Chapter 3 Determination of an ideal regionalization methodology for monthly specific
3.3 Results and discussion
erode soil particles during high flow periods is significant. The minimum Qas and SSYas in C14 (the flattest SRC) imply that, in this catchment, the intensively weathered materials or loose sedimentary deposits are available for transportation at almost all discharges.
Table 3.3 Fitted sediment rating curves, at-site calibration and Jack-knife validation results.
Catchment Sediment rating curve At-site calibration Jack-knife validation*
a b R2 NSE PBIAS RSR NSE PBIAS RSR
1 4.5785 1.1529 0.86 0.62 9.60 0.61 0.64 10.08 0.60 2 1.9945 1.3662 0.75 0.68 29.35 0.56 0.56 –41.84 0.66 3 4.9915 1.4318 0.90 0.87 10.63 0.37 0.85 1.26 0.39 4 1.7532 1.8382 0.72 0.67 16.31 0.57 0.58 38.83 0.65 5 2.9322 1.1672 0.84 0.68 19.82 0.56 0.70 –4.08 0.55 6 2.7697 1.3759 0.86 0.61 29.45 0.62 0.65 10.05 0.59
7 5.8555 1.1597 0.83 0.68 10.24 0.57 ‒ ‒ ‒
8 0.7111 1.9775 0.64 0.53 20.98 0.69 0.54 8.92 0.68 9 2.3037 1.6322 0.79 0.76 9.27 0.49 0.69 31.13 0.56 10 1.1668 1.7518 0.72 0.65 14.75 0.59 0.61 –9.94 0.63 11 1.0742 1.9018 0.64 0.77 23.53 0.48 0.83 –1.39 0.42 12 2.8375 1.4622 0.85 0.79 20.69 0.46 0.67 41.26 0.58 13 2.2467 1.5425 0.85 0.75 15.95 0.50 0.57 32.66 0.65 14 6.3391 1.0793 0.86 0.74 2.85 0.51 0.75 17.92 0.50 15 4.993 1.1311 0.89 0.62 14.25 0.62 0.59 23.15 0.64 16 0.1672 2.231 0.90 0.40 –1.45 0.78 0.63 4.35 0.61 17 0.7075 1.8809 0.79 0.76 24.41 0.49 0.81 3.74 0.44
*Combination method (physical similarity and regression); PBIAS is in percentage (%) and others are unitless.
Figure 3.5 Correlation between the SRC model parameters.
R² = 0.8454 0
1 2 3
0 1 2 3 4 5 6 7
b-value
a-value
Figure 3.6 Graphical illustration of SRC in Catchment No. 8.
The physical shapes (convex, linear and concave) of SRCs could be employed also to infer specific hydrological factors/processes. In this case study, there are no convex forms observed in all 17 catchments (Figure 3.7), suggesting that the river flows are not sediment-starved (or sediment supply-limited). This also indicates that the data used to construct SRCs were not affected by manmade hydraulic structures (e.g. dam-reservoirs).
According to the Lower Mekong Hydropower Database (MRC, 2009b), there were no hydropower dams operating in the study catchments during which the considered datasets were collected. Figure 3.7 illustrates the panel plot of all fitted SRCs. It is apparent that, at low discharge, slopes of the rating curves are not different drastically although catchment characteristics vary spatially. This explains that unit stream power is not a sensitive factor controlling sediment erosion/transport during low flow period. On the other hand, at high discharge, they differ greatly with respect to different catchment characteristics. The fitted SRCs behave from near linear in C14 to severely concave in C16. A linear curve represents a relationship between Qs and SSYs which does not change much during the considered period. A concave shape indicates that re-deposited materials are transported coincidently with flows higher than those of the prior events. In other words, there is a lag time between peak water discharge and peak sediment movement.
The average lag time in the Lower Mekong Basin is approximately 1.7 days (a finding in Chapter 5).
SSYs= 0.7111(Qs)1.9775 R² = 0.6353
0 1,000 2,000 3,000 4,000 5,000 6,000
0 10 20 30 40 50 60 70 80 90 100 SSYs(10-3 ton/day/km2)
Qs(10-3 m3/s/km2)
Figure 3.7 Panel plot of the 17 fitted sediment rating curves.
3.3.2 At-site calibration
Table 3.3 also presents the at-site calibration results in terms of model efficiency measured by NSE, PBIAS and RSR. The predictive accuracy in most of the study catchments is satisfactory, with NSE ranging from 0.40 to 0.87 (median = 0.68), PBIAS from –1.45% to 29.45% (median = 15.95%) and RSR from 0.37 to 0.78 (median = 0.56).
The different non-linear behaviors of sediment erosion/transport in space could explain the difference in model efficiency in different catchments. Only in C16, the predictive accuracy is marginally lower than the minimum satisfactory criteria (NSE > 0.50, PBIAS
±55% and RSR ≤ 0.70), but it is not dire since the NSE value (0.40) is greater than zero.
Negative NSE values indicate that the observed mean value is a better predictor than the model being used (Moriasi et al., 2007). The indicators of slightly low accuracy for this catchment could be due to significant variation of sediment erosion/transport temporally.
C16 is characterized by steep slope terrain (Sc = 37.95%), and, in consequence, the dominantly high erosivity and transport power may initiate high rates of sediment transport over a short time, especially during flood events. Furthermore, the large drainage area (19,704 km2) and complex physical characteristics (high Sc and Sr but low CUSLE and KUSLE) of the catchment might be the main factors leading to significant hysteretic effect (lag between Qs and SSYs) or the eroded materials may require several transporting events to reach the catchment outlet. Data uncertainty, including
0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
0 20 40 60 80 100 120 140 160
SSYs(10-3ton/day/km2)
Qs(10-3m3/s/km2)
16
11
4
12 8
6 13
5 9
10 17
7
2 1
15 3
14
Rema rk: curve la bel is the ca tchment number/name
measurement errors and low sampling frequency, might be also the reason because the catchment is situated in a remote mountainous area. Another factor could be attributed to shortcomings of the model itself that cannot deal with the entire erosion and sediment transport processes. For regionalization purpose, this modeled catchment (C16) was not discarded because it can introduce a diversity that could be advantageous for ungauged catchment modeling (Oudin et al., 2008).
Apart from statistical analyses, more qualitative graphical investigations (time series comparison and scatter plot) were conducted as well. The observed and predicted SSYs
time series generally show similar trends in all years for all catchments. Figure 3.8a shows an example of graphical comparison between the observed and predicted SSYs (at-site calibration) in C3. The model over- and under-estimates the extreme low and high values, respectively. This situation was found in the majority of catchments. This is a common issue when the prediction is carried out using a sediment rating curve because the model, in general, fails to encompass flood events in their entirety (Horowitz, 2003;
Zhang et al., 2012). The SRC model describes the average relationship between Qs and SSYs, and therefore cannot simulate well the extreme low and high values. Although this shortcoming is often noted, this model has been widely used for many engineering and scientific purposes (Wang et al., 2007).
Figure 3.8 Graphical comparison between the observed and predicted SSYs in Catchment No. 3.
0 500 1,000 1,500 2,000
Ja n-80 Ja n-84 Ja n-88 Ja n-92 Ja n-96 Ja n-00 SSYs(10-3ton/day/km2)
Observed Predicted
0 1 10 100 1,000 10,000
0 1 10 100 1,000 10,000 PredictedSSYs(10-3ton/day/km2)
Observed SSYs(10-3ton/day/km2) (a) At-site calibration (no data in 1995-96)
0.1 0.1
0 500 1,000 1,500 2,000
Ja n-80 Ja n-84 Ja n-88 Ja n-92 Ja n-96 Ja n-00 SSYs(10-3ton/day/km2)
Observed Predicted
0 1 10 100 1,000 10,000
0 1 10 100 1,000 10,000 PredictedSSYs(10-3ton/day/km2)
Observed SSYs(10-3ton/day/km2) (b) Jack-knife validation (no data in 1995-96)
0.1 0.1
3.3.3 Level 1 regionalization
This section firstly discusses results of each basic regionalization approach (physical similarity, regression and spatial proximity). Then a comparative analysis was performed so as to highlight each individual approach’s potential for prediction. This information was further used in the Level 2 regionalization, coming up next.
3.3.3.1 Regionalization using physical similarity approach
There are two main parts in this sub-section. The first part is the comparison between the four CSI measures, on the basis of single donor method. In using the best CSI measure, the second part is the comparison between the single donor and multiple donors method.
Four measures of catchment similarity index (CSI), namely CSI1, CSI2, CSI3 and CSI4, were employed alternatively for regionalization of the SRC model parameters from donor catchments to ungauged catchments. Figure 3.9 shows the predictive accuracy corresponding to each CSI measure (using 17 catchments). Based on the statistical model performance and rate of satisfactorily modeled catchments, CSI2, CSI3 and CSI4 are comparable and they provide slightly better results than CSI1. Although only a marginal difference was observed, the ideal similarity measure can be arranged downwards as CSI4, CSI3, CSI2 and CSI1. By using CSI4, satisfactory results were obtained for most of the catchments except C3 and C7. C3 is the donor catchment of C7 and vice versa. More interestingly, this situation was found also in the cases using CSI1, CSI2 and CSI3 (Table 3.4). The poor predictive power for these two catchments might be due to the effect of data heterogeneity caused by various factors such as local human activities, climate variation, land use changes and extreme events over the study period, about 20 years or more (Sivapalan et al., 2003). In order to verify this suspicion, the SSY annual series (SSYas time series) at sites having 20-year data or more were tested against homogeneity by using the Pettitt test. This non-parametric test was employed because it has been used widely and does not require any statistical assumption of the data distribution (Eris &
Agiralioglu, 2012). As a result, a heterogeneous dataset can be detected in C7 (Table 3.5).
This evidence clearly explains why the model predictive accuracy in this catchment is extremely worse (NSE = –1.30, PBIAS = –89.02%, RSR = 1.52). Moreover, it results in a poorly calibrated model, leading to low predictive accuracy in C3.
When C7 is suspended, the predictive accuracy in C3 is improved significantly with C4 as the donor catchment. NSE increases from 0.47 to 0.85, PBIAS decreases from 49.28% to 1.26%, and RSR decreases from 0.73 to 0.39. This is for the cases using CSI2, CSI3 and CSI4. In the case using CSI1, the results in C3 are not improved with C2 as the donor catchment. This might be due to the weakness of CSI1 itself in searching proper donor catchment. This issue was discussed in the latter part. Hence, C7 was considered as an outlier catchment and discarded from the analysis. After discarding C7, the effectiveness of each CSI was re-evaluated. The predictive accuracy is enhanced overall when comparing with the evaluation based on 17 catchments (Figure 3.9). A satisfactory result was obtained in all 16 modeled catchments when a donor catchment was selected
according to the minimum CSI4. CSI3, CSI2 and CSI1 provide unsatisfactory results for one, two and six catchments, correspondingly. These catchments are reported in Table 3.4.
Table 3.4 List of donor catchments selected using different CSI measures.
Catchment Using 17 catchments Using 16 catchments
CSI1 CSI2 CSI3 CSI4 CSI1 CSI2 CSI3 CSI4
1 15 15 15 15 15 15 15 15
2 12 12 12 12 12 12 12 12
3 7 7 7 7 2 4 4 4
4 8 11 11 11 8 11 11 11
5 15 15 15 15 15 15 15 15
6 12 12 12 12 12 12 12 12
7 3 3 3 3 ‒ ‒ ‒ ‒
8 4 11 11 11 4 11 11 11
9 10 10 10 10 10 10 10 10
10 9 9 9 9 9 9 9 9
11 4 4 4 4 4 4 4 4
12 2 2 2 6 2 2 2 6
13 6 6 6 6 6 6 6 6
14 3 1 1 1 3 1 1 1
15 5 5 1 1 5 5 1 1
16 17 17 17 17 17 17 17 17
17 9 16 9 9 9 16 9 9
Donor catchments in bold format with grey highlight indicate unsatisfactory model results.
CSI3 and CSI4 provide the same results in 15 catchments. The results are different only in C12. Using CSI3, the predictive accuracy in this catchment is not satisfactory with C2 as the donor catchment. In the case using CSI4, an acceptable result was obtained while the selected donor is C6. Normalization by standard deviation used in CSI3 is ideal with data normally distributed. Among the six catchment descriptors considered in this research, the degree of being normally distributed is rather low for the A0 and Sr dataset.
Their skewness coefficient (2.37 for A0 and 1.57 for Sr) is relatively larger than zero, indicating highly skewed to the right. This is because the study includes few catchments having extremely large drainage area and few having extremely steep river channel, in comparison with the majority. For other catchment descriptors, their skewness coefficient is around zero. It should be noted that a data normal distribution is corresponding to skewness coefficient about zero. This issue might be a drawback of CSI3, causing a mal-selection of donor catchment for C12. For CSI4, it does not depend on the statistical distribution pattern of catchment descriptor datasets.
Between CSI2 and CSI4, the results are different in C12, C15 and C17. CSI2 is inferior to CSI4 in all the three catchments. This inferiority is due to the fact that, for each catchment descriptor, CSI2 does not put heavy penalty on candidate donor catchments
behaving extremely different from the target ungauged catchment. For instance, CSI2
points out C16 as the best donor for C17 although both catchments are very dissimilar in terms of A0 and CUSLE. Because of the squared difference (Eq. (3.10)), CSI4 penalizes severely the outlier candidate donor catchments and therefore points out C9 as the best donor for C17 since both catchments are moderately similar with regard to all descriptors.
CSI1 and CSI4 provide different results in six modeled catchments (Table 3.4). In all the six catchments, results of CSI1 are totally worse than those of CSI4, and they also do not pass the minimum satisfactory criteria. This shortcoming could be explained by the rank value which is the positive integer varying from 1 to N (number of candidate donor catchments); hence, it does not express well the degree of goodness (similarity magnitude to the target ungauged catchment) of different candidate donor catchments. Moreover, some catchment information might be lost because the mean rank (CSI1) was computed by just averaging the rank values from ranking processes based on different catchment descriptor sets. Unlikely, CSI4 was computed as a function of catchment descriptors directly and therefore contains all the catchment information.
Briefly, CSI4 was judged as the most superior CSI measure in searching a proper donor catchment for regionalization process. It is followed subsequently by CSI3, CSI2
and CSI1. Among the six catchment descriptors used to compute CSI4, Qas and KUSLE are more sensitive than the others (Figure A.10). In using the CSI4 measure, the comparative analysis between the single donor and multiple donors method is presented as below.
Table 3.5 Homogeneity test of the SSY annual series at 0.01 significance level.
Catchment p-value Accept/reject H0
1 0.434 Accept
2 0.297 Accept
3 0.544 Accept
4 0.024 Accept
5 N/A N/A
6 N/A N/A
7 0.001 Reject
8 N/A N/A
9 N/A N/A
10 0.475 Accept
11 0.803 Accept
12 0.358 Accept
13 0.453 Accept
14 0.338 Accept
15 0.336 Accept
16 N/A N/A
17 N/A N/A
Null hypothesis (H0): data series is homogeneous; N/A: not applicable (available data less than 20 years, not tested).
Figure 3.9 Distribution of error indicators (NSE, PBIAS and RSR) and rate of satisfactorily modeled catchment corresponding to different regionalization methodologies in the physical similarity approach. Each circular point stands for one modeled catchment. The dash mark indicates the median value. The bar chart shows the rate of satisfactorily modeled catchment.
-5 -4 -3 -2 -1 0 1
NSE
-200 -150 -100 -50 0 50 100
PBIAS(%)
0.0 0.5 1.0 1.5 2.0 2.5
RSR
20 40 60 80 100
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Rate of satisfactorily modeled catchment (%)
0.50
-55%
+55%
0.70
CSI1 CSI2 CSI3 CSI4 CSI1 CSI2 CSI3 CSI4 CSI4≤ 0.5 CSI4≤ 0.8 CSI4≤ 1.2 CSI4≤ 1.5 Global mean CSI4≤ 0.5 CSI4≤ 0.8 CSI4≤ 1.2 CSI4≤ 1.5 Global mean
Output a vera ging
Single donor method Multiple donors method 17
ca tchments
16 ca tchments
Pa ra meter a vera ging Loca l
mea n
Loca l mea n
It should be noted that C7 was not included in the following analysis. Based on the distribution of CSI4 values (0.23–2.12), for the local mean method, multiple donor catchments were selected within four alternative regions: CSI4 ≤ 0.5, CSI4 ≤ 0.8, CSI4 ≤ 1.2 and CSI4 ≤ 1.5. Figure 3.9 apparently shows that the predictive accuracy decreases with an increase in radius of CSI or number of donor catchments, in both output and parameter averaging option. This is due to large errors introduced by inclusion of some donor catchments having less similarity to the target ungauged catchment. Even if the two options provide comparable results, parameter averaging is slightly superior to output averaging because large errors contained in model parameters of some selected donor catchments are reduced by compensation with the others. This also reveals that parameter uncertainty is a major source of output uncertainty.
In comparison with the single donor method, the multiple donors one provides results with higher uncertainty, larger range of error indicators (NSE, PBIAS and RSR), and less number of satisfactorily modeled catchments (Figure 3.9). Since there have been no similar studies conducted previously, this finding was discussed with some earlier researches related to regionalization for continuous rainfall-runoff models. McIntyre et al.
(2005), Oudin et al. (2008) and Zhang & Chiew (2009) found that using a number of donor catchments gives better results than using only one donor because the effect of choosing a poor donor is averaged out. Nevertheless, there is no common finding on the optimum number of donor catchments. It is observed that it mainly varies with the number of candidate donor catchments available for regionalization analysis. Compared to these three earlier researches, the amount of candidate donor catchments available for use in the present study is relatively less. Therefore, it is impossible to get complementary information from many good donors. However, the chance of successfully choosing the best donor (single donor method) is high because the degree of goodness of all candidate donor catchments can be differentiated easily. It also means that the single donor method is more powerful than the multiple donors one, in studies having less number of available candidate donor catchments.
To sum up, in the physical similarity approach, the single donor method was judged to provide better regionalization results than the multiple donors method. By applying the CSI4-based regionalization approach (single donor method), SSYs in ungauged catchments could be predicted with good accuracy, showing NSE results between 0.54 and 0.85 (median = 0.63), PBIAS between –41.84% and 44.62% (median = 6.44%), and RSR between 0.39 and 0.68 (median = 0.61). A satisfactory result was obtained in all 16 (100%) modeled catchments. This refined methodology was selected to compare with the other two regionalization approaches.
3.3.3.2 Regionalization using regression approach
It should be noted that C7 was also excluded in this sub-section. As presented in Table 3.6, the rating coefficient (a) exhibits good relationship with Qas, Sc, Sr and CUSLE, but very poor relationship with A0. In the case of the rating exponent (b), it has a good relationship with Sc, Sr and CUSLE, but very poor relationship with A0. In the Universal Soil Loss Equation family (USLE, RUSLE and MUSLE), KUSLE and CUSLE are generally
integrated in form of multiplication (USBR, 2006). Since not only a-KUSLE but also b-KUSLE shows relatively low correlation, the integrated descriptor (KUSLE×CUSLE) was investigated. As a result, better correlation was obtained if comparing with KUSLE or CUSLE alone (Table 3.6). Therefore, KUSLE×CUSLE was accounted to build the model parameter-catchment descriptor relationship instead of KUSLE and CUSLE separately.
Table 3.6 Correlation between model parameters and catchment descriptors.
Catchment descriptor
Rating coefficient (a) Rating exponent (b)
Function type R2 p-value Function type R2 p-value
A0 Linear 0.00 0.8235 Linear 0.09 0.2790
Qas Exponential 0.62 0.0005 Linear 0.35 0.0190
Sc Exponential 0.64 0.0004 Exponential 0.85 < 0.0001
Sr Power 0.70 < 0.0001 Logarithmic 0.59 0.0008
KUSLE Linear 0.16 0.1451 Linear 0.30 0.0344
CUSLE Power 0.62 0.0005 Power 0.83 < 0.0001
KUSLE×CUSLE Power 0.63 0.0004 Power 0.85 < 0.0001
Strategy 1 ML 0.75 < 0.0001 ML 0.86 < 0.0001
Strategy 1 EML 0.80 < 0.0001 EML 0.86 < 0.0001
Strategy 1 PN 0.82 < 0.0001 PN 0.87 < 0.0001
Strategy 2 ML 0.75 < 0.0001 ML 0.89 < 0.0001
Strategy 2 EML 0.80 < 0.0001 EML 0.90 < 0.0001
Strategy 2 PN 0.82 < 0.0001 PN 0.94 < 0.0001
Strategy 1: a = f(Qas, Sc, Sr, KUSLE×CUSLE) and b = f(Sc, Sr, KUSLE×CUSLE); Strategy 2: a = f(Qas, Sc, Sr, KUSLE×CUSLE) and b = f(Qas, Sc, Sr, KUSLE×CUSLE); ML: multiple linear; EML: exponential multiple linear;
PN: polynomial.
In Strategy 1, a-parameter is in function with Qas, Sc, Sr and KUSLE×CUSLE, and b-parameter is similar but without Qas. In Strategy 2, both a- and b-parameter are in function with Qas, Sc, Sr and KUSLE×CUSLE. In both strategies, the both sediment yield curve model parameters and the catchment descriptors from all 16 catchments were used firstly to fit three types of regression functions, as mentioned earlier in Section 3.2.4.2.
The polynomial function produces the largest value of R2 and it is followed subsequently by the exponential multiple linear and multiple linear one (Table 3.6). However, the difference is likely not significant. Good relationships (R2 ≥ 0.49 and p-value < 0.01) were observed in all cases and this indicates the use of enough sample size for regression fitting. Although the exponential multiple linear function is slightly inferior to the polynomial one, it has a rather simpler form, and thus preferable (simpler calculation process due to less number of parameters). Shortly, the exponential multiple linear form was selected to perform the Jack-knife validation.
Table 3.7 tabulates the Jack-knife validation results in all modeled catchments.
Strategy 1 and 2 produce four and three unsatisfactorily modeled catchments, respectively.
This could be explained by some uncertainties present in the model parameter-catchment descriptor relationships. Additionally, in the majority of catchments, Strategy 2 is
superior to Strategy 1. This superiority reveals that Qas is also an important descriptor although it has little correlation with model parameters. As shown in Table 3.7, Strategy 2 does not perform well in C2, C8 and C9 but the corresponding results are not very poor, since the NSE values are greater than zero while the PBIAS values are within the satisfactory criterion.
Table 3.7 Jack-knife validation results (regionalization using regression approach).
Catchment Strategy 1 Strategy 2
NSE PBIAS (%) RSR NSE PBIAS (%) RSR
1 0.64 15.30 0.60 0.64 10.08 0.60
2 0.18 –68.35 0.91 0.48 –48.76 0.72
3 0.88 17.63 0.35 0.78 33.75 0.47
4 0.57 –14.99 0.66 0.67 20.38 0.58
5 0.68 21.55 0.56 0.70 –4.08 0.55
6 0.63 25.48 0.61 0.65 10.05 0.59
7 ‒ ‒ ‒ ‒ ‒ ‒
8 0.49 33.51 0.71 0.02 –39.28 0.99
9 0.61 40.92 0.63 0.50 49.24 0.71
10 0.63 13.25 0.61 0.61 7.17 0.62
11 0.74 13.19 0.51 0.79 3.92 0.46
12 0.63 45.53 0.61 0.67 41.26 0.58
13 0.73 7.06 0.52 0.57 32.66 0.65
14 0.66 –5.82 0.58 0.75 17.92 0.50
15 0.55 32.56 0.67 0.59 23.15 0.64
16 0.38 61.99 0.79 0.57 42.81 0.66
17 0.11 –57.67 0.94 0.81 5.24 0.44
Bold figures with grey highlight indicate unsatisfactory model results.
Last but not least, Strategy 2 was judged to provide better regionalization results than Strategy 1. By applying the regression-based regionalization approach (exponential multiple linear function, Strategy 2), SSYs in ungauged catchments could be predicted with resulting NSE between 0.02 and 0.81 (median = 0.65), PBIAS between –48.76% and 49.24% (median = 14.00%), and RSR between 0.44 and 0.99 (median = 0.59). A satisfactory result was obtained in 13 (81%) out of 16 modeled catchments. This refined methodology was selected to compare with the other two regionalization approaches.
3.3.3.3 Regionalization using spatial proximity approach
In this sub-section, C7 was also excluded from the analysis. For the local mean method, multiple donor catchments were selected within four alternative regions: D ≤ 50 km, D ≤ 100 km, D ≤ 200 km and D ≤ 300 km. Figure 3.10 shows the distribution of error indicators (NSE, PBIAS and RSR) and rate of satisfactorily modeled catchment corresponding to different regionalization methodologies. In both output and parameter averaging option, the predictive accuracies are comparable among the last three cases of the local mean method. This is because the number of donor catchments is not greatly different between each case (particularly for the cases of D ≤ 100 km and D ≤ 200 km), and/or catchments situated within a region of D ≤ 300 km may not behave very differently. In the case of D ≤ 50 km, there are only nine feasible catchments and therefore, quality of the corresponding results is rather low. The relatively poor results of the global mean method could be explained by spatial catchment heterogeneity. Donor catchments located farther than 300 km might behave more differently from the target ungauged catchment and thus introduce large errors in the average outputs or model parameters.
Parameter averaging is somewhat superior to output averaging even though there is only a marginal difference between the two options (Figure 3.10). This is consistent with the regionalization using physical similarity approach. Moreover, the best case of the multiple donors method (D ≤ 300 km, parameter averaging option) provides to some extend a better regionalization solution than the single donor method. On the contrary, in the physical similarity-based regionalization approach, the multiple donors method is inferior to the single donor one. Such difference could be due to the fact that the nearest donor catchment selected by using the single donor method (spatial proximity) is not the best one. In the group of donor catchments determined by the multiple donors method, there could be the best donor which is not the nearest to the target ungauged catchment, or it contains at least some donors which are better than the nearest one. Consequently, the geographical closeness of catchments does not guarantee their similar behavior. To justify this statement, D and CSI (CSI4) between the entire catchments were calculated and are presented as a bivariate plot in Figure 3.11. D exhibits a positive correlation with CSI but the relationship is rather weak. Therefore, the rationale for the spatial proximity approach has a reasonable basis in light of this relationship.
Shortly, in the spatial proximity approach, the use of multiple donor catchments provides a better regionalization solution than the use of only one donor. By applying the multiple donors method (D ≤ 300 km, parameter averaging option), SSYs in ungauged catchments could be predicted with resulting NSE between 0.01 and 0.88 (median = 0.59), PBIAS between –48.14% and 48.76% (median = 9.46%), and RSR between 0.35 and 0.99 (median = 0.64). A satisfactory result was obtained in 12 (75%) out of 16 modeled catchments. This refined methodology was selected to compare with the other two regionalization approaches.
Figure 3.10 Distribution of error indicators (NSE, PBIAS and RSR) and rate of satisfactorily modeled catchment corresponding to different regionalization methodologies in the spatial proximity approach. Each circular point stands for one modeled catchment. The dash mark indicates the median value. The bar chart shows the rate of satisfactorily modeled catchment.
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0
NSE
-150 -100 -50 0 50 100
PBIAS(%)
0.0 0.5 1.0 1.5 2.0
RSR
20 40 60 80 100
0 1 2 3 4 5 6 7 8 9 10 11
Rate of satisfactorily modeled catchment (%)
0.50
-55%
+55%
0.70
D≤ 300 km
D≤ 200 km
D≤ 100 km
D≤ 50 km
Single donor Globalmean D≤ 300 km
D≤ 200 km
D≤ 100 km
D≤ 50 km Globalmean
Multiple donors method Loca l mea n
Pa ra meter a vera ging Output a vera ging
Loca l mea n
Figure 3.11 Bivariate plot between CSI and D.
3.3.3.4 Comparative analysis
The three basic regionalization approaches, based on their refined methodology determined above, were compared in this sub-section. They are:
Physical similarity approach: single donor method (CSI4)
Regression approach: exponential multiple linear function (Strategy 2)
Spatial proximity approach: multiple donors method (D ≤ 300 km, parameter averaging option)
The statistical performance of each basic regionalization approach in parameterizing SRC in ungauged catchments for subsequent SSYs prediction is summarized in Table 3.8.
Physical similarity was judged as the most outstanding approach because it produces satisfactory results for all modeled catchments. Furthermore, the uncertainty (range of NSE, PBIAS and RSR) of this superior approach is less than that of the other two techniques (Figure 3.12). The regression approach is intermediate, while spatial proximity is the least satisfactory. The inferiority of the regression approach could be explained by the uncertainty existing in the fitted model parameter-catchment descriptor relationships.
The diminished effectiveness of the spatial proximity approach is due to catchment heterogeneity. The hypothesis of nearby catchments having similar characteristics has little validity in the study area because of the sparse gauging system. The result of this study is in contrast with that of Parajka et al. (2005), Oudin et al. (2008) and Zhang &
Chiew (2009) in which the analysis was based on a large set of catchments (hundreds).
On the other hand, it is consistent with that of Bao et al. (2012) whose study investigated in 55 catchments. It is worth emphasizing that these earlier research efforts are in the context of streamflow modeling. Briefly, any study area with a low density network of gauging stations is favorable disposed to the application of a physical similarity-based regionalization approach.
R² = 0.3445 0.0
0.5 1.0 1.5 2.0 2.5
0 200 400 600 800 1,000
CSI
D(km)
Table 3.8 Statistical performance of refined regionalization methodologies in Level 1 and 2.
Approach Indicator Maximum Minimum Median Pass
Physical similarity: single donor method (CSI4)
NSE 0.85 0.54 0.63
16 PBIAS (%) 44.62 –41.84 6.44
RSR 0.68 0.39 0.61
Regression: exponential multiple linear function (Strategy 2)
NSE 0.81 0.02 0.65
13 PBIAS (%) 49.24 –48.76 14.00
RSR 0.99 0.44 0.59
Spatial proximity: multiple donors method (D ≤ 300 km, parameter averaging option)
NSE 0.88 0.01 0.59
12 PBIAS (%) 48.76 –48.14 9.46
RSR 0.99 0.35 0.64
Ensemble: physical similarity & regression
NSE 0.88 0.38 0.64
15 PBIAS (%) 42.94 –45.30 12.43
RSR 0.79 0.35 0.60
Combination: physical similarity & regression
NSE 0.85 0.54 0.65
16 PBIAS (%) 41.26 –41.84 9.49
RSR 0.68 0.39 0.59
Pass: number of satisfactorily modeled catchments (NSE > 0.50, PBIAS ±55%, RSR ≤ 0.70).
Figure 3.12 Distribution of error indicators (NSE, PBIAS and RSR) and rate of satisfactorily modeled catchment corresponding to refined regionalization methodologies of physical similarity (PS), regression (RE) and spatial proximity (SP) approach in Level 1, and ensemble (ENS) and combination method (COM) in Level 2. PS: single donor method (CSI4); RE: exponential multiple linear function (Strategy 2); SP: multiple donors method (D ≤ 300 km, parameter averaging option); ENS1: PS, RE and SP; ENS2: PS and RE; ENS3: PS and SP; COM: PS and RE. Each circular point stands for one modeled catchment. The dash mark indicates the median value. The bar chart shows the rate of satisfactorily modeled catchment.
0.0 0.2 0.4 0.6 0.8 1.0
NSE
-75 -45 -15 15 45 75
0 1 2 3 4 5 6 7
PBIAS(%)
0.2 0.4 0.6 0.8 1.0
RSR
50 60 70 80 90 100
0 1 2 3 4 5 6 7 Rate of satisfactorily modeled catchment (%)
0.50
0.70
ENS3
+55%
-55%
ENS2
ENS1 COM
SPRE
PS ENS3
ENS2
ENS1 COM
SPRE
PS
3.3.4 Level 2 regionalization
According to the finding in Level 1 above, two alternatives mainly associating the physical similarity approach (the best out of the three) were investigated in this Level 2 regionalization. They are based on the ensemble and combination method. In the following sub-sections, step by step, the results of each alternative were compared with those of the outstanding basic approach, i.e. physical similarity: single donor method (CSI4). Finally, the best alternative was considered as the ideal regionalization methodology. It should be noted that, in this section, the use of the three basic regionalization approaches (physical similarity, regression and spatial proximity) is referred to their refined methodology as stated in Section 3.3.3.4.
3.3.4.1 Regionalization using ensemble method
Three different cases were considered in the ensemble method: ENS1 composes of the three basic regionalization approaches; ENS2 composes of the physical similarity and regression approach; and ENS3 composes of the physical similarity and spatial proximity approach. Figure 3.12 presents the results corresponding to each ensemble case. ENS1 and ENS3 are comparable and both of them are worse than ENS2 to some extent. ENS2 yields a satisfactory result in 15 (94%) out of 16 modeled catchments. ENS1 and ENS3 offer the same rate of satisfactory modeled catchment (88%). The lower predictive accuracy in ENS1 and ENS3 is due to large errors produced by the spatial proximity approach.
Because of the predominantly good results provided by the physical similarity approach, the ensemble method (all three cases) outperforms the stand-alone regression and spatial proximity approach (Figure 3.12). However, even the best ensemble case (ENS2), it is inferior to the outstanding basic approach (Figure 3.12 and Table 3.8). In conclusion, the ensemble method does not improve the overall predictive accuracy.
3.3.4.2 Regionalization using combination method
According to the results and discussion in Section 3.3.4.1, spatial proximity was not involved in this alternative. Moreover, physical similarity performs better than or equally to this approach in a large majority of catchments (more than 70%). Between the physical similarity and regression approach, the number of catchments with satisfactory scores is comparable. Therefore, in this alternative, only a combined formulation of physical similarity and regression was investigated.
As a result of catchment classification, only Sc and KUSLE×CUSLE provide consistent results (Figure 3.13). Almost all catchments (6/7) characterizing Sc < 21.40% and KUSLE×CUSLE > 0.01 can be modeled with strongly favorable results using the regression-based approach. A majority of catchments (6/9) characterizing Sc > 21.40% and KUSLE×CUSLE < 0.01 are likely to be well characterized using the physical similarity approach. As Figure 3.14 showed, there is a larger variance for the group of catchments with Sc < 21.40% and KUSLE×CUSLE > 0.01, indicating higher spatial variability of model parameters or higher degree of catchment heterogeneity. In this circumstance, the