How Kriging-informed Conditional Diffusion Maps Regional Sea-Level Downscaling

Introduction

For instance, Figure 1 shows a geographic area near Ecuador and Peru in two different time frames. The ability to capture localized variations is crucial for accurately predicting climate change effects (e.g., sea-level rise) in a specific area.

The regional downscaling problem is vital for developing comprehensive climate policies and strategies.

The impacts of climate change, as predicted by global climate models, range from extreme weather events to rises in sea levels and shifts in agricultural productivity.

Methodology

Additional physical constraints can be added to the proposed method to explore downscaling climate variables with conservation properties. This method reverses the forward diffusion process by reconstructing the signal from noise using a backward Markov chain conditioned on y.

Study Design

Universal Kriging (U-Krig) is an advanced geostatistical method that allows for interpolation by accounting for deterministic trends and spatial correlation in the data.

Experimental Goal: Our experimental goal was to compare the solution quality of downscaling from our proposed Ki-CDPM model against state-of-the-art downscaling methods and provide both qualitative and quantitative analysis.

Results & Findings

Given coarse-resolution climate projections from global climate models or satellite data, the problem of statistical downscaling aims to estimate high-resolution regional climate data, capturing finescale spatial patterns and variability for a climate variable (e.g., sea-level rise). Since downscaling generates high-resolution data from low-resolution variables, statistical downscaling uses statistical methods to establish relationships between coarse-resolution climate data and high-resolution historical observations.

• Given coarse-resolution climate projections from global climate models or satellite data, the problem of statistical downscaling aims to estimate high-resolution regional climate data, capturing finescale spatial.
• Since downscaling generates high-resolution data from low-resolution variables, statistical downscaling uses statistical methods to establish relationships between coarse-resolution climate data and high-resolution historical observations.
• In both images, the blurry coarse-resolution projections display limited variation in sea surface height anomalies compared to the fine-scale resolution, as shown in the rectangular strips.
• For example, coastal areas worldwide face severe risks associated with sea-level rise, where even small changes can lead to significant flooding, erosion, and habitat loss .
• To address these limitations, we propose a Kriging-informed Conditional Diffusion Probabilistic Model (Ki-CDPM), which combines the strengths of Kriging’s spatial interpolation capabilities with the flexibility and.

Problem Formulation

Problem Formulation The problem of downscaling a climate variable (e.g., sea-level elevation) is formally defined as follows: Input: ( Inverse Problem: Downscaling sea-level rise projections from coarse-resolution climate models to finer regional scales can be thought of as an inverse problem aimed at estimating high-resolution sea-level changes based on limited low-resolution observations and a forward model [24, 31] . This problem is complex due to nonlinear relationships between inputs and outputs, sparse and unevenly distributed observations, and model errors and uncertainties [3, 8, 37, 47] . Additionally, the high-dimensional nature.

Kriging-informed Conditional Diffusion Probabilistic Model

Kriging-informed Conditional Diffusion Probabilistic Model This section will introduce a novel architecture based on Kriging interpolation as a conditional input to preserve spatial variability while transforming coarser-resolution climate variables (e.g., sealevel elevation) to finer-scale resolution. Section 3.3 provides a detailed explanation of the proposed architecture, and Section 3.4 shows the Kriging-informed training and regularization.

Conditional Diffusion Probabilistic Model

Conditional Diffusion Probabilistic Model In this approach, the goal is to generate a fine-scale resolution map from a coarse-resolution input map in which samples were drawn from an unknown conditional distribution \ud835\udc5d (x | y) where \ud835\udc5d (y) is a distribution of Kriging-interpolated map of the coarse-scale resolution input ( \u1ef9). The objective is to learn a parametric approximation of \ud835\udc5d (x | y) via stochastic refinements which iteratively maps source condition y to a target output x \u2208 R \ud835\udc51 via denoising diffusion probabilistic (DDPM) model [20, 48] .

Interpolation with Kriging

Interpolation with Kriging Universal Kriging (U-Krig) is an advanced geostatistical method that allows for interpolation by accounting for deterministic trends and spatial correlation in the data. For instance, let \u1ef9 represent a coarser resolution map and \ud835\udc66 represent a finer resolution map. We then model the trend using a second-order polynomial function of the spatial coordinates: \ud835\udc5a(\ud835\udc60) = \ud835\udefd 0 + \ud835\udefd 1 \ud835\udc65 + \ud835\udefd 2 \ud835\udc66 + \ud835\udefd 3 \ud835\udc65 2 + \ud835\udefd 4 \ud835\udc66 2 + \ud835\udefd 5 \ud835\udc65\ud835\udc66 (12) Where \ud835\udc65 and \ud835\udc66 are the spatial.

Proposed Model Architecture

Proposed Model Architecture The Ki-CDPM extends the CDPM by incorporating a conditioned input obtained from Universal-Kriging (U-Krig) on the coarseresolution elevation map \u1ef9 \u2208 R \ud835\udc40 \u00d7\ud835\udc40 providing local variability for the climate variable. The objective is to find an interpolated elevation map y \u2208 R \ud835\udc41 \u00d7\ud835\udc41 (where \ud835\udc41 > \ud835\udc40) with the exact resolution as \ud835\udc65 0 . Hence, y is later used as a conditional input concatenated with the noisy elevation map x \ud835\udc61 \u2208 R \ud835\udc41 \u00d7\ud835\udc41 at each diffusion step \ud835\udc61 along the channel dimension.

Experiment Design

Experiment Design Datasets: Our experimental evaluation focused on downscaling two key climate variables: sea-level anomaly (SLA) and eddy kinetic energy (EKE). We use high-resolution Copernicus and CMIP6 datasets and examined various sub-regions, including Eastern North America (ENA), western North America (WNA), and the Bay of Bengal (BoB) [23] , an area particularly vulnerable to coastal flooding, due to the absence of ground truth data for climate models and the need for bias correction. We tested our methodology on satellite observations where the ground truth is known. Climate model outputs on.

Related Work

Related Work Spatial variability [5, 7, 15] , is a significant characteristic of all geographic phenomena, such as climate zones, USDA plant hardiness zones [54] , and different terrestrial habitats like forests, grasslands, wetlands, and deserts. This variability influences the flora and fauna within different regions. Additionally, variations in laws, policies, and cultural norms are evident across and within nations. Often referred to as geography’s second law, spatial variability is utilized in analytical models like geographically weighted regression (GWR) [35] to measure the interactions between variables in a given area.

Conclusion

Section 3 describes the overall architecture of the Kriging-informed Conditional Diffusion Probabilistic Model (Ki-CDPM) and the variogrambased regularization.