Topographic Visualization of Near-surface Temperatures for Improved Lapse Rate Estimation

TL;DR

This work tackles the problem of fixed lapse-rate corrections for near-surface temperatures over complex terrain, where true lapse rates vary widely and standard models struggle. It introduces a topographic visualization framework and an adaptive, data-driven lapse-rate scheme that estimates local gradients from neighboring temperature-elevation samples within a radius, using Gaussian weighting and $R^2$-based clamping. The approach is implemented in Python with PyVista and evaluated against global HDOBS observations and ECMWF data, showing $\approx$10–20% RMSE improvements for challenging valley and mountain stations. The findings demonstrate the practical value of topology-aware downscaling, with potential integration into operational meteograms and ensemble forecast post-processing, while highlighting avenues for robust regression and extension to rainfall.

Abstract

Numerical model forecasts of near-surface temperatures are prone to error. This is because terrain can exert a strong influence on temperature that is not captured in numerical weather models due to spatial resolution limitations. To account for the terrain height difference between the forecast model and reality, temperatures are commonly corrected using a vertical adjustment based on a fixed lapse rate. This, however, ignores the fact that true lapse rates vary from 1.2 K temperature drop per 100 m of ascent to more than 10 K temperature rise over the same vertical distance. In this work, we develop topographic visualization techniques to assess the resulting uncertainties in near-surface temperatures and reveal relationships between those uncertainties, features in the resolved and unresolved topography, and the temperature distribution in the near-surface atmosphere. Our techniques highlight common limitations of the current lapse rate scheme and hint at their topographic dependencies in the context of the prevailing weather conditions. Together with scientists working in postprocessing and downscaling of numerical model output, we use these findings to develop an improved lapse rate scheme. This model adapts to both the topography and the current weather situation. We examine the quality and physical consistency of the new estimates by comparing them with station observations around the world and by including visual representations of radiation-slope interactions.

Figures (16)

• Figure 1: Comparison of the orography around Mont Blanc at different resolutions. (a) Average grid spacing 9 km, as used in the ECMWF medium range model; (b) Average spacing 1 km.
• Figure 2: Vertical temperature profiles in the bulk atmosphere above selected grid points in the domain of \ref{['fig:orography']}. Each line represents the temperature profile over one grid point. Dashed lines are shown for reference. (a) Temperature profiles on a summer afternoon (July 23, 2021, 1400 UTC); the profiles are dominated by regular negative temperature gradients. (b) Inversion situation on a winter morning (December 19, 2021, 0600 UTC); at the lower end of the profiles, the temperature increases with altitude, indicating an inversion situation close to the earth's surface. Towards the upper end of the profiles -- i.e., away from the surface -- the regular temperature stratification is resumed.
• Figure 3: Low-res orography with near-surface temperature encoded in color. Station locations are shown as spheres, with their color displaying temperature differences. Vertical lines below station sites provide a reference for locating the stations in the 2D domain. Dots on the terrain suggest the presence of stations below the surface at this location. The shading of the spheres can be toggled off (a) or on (b) to enhance the readability of the color scale. A 2D map-like view (c) is obtained by toggling a bird view with parallel projection along the elevation axis.
• Figure 4: Visualizing two terrains simultaneously. (a) High-res orography occludes low-res geometry. (b) Color coding elevation difference on the low-res domain helps to display positive and negative offsets equally.
• Figure 5: (a) The 3D terrain-following model grid as wireframe. (b) Direct volume rendering of the 3D temperature field. (c) Slicing the 3D temperature volume.