Hard-Constrained Deep Learning for Climate Downscaling

TL;DR

Besides enabling faster and more accurate climate predictions through downscaling, these methods can improve super-resolution for satellite data and natural images data sets and demonstrate their applicability across different neural architectures as well as a variety of climate and weather data sets.

Abstract

The availability of reliable, high-resolution climate and weather data is important to inform long-term decisions on climate adaptation and mitigation and to guide rapid responses to extreme events. Forecasting models are limited by computational costs and, therefore, often generate coarse-resolution predictions. Statistical downscaling, including super-resolution methods from deep learning, can provide an efficient method of upsampling low-resolution data. However, despite achieving visually compelling results in some cases, such models frequently violate conservation laws when predicting physical variables. In order to conserve physical quantities, here we introduce methods that guarantee statistical constraints are satisfied by a deep learning downscaling model, while also improving their performance according to traditional metrics. We compare different constraining approaches and demonstrate their applicability across different neural architectures as well as a variety of climate and weather data sets. Besides enabling faster and more accurate climate predictions through downscaling, we also show that our novel methodologies can improve super-resolution for satellite data and natural images data sets.

Figures (20)

• Figure 1: Our Softmax Constraining Layer (SmCL) is shown for one input pixel $x$ and the corresponding predicted $2\times 2$ super-pixel for the case of $2\times$ upsampling. This layer is added at the end of a NN and enforces given constraints guaranteed by construction. Besides equality constraints, it enforces positivity of the outputs.
• Figure 2: The CNN architecture used here for $2\times$ upsampling including the constraint layer (in red). The LR input is passed to the last layer, the constraint layer, to enforce the constraint and produce a consistent HR output.
• Figure 3: Samples of the three different data set types used in this work. a) A data pair we use for our standard spatial super-resolution task. The input is an LR image and the target is the HR version of that. b) A data pair for performing SR for multiple time steps simultaneously. The input is a time series of LR images and the output is the same time series in HR. c) A data pair where SR is performed both temporally and spatially, with two LR time steps as input and 3 HR time steps as a target.
• Figure 4: A LR-HR pair from the WRF temperature data. HR and LR come from different runs using the same model at different resolutions. Here we compare the real LR with the low-resolution data created by average pooling of the HR, written as DS(HR). It shows that there is not an exact match between LR and downsampled HR, which makes the success of a constraint layer more difficult. The violation of the downscaling constraint in the WRF data set is 0.684 on average.
• Figure 5: Our novel spatio-temporal architecture, combining Deep Voxel Flow and a ConvGRU. The inputs are two LR images at two times, the first part predicts the in-between time step using the Deep Voxel Flow model, the second part increases the spatial resolution of the three time steps using a Convolutional GRU net.