# A Merging Framework for Rainfall Estimation at High Spatiotemporal Resolution for Distributed Hydrological Modeling in a Data-Scarce Area

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data

#### 2.1.1. The Qinghai Lake Basin

^{2}, and the altitude of the basin ranges from 3167 (the elevation at the bottom of the lake) to 5279 m above sea level (asl). Land cover is dominated by alpine meadow, bare soil, everglade, tundra, and alpine desert. The primary soil types include felty, thin dark felty, castanozems, peaty bog, and dark frigid calcic soils. Over 40 rivers drain into Qinghai Lake, but most are intermittent. Only the two largest rivers, the Buha and the Ike’ulan, have longstanding and continuous hydrological records. The Buha River is the largest, contributing almost half of the lake’s total runoff. The basin is dominated by a cold and semi-arid climate and influenced by three different monsoon systems: the East Asian monsoon, the Indian monsoon, and westerly jet streams, which make it one of the most sensitive regions to global climate change [23]. The water level of the lake decreased overall by about 3.7 m from 1959 to 2004, but increased by almost 1.5 m from 2004 to 2013 according to the observational records of the Hydrology and Water Resources Survey Bureau of Qinghai Province, China. Causes of this trend are uncertain. Therefore, a study of the hydrological processes of the basin is necessary, with the accurate estimation of precipitation levels being one prerequisite.

#### 2.1.2. Datasets

#### 2.2. Merging Framework

#### 2.2.1. Spatial Downscaling of TRMM

#### 2.2.2. The Double Kernel Smoothing Technique

- Estimating the point residuals at each gauge location s
_{i}:$$D({s}_{i})={X}_{B}({s}_{i})-{X}_{O}({s}_{i})$$_{B}, X_{O}, and D denote the background (satellite), observed, and residual fields, respectively. - Performing a first level interpolation of point residuals to generate gridded pseudo-residuals $\widehat{D}$ with a grid size of 25 km:$$\widehat{D}({s}_{k}^{*})=\frac{{\displaystyle \sum _{i=1}^{n}{K}_{1}(\Vert {s}_{k}^{*}-{s}_{i}\Vert /{h}_{1})}D({s}_{i})}{{\displaystyle \sum _{i=1}^{n}{K}_{1}(\Vert {s}_{k}^{*}-{s}_{i}\Vert /{h}_{1})}}$$
- Applying a second level of interpolation on both the observed point residuals D and the gridded pseudo-residuals $\widehat{D}$ to generate the error field µ
_{B}on each grid of the 1 km downscaled satellite data:$${\mu}_{B}(s)=\frac{{\displaystyle \sum _{i=1}^{n}{K}_{2}(\Vert s-{s}_{i}\Vert /{h}_{2})D({s}_{i})+{\displaystyle \sum _{k=1}^{n1}{K}_{2}(\Vert s-{s}_{k}^{*}\Vert /{h}_{2})\widehat{D}({s}_{k}^{*})}}}{{\displaystyle \sum _{i=1}^{n}{K}_{2}(\Vert s-{s}_{i}\Vert /{h}_{2})+{\displaystyle \sum _{k=1}^{n1}{K}_{2}(\Vert s-{s}_{k}^{*}\Vert /{h}_{2})}}}$$

_{1}and K

_{2}kernel functions are defined as Gaussian kernels, following Nerini et al. [16]:

- 4.
- Estimating the merged field X
_{M}by subtracting the error field µ_{B}from the background field X_{B}:$${X}_{M}(s)={X}_{B}(s)-{\mu}_{B}(s)$$

#### 2.2.3. Bandwidth Estimation

_{1}and h

_{2}in steps 2 and 3 were automatically determined using the shuffled complex evolution (SCE) method developed by Duan et al. [29], which is a global optimization strategy combining the concepts of controlled random search, competitive evolution, and complex shuffling. The objective function of the SCE method is based on cross-validation, given by:

_{i}by Equation (3) without using the point residual D(s

_{i}).

#### 2.2.4. Accounting for Spatial Intermittency

- Convert the 25 km gridded daily TRMM rainfall values into point features and append the rain gauges with their rainfall values to the TRMM-derived point file. This ensures TRMM and gauge rainfall values are considered in the indicator field generation.
- Transform the rainfall values generated from the previous step to create a binary variable indicating where the rainfall value is zero (0) or nonzero (1).
- Under the assumption that the binary variable is stationary and autocorrelated, generate a soft indicator field at 1 km resolution, presenting the probability of rainfall occurrence by using ordinary kriging with a Gaussion model fitting its semi-variogram.
- Produce a hard indicator field by assigning a probability threshold to the soft indicator field (0.5 in this study).
- Estimate the final rainfall field by multiplying the merged rainfall field by the hard indicator field.

#### 2.3. Evaluation Statistics

#### 2.3.1. Performance Indicators

#### 2.3.2. Hydrological Evaluation

^{2}) [39], percent bias (PBIAS), and ratio of the root mean square error (RSR) [35] at the daily scale. Model performance can be evaluated as “very good” if 0.75 < NSE < 1.0, PBIAS < ±10%, and 0 ≤ RSR ≤ 0.50 [35]. The data and parameter sets used to setup the model are listed in Table 1.

## 3. Results

#### 3.1. Merging Process

#### 3.2. Performance of Estimation

#### 3.2.1. Overall Performance

#### 3.2.2. Performance at the Tianjun Station

#### 3.2.3. Hydrological Evaluation

^{2}, which indicates a good correlation between the simulated and observed stream flow, but low NSE and large PBIAS, which are easily influenced by outliers. From the daily stream flow simulations, it can be drawn that the original TRMM product cannot be directly applied to stream flow simulation in this study area. Interpolation based on the sparse rain gauge network is practicable if heavy rainfall events are especially considered. The proposed merging framework can be used for rainfall estimation for distributed hydrological modeling in this study area.

## 4. Discussion

_{1}and then automatically selected bandwidth h

_{2}, which needs some prior knowledge and does not apply to all cases. This study employed the SCE global optimization algorithm to automatically estimate the two bandwidths for each rainy day and, thus, can achieve optimal calibration of the TRMM rainfall. For most days, however, the amount of precipitation was underestimated by the original TRMM, leading to negative point residuals. The searching space of SCE was from 25 km to the length of analysis window diagonal, and the estimated bandwidths might, therefore, be larger than the influence distance of the weather stations, which would exaggerate the underestimation area. This was why the spatial averaged precipitations were overestimated.

^{2}, PBIAS, and RSR were 0.83, 0.85, −25.53%, and 0.41, respectively. These figures show larger cross-validation error and similar performance of stream flow simulation, compared with the results obtained by the merging framework proposed in this study. Annual precipitation shows a similar spatial pattern, but are roughly varying, with short and straight fringes of rainfall amount classes (see Figure 7b). Thus, our merging framework is more adaptive than the kriging-based merging scheme for rainfall estimation in this data-limited area.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Map of the Qinghai Lake Basin, showing the regional topography, main river network, rain gauges, and discharge station at Buhahekou.

**Figure 3.**Rainfall merging process for date 30 July 2008, with rainfall amount (mm) at gauges annotated: (

**a**) The TRMM derived daily rainfall field at 25 km resolution; (

**b**) the spatial downscaled TRMM rainfall field at 1 km resolution; (

**c**) the merged rainfall field from the downscaled TRMM and gauged rainfall; and (

**d**) the final indicator conditioned rainfall field. The gray color indicates non-rainfall areas, and the rainfall amount at weather stations are annotated.

**Figure 4.**Annual precipitation (mm) for 2008 and the PBIAS between merging results and rain gauge time series: (

**a**) the original TRMM at 25 km resolution; (

**b**) the spatial downscaled TRMM at 1 km resolution; (

**c**) the DS Merged result; and (

**d**) the final indicator conditioned estimates.

**Figure 5.**Comparison of daily mean errors for (

**a**) spatial downscaled TRMM; (

**b**) DS merged rainfall; and (

**c**) the final indicator conditioned rainfall

**Figure 7.**Annual precipitation (mm) for 2008 from (

**a**) the proposed merging framework; and (

**b**) co-kriging combined with indicator kriging.

Item | Source |
---|---|

DEM | STRM V4.0 [28] |

Landuse | the 1:100,000 land use map of China [40] |

Soil parameters | the 1:1,000,000 soil database of China [41] |

LAI | MODIS MCD15A3 [42] |

NDVI | MODIS MOD13Q1 [43] |

Downscaling | Regression Model | r^{2} | p |

y = 0.001ELE + 1.042TEM − 13.230 | 0.173 | <0.05 | |

DS Merging | h_{1} (km) | h_{2} (km) | CV (mm) |

30.609 | 548.255 | 1596.1 | |

Indicator Kriging | Range (km) | Nugget | Sill |

81.953 | 0.101 | 0.048 |

**Table 3.**Evaluation statistics of the intermediate and final results for rainfall estimation on 30 July 2008.

Spatial Averaged Precipitation (mm) | ME | PBIAS | RMSE | NSE | |
---|---|---|---|---|---|

Original TRMM | 1.90 | −10.99 | −58.05% | 15.32 | −1.11 |

Downscaled TRMM | 1.89 | −10.22 | −53.99% | 14.52 | −0.89 |

Merged Rainfall | 12.54 | 0.46 | 2.42% | 10.34 | 0.04 |

Final Rainfall | 11.40 | −0.44 | −2.33% | 9.90 | 0.12 |

**Table 4.**Evaluation statistics for rainfall estimation based on observations at the 13 stations, 2008.

Spatial Average Precipitation (mm) | ME | PBIAS | RMSE | NSE | |
---|---|---|---|---|---|

Original TRMM | 305.39 | −0.13 | −12.64% | 2.89 | 0.13 |

Downscaled TRMM | 332.95 | −0.09 | −9.23% | 2.71 | 0.24 |

Merged Rainfall | 416.20 | 0.08 | 8.44% | 1.71 | 0.70 |

Final Rainfall | 330.27 | −0.07 | −6.72% | 1.88 | 0.63 |

ME | PBIAS | RMSE | NSE | |
---|---|---|---|---|

Original TRMM | −0.29 | −29.44% | 2.33 | 0.46 |

Downscaled TRMM | −0.17 | −17.09% | 2.13 | 0.55 |

Merged Rainfall | 0.06 | 6.17% | 1.87 | 0.65 |

Final Rainfall | −0.19 | −18.77% | 2.04 | 0.59 |

NSE | R^{2} | PBIAS | RSR | |
---|---|---|---|---|

Simulation I | 0.33 | 0.84 | 41.02% | 0.82 |

Simulation II | 0.37 | 0.42 | −35.87% | 0.79 |

Simulation III | 0.82 | 0.83 | 0.85% | 0.43 |

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**MDPI and ACS Style**

Long, Y.; Zhang, Y.; Ma, Q.
A Merging Framework for Rainfall Estimation at High Spatiotemporal Resolution for Distributed Hydrological Modeling in a Data-Scarce Area. *Remote Sens.* **2016**, *8*, 599.
https://doi.org/10.3390/rs8070599

**AMA Style**

Long Y, Zhang Y, Ma Q.
A Merging Framework for Rainfall Estimation at High Spatiotemporal Resolution for Distributed Hydrological Modeling in a Data-Scarce Area. *Remote Sensing*. 2016; 8(7):599.
https://doi.org/10.3390/rs8070599

**Chicago/Turabian Style**

Long, Yinping, Yaonan Zhang, and Qimin Ma.
2016. "A Merging Framework for Rainfall Estimation at High Spatiotemporal Resolution for Distributed Hydrological Modeling in a Data-Scarce Area" *Remote Sensing* 8, no. 7: 599.
https://doi.org/10.3390/rs8070599