# CliGAN: A Structurally Sensitive Convolutional Neural Network Model for Statistical Downscaling of Precipitation from Multi-Model Ensembles

^{*}

## Abstract

**:**

## 1. Introduction

- Develop a methodology to downscale large-scale precipitation, given by several AOGCMs, to regional-scale precipitation by statistical downscaling using convolution neural network and generative adversarial training.
- Propose a novel loss function which is a combination of content loss, structural loss, and adversarial loss, which improves the prediction of global and regional qualities of the downscaled precipitation.

## 2. Methods

#### 2.1. Study Area and Datasets

^{2}. The rate of environmental change in northern Canada has been widely documented, including landform transformation [60], shrub expansion in the tundra [61], permafrost thaw and related hydrological impacts [62], wildlife declines [63], and changes affecting local communities and culture [64]. Furthermore, scarce weather data due to sparse observational stations make the estimation of the change through in-situ observation more difficult. It is evident the local communities in Canada’s north need to adapt and prepare for the anticipated impacts of climate change with help of the climatic data at hydrologically-relevant scales. This sets up a critical need for better climate impact prediction and estimation at regional scales. Figure 1 shows Great Bear Lake and its adjacent regions within Tsá Túé Biosphere Reserve, which is used as a downscaling region of interest in this study.

#### 2.2. Downscaling Method

_{GCM}) to regional scale fine resolution extreme precipitation (P

_{obs}). The technical difficulties of the problem involve increment of the resolution, bias correction, and regional scale precipitation feature corrections. The number of training years y=1,…, n then the θ

_{G}is obtained through solving the minimization of the downscaling total loss function ${l}^{D}$:

#### 2.2.1. Adversarial Training

#### 2.2.2. Downscaling Total Loss

#### 2.2.3. Networks

_{2}-norm regularization with weights 1

^{−5}on model weights and biases to prevent over-fitting.

#### 2.2.4. Training Details

_{2}-norm regularization was used on both weight and bias of the generator to prevent over-fitting. Furthermore, we employed a random sub-sampling strategy to train the network to capture the stochasticity of the entire population. The entire dataset is temporally split into random training and testing set for each training epoch. The network is trained using the training set and the performance is tested on the testing set. We used 66%/33% training/testing data divide, which resulted in 41 temporal points for training and 20 temporal points for testing. We avoided any kind of rescaling of the input or output data and allowed the model to learn and evolve the climate signal present in the different model datasets and observations. The generator was optimized using Adam first-order gradient-based optimization [70] based on the L

_{inf}norm (Adamax) [71] with initial learning rate m = 0.02 and ${\beta}_{1}$ decay 0.5. We wanted the discriminator to compute the gradient-based on an adaptive window near the present iteration and did not want to use all the previous generator results of the gradient information. Therefore, we used a moving window update of the gradient in Adam (Adadelta) [72] to train the discriminator Wasserstein distance computer. The initial 500 iterations were discarded as burn-in and subsequently the model was trained for 10,000 iterations until convergence. These settings were found to be more than adequate for simulating realistic high-resolution precipitation patterns.

## 3. Results and Discussion

^{−3}after 10,000 iterations (Figure 6b), while the structural loss stabilized around a value of 2.4

^{−2}(Figure 6c). The adversarial loss in Figure 6d keeps on increasing after 10,000 iterations indicating the discriminator is resolving the differences between the observed and predicted precipitation patterns. The discriminator error also keeps on increasing (Figure 6e), signifying the good performance of the generator. However, the loss of the discriminator is still lower than the adversarial error. As an extra diagnostic, we also tracked a widely popular loss metric mean absolute error. Figure 6f shows the trace of mean absolute error which stabilized around a value of 0.1 mm/day after 10,000 iterations.

## 4. Conclusions

- Our framework can utilize diverse information present in different AOGCM simulations to create a spatially coherent field similar to observational data. The approach is similar in spirit to reliability ensemble averaging (REA) proposed by [75], within a CNN and adversarial training context.
- The MSSIM index allowed us to get an insight into the model’s regional characteristics and suggest relying solely on point-based error functions that are widely used in statistical downscaling and may not be enough to simulate regional characteristics of precipitation variables reliably.
- Further use of total loss function, which is a combination of adversarial, content, and structural loss within a CNN-based downscaling method, may lead to higher quality downscaled products.
- The adversarial loss can provide a meaningful gradient to weight optimization when traditional loss functions fail in near convergence variabilities.

## Author Contributions

## Funding

## Conflicts of Interest

## Availability of Data and Material

## Code Availability

## References

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**Figure 1.**Study domain over the Tsa Tue Bio-reserve, located in Northwest Territories, Canada. In the inset, the location is shown in the box in the perspective of the entire Canada. The basemap is downloaded from ESRI

^{©}using opensource python package.

**Figure 3.**Temporal median of AOGCM annual maximum precipitation of (

**a**) BCC ESM, (

**b**) CAN ESM5, (

**c**) CESM2, (

**d**) CNRM CM6.1, (

**e**) CNRM ESM2, (

**f**) GFDL CM4, (

**g**) HAD GEM3, (

**h**) MRI, and (

**i**) UK ESM1.

**Figure 5.**(

**a**) Total loss of training, (

**b**) content loss, (

**c**) structural loss, (

**d**) adversarial loss, (

**e**) discriminator loss, (

**f**) mean absolute error of the training.

**Figure 6.**(

**a**) Total loss of training, (

**b**) content loss, (

**c**) structural loss, (

**d**) adversarial loss, (

**e**) discriminator loss, (

**f**) mean absolute error of the training.

**Figure 8.**Performance of the downscaling (

**a**) mean absolute percentage error, (

**b**) temporal correlation, and (

**c**) P-value for Kolmogorov-Smirnov test of temporal distribution equivalency.

AOGCM | Institution | Grid Type | Horizontal Dimension (Lon/Lat) | Vertical Levels |
---|---|---|---|---|

BCC ESM | Beijing Climate Center | T42 | 128 × 64 | 26 |

CAN ESM5 | Canadian Centre for Climate Modelling and Analysis, Environment and Climate Change Canada | T63 | 128 × 64 | 49 |

CESM2 | National Center for Atmospheric Research | 0.9 × 1.25 finite volume grid | 288 × 192 | 70 |

CNRM CM6.1 | Centre National de Recherches Meteorologiques | T127 | 256 × 128 | 91 |

CNRM ESM2 | Centre National de Recherches Meteorologiques | T127 | 256 × 128 | 91 |

GFDL CM4 | Geophysical Fluid Dynamics Laboratory | C96 | 360 × 180 | 33 |

HAD GEM3 | Met Office Hadley Centre | N96 | 192 × 144 | 85 |

MRI | Meteorological Research Institute, Tsukuba, Ibaraki 305-0052, Japan | TL159 | 320 × 160 | 80 |

UK ESM1 | Met Office Hadley Centre | N96 | 192 × 144 | 85 |

**Table 2.**Performance of different objective functions for the model. The median of the last 50 iterations has been used to measure the performance.

Loss Combination | Content Loss | Structural Loss | ||
---|---|---|---|---|

Train | Test | Train | Test | |

Adversarial + NS | 0.015 | 0.142 | 0.025 | 0.100 |

Adversarial + MSSIM | 0.070 | 0.110 | 0.019 | 0.025 |

NS + MSSIM | 0.011 | 0.774 | 0.024 | 0.283 |

Adversarial + NS + MSSIM | 0.015 | 0.043 | 0.024 | 0.033 |

Adversarial + NS + MSSIM LT | 0.011 | 0.020 | 0.021 | 0.017 |

Performance/Model | GAN | MAE | PCA |
---|---|---|---|

MAE | 1.71 | 1.85 | 2.7 |

NS | 0.996 | 0.995 | 0.991 |

Correlation | 0.9987 | 0.9986 | 0.995 |

KS p-value | ~1^{−48} | ~1^{−25} | ~1^{−8} |

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Chaudhuri, C.; Robertson, C.
CliGAN: A Structurally Sensitive Convolutional Neural Network Model for Statistical Downscaling of Precipitation from Multi-Model Ensembles. *Water* **2020**, *12*, 3353.
https://doi.org/10.3390/w12123353

**AMA Style**

Chaudhuri C, Robertson C.
CliGAN: A Structurally Sensitive Convolutional Neural Network Model for Statistical Downscaling of Precipitation from Multi-Model Ensembles. *Water*. 2020; 12(12):3353.
https://doi.org/10.3390/w12123353

**Chicago/Turabian Style**

Chaudhuri, Chiranjib, and Colin Robertson.
2020. "CliGAN: A Structurally Sensitive Convolutional Neural Network Model for Statistical Downscaling of Precipitation from Multi-Model Ensembles" *Water* 12, no. 12: 3353.
https://doi.org/10.3390/w12123353