# Applicability Assessment and Uncertainty Analysis of Multi-Precipitation Datasets for the Simulation of Hydrologic Models

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## Abstract

**:**

## 1. Introduction

## 2. Material and Methods

#### 2.1. Study Area

^{2}. The basin is an important headwater for the downstream Guilin City and has a sparse and unevenly distributed meteorological observation network.

#### 2.2. Dataset Acquisition

^{4}km

^{2}) is 0.91 (calculated using the kernel-density estimation for a search radius of 100 km; see Supplementary Materials for more details). The remote-sensing products are using the TRMM–TMPA product (also denoted TMPA-3B42V7) available from the National Aeronautics and Space Administration (NASA) official website (https://pmm.nasa.gov/trmm). The reanalysis data originate from the CMADS V1.0 product available from World Data System for Cold and Arid Regions (CARD) official website (http://westdc.westgis.ac.cn). The precipitation and maximum temperature values from 13 national meteorological stations are available from the Meteorological Data network (http://data.cma.cn/).

#### 2.3. Rainfall–Runoff Models

#### 2.4. Model Performance Evaluation Criteria

_{sq}and NSE

_{log}hereafter), which makes it possible to assess the model efficiency for low flowrates [62]. The use of these three criteria (NSE, NSE

_{sq}and NSE

_{log}) gives a more general overview of the model efficiency and are defined as

#### 2.5. Performance of Precipitation Detection

#### 2.6. Generalized Likelihood Uncertainty Estimation Method

- (1)
- A large number of models are run with randomly chosen parameter sets selected from a probability distribution; here, 100,000 group parameters are chosen obeying a uniform distribution.
- (2)
- Definition of the “likelihood” function (here, the performance measures NSE and NSElog) and calculation of likelihood values corresponding to each parameter set.
- (3)
- Definition of a cut-off threshold value for the likelihood function to distinguish between the “behavioral” parameter sets and the “non-behavioral” parameter sets.
- (4)
- Rescaling of the cumulative likelihood values of all behavioral models to unity.
- (5)
- Calculation of the percentiles of the cumulative distribution of the likelihood measure. The GLUE method integrates the outputs of all behavioral models in an ensemble prediction. For each timestep of the simulation, the output prediction is obtained as the median of the distribution of all ensemble members, with its uncertainty bounds estimated as the 5% and 95% percentiles of the distribution.

## 3. Results

#### 3.1. Evaluation of Model Performance

_{sq}and NSE

_{log}is also calculated. Since NSE

_{sq}and NSE

_{log}shift the focus from high flows to progressively lower flows, using NSE

_{sq}and NSE

_{log}help us judge the performance of the models in simulating over a broader range of flows. The performance of the IHACRES model shows that the CMADS dataset has the best performance among all three precipitation products during the calibration period. The TMPA-3B42V7 and gauge-interpolated product have a similar performance but perform slightly worse than the CMADS dataset. During the validation period, the NSE, NSE

_{sq}and NSE

_{log}values when using the CMADS dataset show a better performance than other precipitation datasets, which indicates the CMADS dataset performs better than other precipitation datasets in simulating both high flow and low flows. Overall, all the three precipitation datasets perform well, with the CMADS dataset performing slightly better.

#### 3.2. Precipitation Detection

#### 3.3. Uncertainty Analysis

_{log}are used as the “likelihood” functions. Using a threshold value of NSE > 0.67 (or NSE

_{log}> 0.78) for the CMADS product, the GLUE algorithm finds 2000 (1416) behavioral solutions in 100,000 simulations with the IHACRES model. Using a threshold value of NSE > 0.56 (or NSE

_{log}> 0.69) for the TMPA-3B42V7 product, the GLUE algorithm finds 3180 (2819) behavioral solutions in 100,000 simulations with the IHACRES model.

_{log}(NSE) as the likelihood function, with the calibrated parameter set for each rainfall dataset indicated. From the distribution of behavioral parameter sets, we see the parameters d, f and tau_s have behavioral values distributed across the full parameter range, indicating these have the greatest uncertainty. In comparison, the distribution of v_s for behavioral parameter sets is constricted to smaller values (<~0.5), particularly when using considering NSE. The values of tau_q are more constrained when considering NSE, due to the focus NSE gives to high flows compared to NSElog. Generally, there is little interaction between most of the parameters. The main exception is the e and f parameters. The value of the e parameter is constrained to <~0.1 providing f > ~1, increasing rapidly for smaller values of f. This indicates a highly non-linear interaction between these parameters. It should also be noted that the optimal value of the e parameter is considerably smaller than that found in Australia (0.166) found by Chapman (2001) [68], due to the influence of other factors (e.g., atmospheric transmissivity).

_{log}are again defined as the likelihood functions. Using a threshold value of NSE > 0.45 (or NSE

_{log}> 0.53), the GLUE algorithm finds 929 (359) behavioral solutions in 100,000 simulations for the CMADS product with the Sacramento model. Using a threshold value of NSE > 0.32 (or NSE

_{log}> 0.43), the GLUE algorithm finds 1294 (140) behavioral solutions in 100,000 simulations for the TMPA-3B42V7 product with the Sacramento model. The pairwise correlation of behavioral parameters for the Sacramento model is shown in Figure 7.

_{log}is selected as the likelihood function, the distribution of the parameters uztwm, lztwm and adimp is relatively low and the distribution of the parameter pfree is relatively high, which indicates that these parameters may be more sensitive and less uncertain.

_{log}> 0.5), the GLUE algorithm finds 5186 (12,095) behavioral solutions in 100,000 simulations for the CMADS precipitation product with the IHACRES model, while the GLUE algorithm achieves 1056 (9929) and 576 (9144) behavioral solutions in 100,000 simulations for the TMPA-3B42V7 and gauge-interpolated products with the IHACRES model. Therefore, the behavioral parameter space of the IHACRES model driven by the CMADS precipitation is larger than the behavioral parameter space driven by the other two precipitation inputs. The CMADS product gives a better performance than the TMPA-3B42V7 and gauge-interpolated products, because CMADS assimilated datasets are based on the large number of stations (nearly 40,000 regional automatic stations and 2421 national automatic stations in China), which gives it any priority in reflecting the actual processes of areal precipitation.

_{log}> 0.5), the GLUE algorithm finds 32 (60) behavioral solutions in 100,000 simulations for the CMADS precipitation dataset within the Sacramento model, while the GLUE algorithm achieves 0 (11) and 0 (5) behavioral solutions in 100,000 simulations for the TMPA-3B42V7 and gauge-interpolated products with the Sacramento model. Similar to their performance with the IHACRES model, the behavioral parameter space of the Sacramento model driven by the CMADS precipitation dataset is larger than the behavioral parameter space driven by the other two precipitation inputs. The CMADS product shows a better performance than the TMPA-3B42V7 and gauge-interpolated products, which, as mentioned before, is probably because the CMADS assimilated datasets are based on the strongly underconstrained large number of stations.

## 4. Discussion

_{log}, which gives more emphasis to low flowrates, is presented in the Supplementary Materials, as well as the model performance calibrated using NSE

_{log}as an objective function. Similar conclusions can be reached with the models calibrated using the performance measure NSE

_{log}as the objective function. The CMADS precipitation datasets perform best in all three precipitation datasets, followed by the TMPA-3B42V7 precipitation and then the gauge-interpolated product. Comparing the model performance using NSE

_{log}and NSE as the objective functions for calibration, the model calibrated using the performance measure NSE performed better in simulating peak flows, while underestimating low flowrates. In contrast, the model calibrated using the performance measure NSE

_{log}performs well in simulating low flowrates but underestimates the flood peak in the simulations.

## 5. Conclusions

_{log}as the likelihood function, the number and percentage of behavioral parameters for the corresponding precipitation datasets are 12,095 (12.1%), 9929 (9.93%) and 9144 (9.14%). Similar phenomena can be found with the same analysis of the Sacramento model in Table 8 but the behavioral parameter sets for that model are very sparse. We conclude that the CMADS precipitation-driven hydrologic models are more accurate, as they are responsible for more behavioral parameters than the hydrologic models driven by the other two precipitation datasets. The TMPA-3B42V7 datasets show slightly better performance than the gauge-interpolated product in this case study, indicating that global datasets are particularly useful in poorly gauged areas.

## Supplementary Materials

^{2})), Table S1: Mean absolute error (MAE), root mean square error (RMSE) and relative error of cross-validation for daily interpolated precipitation grids, Table S2: Overall performance (daily NSE

_{log}(monthly NSE)) of precipitation datasets for models using NSE

_{log}as the objective function for calibration, Table S3 Model performance of IHACRES model (calibrated using NSE

_{log}) for the calibration period and validation periods, Table S4 Model performance of Sacramento model (calibrated using NSE

_{log}) for the calibration period and validation periods, Figure S2: Observed and IHACRES-model-simulated daily and monthly runoffs for (a) Gauge-interpolated, (b) TMPA-3B42V7 and (c) CMDAS rainfall datasets (for the IHACRES model calibrated using NSE

_{log}as the objective function), Figure S3: Observed and Sacramento-model-simulated daily and monthly runoffs for (a) Gauge-interpolated, (b) TMPA-3B42V7 and (c) CMDAS rainfall datasets (for the Sacramento model calibrated using NSE

_{log}as the objective function)).

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Location of Lijiang River basin, China and meteorological stations for the ANUSPLIN interpolation technique.

**Figure 3.**Observed and IHACRES-model-simulated daily and monthly runoffs for (

**a**) Gauge-interpolated, (

**b**) TMPA-3B42V7 and (

**c**) CMDAS rainfall datasets (for the IHACRES model calibrated using NSE as the objective function).

**Figure 4.**Observed and Sacramento-model-simulated daily and monthly runoffs for (

**a**) Gauge-interpolated, (

**b**) TMPA-3B42V7 and (

**c**) CMDAS rainfall datasets (for the Sacramento model calibrated using NSE as the objective function).

**Figure 5.**The box plots for the contingency statistics of (

**a**) Proportion Correct (PC), (

**b**) Probability of Detection (POD), (

**c**) Frequency Bias Index (FBI), (

**d**) False Alarm Ratio (FAR), (

**e**) Critical Success Index (CSI), (

**f**) Heidke Skill Score (HSS). The labelled asterisk dot represent the mean value and the middle line in the box represent the median value. Each box ranges from the lower (25th) to upper quartile (75th).

**Figure 6.**Two-dimensional projections of pairwise correlation of behavioral parameters for the IHACRES model using the CMADS (above diagonal) and TMPA-3B42V7 (below diagonal) precipitation datasets. The heavy dots represent the location of the best objective function value obtained from the GLUE sample.

**Figure 7.**Two-dimensional projections of the pairwise correlation of behavioral parameters for the Sacramento model using CMADS (above diagonal) and TMPA-3B42V7 (below diagonal) precipitation datasets. The heavy dots represent the location of the best objective function value obtained from the GLUE sample.

Parameter Name | Unit | Range | Description |
---|---|---|---|

IHACRES-CMD | |||

f | - | 0.01–3 | CMD stress threshold as a proportion of d |

e | - | 0.01–1.5 | Temperature to potential evapotranspiration (PET) conversion factor |

d | mm | 50–550 | CMD threshold for producing flow |

tau_s | day | 30–600 | Time constant for slow flow store |

tau_q | day | 1–10 | Time constant for quick flow store |

v_s | - | 0.1–1 | Fractional volume for slow flow |

Sacramento | |||

UZTWM | mm | 1–150 | Upper zone tension water maximum capacity |

UZFWM | mm | 1–150 | Upper zone free water maximum capacity |

UZK | 1/day | 0.1–0.5 | Upper zone free water lateral depletion rate |

PCTIM | - | 0.000001–0.1 | Fraction of the impervious area |

ADIMP | - | 0–0.4 | Fraction of the additional impervious area |

ZPERC | - | 1–250 | Maximum percolation rate coefficient |

REXP | - | 0–5 | Exponent of the percolation equation |

LZTWM | mm | 1–500 | Lower zone tension water maximum capacity |

LZFSM | mm | 1–1000 | Lower zone supplementary free water maximum capacity |

LZFPM | mm | 1–1000 | Lower zone primary free water maximum capacity |

LZSK | 1/day | 0.01–0.25 | Lower zone supplementary free water depletion rate |

LZPK | 1/day | 0.0001–0.25 | Lower zone primary free water depletion rate |

PFREE | - | 0–0.6 | Fraction percolating from upper to lower zone free water storage |

**Table 2.**Contingency table for the ground observations and the Satellite/reanalysis estimate with a threshold of 1.0 mm.

Satellite/Reanalysis Estimate | Ground Observation | |
---|---|---|

Observation ≥ 1.0 mm | Observation < 1.0 mm | |

Estimate ≥ 1.0 mm | H | F |

Estimate < 1.0 mm | M | Z |

Metric | Formula | Range | Optimal Value |
---|---|---|---|

Proportion Correct | $\mathrm{PC}=\frac{H+Z}{N}$ | 0–1 | 1 |

Probability of Detection | $\mathrm{POD}=\frac{H}{H+M}$ | 0–1 | 1 |

Frequency Bias Index | $\mathrm{FBI}=\frac{H+F}{H+M}$ | 0–+∞ | 1 |

False Alarm Ratio | $\mathrm{FAR}=\frac{F}{F+H}$ | 0–1 | 0 |

Critical Success Index | $\mathrm{CSI}=\frac{H}{M+H+F}$ | 0–1 | 1 |

Heidke Skill Score | $\mathrm{HSS}=\frac{2\ast \left(Z\ast H-F\ast M\right)}{\left(Z+F\right)\ast \left(F+H\right)+\left(M+H\right)\ast \left(Z+M\right)}$ | −∞–1 | 1 |

**Table 4.**Overall performance (daily NSE (monthly NSE)) of precipitation datasets for models using NSE as the objective function for calibration.

IHACRES | Sacramento | |
---|---|---|

Gauged | 0.57 (0.83) | 0.52 (0.80) |

TRMM | 0.56 (0.89) | 0.56 (0.87) |

CMADS | 0.69 (0.93) | 0.70 (0.92) |

**Table 5.**Calibrated optimal parameters sets and daily NSE for each precipitation dataset applied to the IHACRES model (2008 to 2012).

Datasets | f | e | d | tau_q | tau_s | v_s | NSE |
---|---|---|---|---|---|---|---|

Gauged | 1.132 | 0.05149 | 80.55 | 2.420 | 30.00 | 0.10 | 0.61 |

TRMM | 1.060 | 0.06742 | 147.45 | 5.061 | 30.00 | 0.10 | 0.52 |

CMDAS | 3.000 | 0.08322 | 50.00 | 3.055 | 30.00 | 0.10 | 0.69 |

**Table 6.**Calibrated optimal parameter sets and daily NSE values for each precipitation dataset applied to the Sacramento model (2008–2012).

Datasets | uztwm | uzfwm | uzk | pctim | adimp | zperc | rexp |

Gauged | 1.000 | 93.5 | 0.322 | 0.0499 | 0.0656 | 149.7 | 3.420 |

TRMM | 1.000 | 140.1 | 0.102 | 1.01 × 10^{−6} | 1.76 × 10^{−8} | 140.8 | 1.205 |

CMDAS | 1.002 | 150.0 | 0.158 | 0.0509 | 9.48 × 10^{−8} | 159.4 | 4.844 |

Datasets | lztwm | lzfsm | lzfpm | lzsk | lzpk | pfree | NSE |

Gauged | 1.000 | 998.9 | 944.7 | 0.250 | 0.250 | 0.0100 | 0.57 |

TRMM | 1.320 | 1000.0 | 119.1 | 0.152 | 0.212 | 0.2156 | 0.51 |

CMDAS | 1.963 | 1000.0 | 1.00 | 0.227 | 0.228 | 0.0842 | 0.68 |

**Table 7.**Model performance of the IHACRES model (calibrated using NSE) for the calibration period and validation periods.

Datasets | Daily rel.bias | DailyNSE | DailyNSE_{sq} | Daily NSE_{log} | Monthly NSE | |
---|---|---|---|---|---|---|

Calibration period | Gauged | −0.18 | 0.61 | 0.63 | 0.51 | 0.86 |

Validation period | Gauged | −0.13 | 0.52 | 0.54 | 0.45 | 0.81 |

Calibration period | TMPA-3B42V7 | −0.12 | 0.52 | 0.62 | 0.56 | 0.89 |

Validation period | TMPA-3B42V7 | −0.15 | 0.61 | 0.59 | 0.49 | 0.89 |

Calibration period | CMADS | −0.21 | 0.69 | 0.57 | 0.32 | 0.93 |

Validation period | CMADS | −0.07 | 0.70 | 0.63 | 0.49 | 0.93 |

**Table 8.**Model performance of the Sacramento model (calibrated using NSE) for the calibration and verification periods.

Datasets | Daily rel.bias | DailyNSE | DailyNSE_{sq} | Daily NSE_{log} | Monthly NSE | |
---|---|---|---|---|---|---|

Calibration period | Gauged | −0.12 | 0.57 | 0.56 | 0.41 | 0.84 |

Validation period | Gauged | −0.11 | 0.47 | 0.41 | 0.29 | 0.77 |

Calibration period | TMPA-3B42V7 | 0.02 | 0.51 | 0.56 | 0.47 | 0.86 |

Validation period | TMPA-3B42V7 | −0.06 | 0.61 | 0.54 | 0.42 | 0.89 |

Calibration period | CMADS | −0.05 | 0.68 | 0.63 | 0.46 | 0.93 |

Validation period | CMADS | 0.01 | 0.71 | 0.57 | 0.40 | 0.91 |

NSE | NSE_{log} | |
---|---|---|

Gauged | 576 (0.58%) | 9144 (9.14%) |

TMPA-3B42V7 | 1056 (1.06%) | 9929 (9.93%) |

CMADS | 5186 (5.19%) | 12,095 (12.10%) |

NSE | NSE_{log} | |
---|---|---|

Gauged | 0(0.00%) | 5(0.01%) |

TMPA-3B42V7 | 0(0.00%) | 11(0.01%) |

CMADS | 32(0.03%) | 60(0.06%) |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Guo, B.; Zhang, J.; Xu, T.; Croke, B.; Jakeman, A.; Song, Y.; Yang, Q.; Lei, X.; Liao, W.
Applicability Assessment and Uncertainty Analysis of Multi-Precipitation Datasets for the Simulation of Hydrologic Models. *Water* **2018**, *10*, 1611.
https://doi.org/10.3390/w10111611

**AMA Style**

Guo B, Zhang J, Xu T, Croke B, Jakeman A, Song Y, Yang Q, Lei X, Liao W.
Applicability Assessment and Uncertainty Analysis of Multi-Precipitation Datasets for the Simulation of Hydrologic Models. *Water*. 2018; 10(11):1611.
https://doi.org/10.3390/w10111611

**Chicago/Turabian Style**

Guo, Binbin, Jing Zhang, Tingbao Xu, Barry Croke, Anthony Jakeman, Yongyu Song, Qin Yang, Xiaohui Lei, and Weihong Liao.
2018. "Applicability Assessment and Uncertainty Analysis of Multi-Precipitation Datasets for the Simulation of Hydrologic Models" *Water* 10, no. 11: 1611.
https://doi.org/10.3390/w10111611