(
k
+1)

Neural Networks
Methods

Results Conclusion

10

3 ways to deal with non stationary

How to adapt the model to the changing environment and process?

o
Changing process or environment

The observed data are used to adapt parameter values

at
different time steps

o
The observed data are used as input data

at different time step

Directed Model

The observed data are used to modify inaccurate inputs

at
different time steps

Data Assimilation

A variationnal approach is used in this work to modify rainfalls,
temperature and snow at each time step

Neural Networks
Methods

Results Conclusion

11

Possible on
the 3 models

Only for
Directed
model

Possible on
the 3 models

Application:

-

Fernow watershed,

-

Durance watershed

Only models able to represent dynamic systems were developed :

Directed (non
-
recurrent model)

Non
-
Directed (recurrent model)

Neural Networks Methods
Results

Conclusion

12

Non
-
directed

NN model

Directed

NN model

φ
RN

u

(
k
)

y
p

(
k
)

g
(
k
+1)

φ
RN

q
-
1

u

(
k
)

g

(
k
)

g

(
k
+1)

2 ways of dealing with non
-
stationary :

No option

Assimilation

Fernow watershed, USA (0,2 km
2
)

Neural Networks
Methods

Results

Conclusion

13

Complete period: 01/01/1959
-

31/12/2009

Snowmelt and sampling too distant (day for a very small basin)

Calibration periods:

P1: 01/01/1959
-

31/12/1968: forest cut of the lower part of the basin (Mar
-

Oct 1964); forest cut of the upper part of the basin (Oct 1967
-

Feb 1968)

P2: 01/01/1969
-

31/12/1978: plantation of firtrees (Mar
-

Apr 1973)

P3: 01/01/1979
-

31/12/1988

P4: 01/01/1989
-

31/12/1998

P5: 01/01/1999
-

31/12/2008

Fernow model

Neural Networks
Methods

Results

Conclusion

14

Fernow model : illustration

Neural Networks
Methods

Results

Conclusion

15

0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
Directed
Directed
Directed
Assimilation
Non Directed
Non Directed
Non Directed
Assimilation
Fernow basin

Train P
1

test P1
test P2
test P3
test P4
test P5
Nash criterion

Durance watershed, France ( 2170 km
2
)

Neural Networks
Methods

Results

Conclusion

16

Observed non
-
stationary: Temperature higher implying decrease of glaciers

Discharge during spring due to snowmelt

Complete period: 01/01/1904
-

30/12/2010

Calibration periods:

P1: 01/01/1904
-

31/12/1924

P2: 01/01/1925
-

31/12/1945

P3: 01/01/1946
-

31/12/1966

P4: 01/01/1967
-

31/12/1987

P5: 01/01/1988
-

31/12/2008

Durance model

Neural Networks
Methods

Results

Conclusion

17

Rain

7j

Temp

10j

PET

4j

Qcalc

2j

Hidden
Layers

3

Architecture defined on P1

Durance model : illustration

Neural Networks
Methods

Results

Conclusion

18

During the spring period, discharge of the Durance is due to snowmelt.

To take into account this process, positive temperatures of winter and spring are
preserved (from 1st of January to 30th of June). All the other temperature are set
to zero.

0
100
200
300
400
500
600
-30
-20
-10
0
10
20
30
19/11/1905
27/02/1906
07/06/1906
15/09/1906
24/12/1906
Discharge (m3/s)

Temperature (
°
C)

Temperature modification for snowmelt process

Temperature
Snowmelt
Discharge

Durance model : illustration

Neural Networks
Methods

Results

Conclusion

19

Model

Input
Temperature

Assimilation
on

Directed

The supplied
ones

Rainfall

Non
-
Directed

The supplied
ones

Rainfall,
Temperatu
re, PET

Non
directed

Snowmelt

Rainfall

Fernow

Durance

Neural Networks
Methods

Results

Conclusion

20

Directed, no option

With the Directed model with Adaptativity
or Assimilation on the Fernow catchment :

Improvement of the Nash

But decrease of the performance on the
low flows on some periods

Not a Gain, nor a deterrioration on the
Durance catchment

Fernow

Durance

Neural Networks
Methods

Results

Conclusion

21

Non
-
Directed, no option

Best results on the Durance catchment

Poor Nash on Fernow

Neural Networks
Methods

Results

Conclusion

22

strongly improve the Nash criterion (in
particular for the Durance catchment)

But have no effect on low flows

Non
-

Non
-
Directed, Assimilation

Fernow

Durance

Neural Networks
Methods

Results

Conclusion

23

Fernow

Non
-
Directed, Assimilation

The data assimilation :

-
improves low flows while
deterioring the Nash on the
Ferrow catchment on some
periods

It was the oppositive result for
the Durance catchment :
improvement of the Nash while
deterioring low flows on
(previous slide)

Neural Networks
Methods

Results

Conclusion

24

Durance

Non
-
Directed, no Option, T
°

The treatment of temprature (Snowmelt) improves the Nash criterion

Non
-
Directed, Assimilation, T
°

0
1000
-100
0
100
19/11/1905
07/06/1906
24/12/1906
Dischar
ge

Temper
ature

Temperature

Non
-
Directed,
no Option

Conclusions

Neural Networks Methods Results
Conclusion

25

The best way (reliable , simple, easy) to adapt the model to the changing
environment consists in using the Directed Model (feedforward model)

When using Directed Model, there has been no appreciable progress when using

When using Non
-
Directed model, the improvement provided by adapatativity and
data assimilation can be high

Neural Network Modelling is more efficient for the largest studied catchment

Work on progres : data assimilation must be studied more deeply (some parameters
to adjust), the criteria used for otpimization have to be complixified (to avoid that
the improvement on high flows appears when decreasing performance on low flows
and vice versa)