M2 - Putika Ashfar Khoiri Water Engineering Laboratory Department of Civil Engineering 24 th Cross-Boundary Seminar International Program of Maritime and Urban Engineering Osaka University Improving Distributed Hydrological Model Simulation Accuracy using Polynomial Chaos Expansion (PCE) *tentative title December 21 st , 2017
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Improving Distributed Hydrologocal Model Simulation Accuracy Using Polynomial Chaos Expansion
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M2 - Putika Ashfar Khoiri
Water Engineering LaboratoryDepartment of Civil Engineering
24th Cross-Boundary SeminarInternational Program of Maritime and Urban EngineeringOsaka University
Improving Distributed Hydrological Model Simulation Accuracy using Polynomial Chaos Expansion (PCE)
*tentative title
December 21st, 2017
1
Background of study
(Data from Japan Meteorological Agency)
There is a change in precipitation
pattern due to climate change
It is necessary to analyse rainfall-
runoff relationship to predict the
risk of flood and drought
increases due to climate change
Perform hydrological model
Input
Hydrological
Model Watershed
characteristics
Output river discharge
grid input set
2
Background of study
based on parameter complexity conceptHydrological
Model
Lumped Model
same parameter (๐ญ)in the sub-basin
Semi-distributed Model
parameters assigned in each grid cell but cells with the same parameters are grouped
๐ญ
๐ญ1
๐ญ2
๐ญ3
Fully-distributed Model
parameters assigned in each grid cell
๐ญ1
๐ญ2๐ญ3
๐ญ4
3
Background of study
based on parameter complexity conceptHydrological
Model
Fully-distributed Model
parameters assigned in each grid cell
Advantages
1. Can consider the spatial distribution of input
2. Can predict output discharge at any point
Disadvantage
1. Require many parameters so the setting and
determination of parameter is difficult
We need to assess the effectiveness of distributed
parameter including the characteristics of every
parameter
Parameter optimization is required to decrease the uncertainty
Approach:
๐ญ1
๐ญ2
๐ญ3
๐ญ4
Approach
In order to optimize the poorly known parameters and improve the model forecast
e.g. GLUE (Generalized Likelihood Method Uncertainty Estimation) , based on Monte-Carlo simulationProblem -> Need large number of parameter sets sample
SWt = final soil water content
SW0 = initial soil water content on day i
Rday = amount of precipitation on day i
Qsurf = amount of surface runoff on day i
Ea = amount of evatranspiration on day i
Wseep = amount of water entering the vadose zone from the soil
Qgw = amount of water return flow on day i
6
Previous study
Improving Distributed Hydrological Model for the flood forecasting accuracy
Spatial distribution view Necessary to reduce grid spatial resolution (not objective)
Land-use correlated parameter
Most-considered parameter:C
Soil related parameters
-evaporation coefficient-roughness coefficient
-tank storage constant-hydraulic conductivity of layer-soil thickness-slope gradient-permeability coefficient
Therefore, I want to focus on land-use correlated parameter and soil related parameter in my study
Density function of parameter ๐approximate by GaussianQuadrature
(Mattern, 2012)
PCE has used to optimize parameter on biological ocean model
8
Objective and Method
Polynomial Chaos Expansion (PCE)
Increasing Distributed Hydrological Model Simulation Accuracy
by using Polynomial Chaos Expansion (PCE) method
Objective
The method of simulating with the value of the quadrature points in the parameter space, and estimating the optimal parameters using the difference between the observations and models (Mattern, 2012)
๐ ๐๐๐ธใๆๅฐ
parameter space
Calculation at all quadrature points and interpolate
๐ ๐๐๐ธ
0 1
๐ ๐๐๐ธ
2 4 6 8 10
x 10-3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
parameter: KDOMf
para
mete
r: r
atio
_n
0.5
1
1.5
2
2.5
3
๐ ๐๐๐ธ
Relative parameter ranges ๐ญ1
Rel
ativ
e p
aram
eter
ran
ges ๐ญ
2
Global minimum of RMSE
(optimal parameter value)
Contour plot of distance function
(Hirose, 2015) 9
Method (PCE)
Emulator techniques
Polynomial Chaos Expansion (PCE)
Advantages:
- More effective than Monte-Carlo
because of their random sampling
- PCE performs a polynomial interpolation
in parameter space so it can estimate
any model output for the parameter
value of choice
Challenges:
- We must know what kind of input
parameters that make large uncertainty
- Upper and lower limits of parameter is
difficult to set
- Only two parameters can be optimized
We need to carefully consider:
1. Uncertain model input (parameters)
2. The prior distributions assigned to these
input
3. kmax (max. order of polynomial) -> we
have to check which value of kmax is
applicable for DHM
10
Previous studyImproving parameter estimation in Hydrological by applying PCE
HYMOD model (Fan, 2014) is a uniformly distributed model
Parameter Description Value
Cmax Maximum soil moisture capacity within the catchment 150-500
bexp Spatial variability of soil moisture capacity 15-5
ฮฑ Distribution factor of water flowing to the quick flow reservoir 0.46
Rs Fraction of water flowing into the river from the slow flow reservoir 0.11
RqFraction of water flowing into the river from the quick flow reservoir
0.82
Soil moisture capacity function
c= soil moisture capacity
๐ญ ๐ = 1 โ 1 โ๐
๐ช๐๐๐
๐๐๐๐
0 โค ๐ โค ๐ช๐๐๐
The PCE are applied for those two parameter, because its uniformly distributed. While another parameter is assumed to be deterministic
The results indicated both 2- and 3- order PCE's could well reflect the uncertainty of streamflow result 11
Previous study
PCE method for HYMOD model (Fan, 2014)
12
Model
Distributed Hydrological Model of Ibo River (Ishizuka, 2010)
In order to know how the impact runoff mechanism and water penetration in soil due to soil capacity can be approached by :
Storage Function method
๐๐
๐๐ก= ๐ โ ๐
๐ = ๐พ๐๐
๐ : storage height๐ : effective amount of rainfall๐: runoff height๐พ: storage constant ๐: storage power constant
Runoff and slope on river drainage effect
Kinematic wave method
๐โ
๐๐ก+๐๐
๐๐ฅ= ๐
๐ =๐ sin ๐
๐พโ +
sin ๐
๐โ โ ๐ท
5
3 ๏ผ โ๏ผ๐ท๏ผ
๐ =sin ๐
๐โ5
3 ๏ผ โ๏ผ๐ท๏ผ
๐ : effective amount of rainfallโ : water depth ๐ : dischargen : roughness coefficient
Try to determine couple of optimal fixed parameter that I want to optimize (e.g. ๐ท and k in Kinematic wave method)
Candidate for parameter optimization which are related to storage capacity of water in the soil (Ishizuka, 2010)
Runoff on slope and river channel
Description Parameter Valueslope gradient ฮธ 0.01-13.5roughness coefficient n 0.01-2layer A thickness D 200effective porosity of layer A ฮณ 0.2hydraulic conductivity of layer A k 0.3distance difference โx 20time interval โt 0.001storage constant of tank I K1 3.2storage constant of tank II K2 14
(Note : The range of value for each parameter should be discussed to avoid many trial and error)
15
1. Try to apply PCE to soil capacity related parameter within the catchment in
the first layer refer to Kinematic Wave equation
2ใTherefore, it is necessary to check which value of polynomial order (k) is
applicable to this model
Future task
16
Test the D and k parameter with PCE to select suitable and optimum
value for the polynomial order (k) within single flood event
Determine time range for the single flood event
Study MATLAB to make modification on PCE code, apply on DHM model