Passive Microwave Emission Theory and Applications to Satellite Measurements of Global Rivers
Authors: Nghiem Son , Brakenridge Robert , Kugler Zsofia , Podkowa Anna 
Published: February 2023

River stage (surface water level H), discharge (volumetric water flow rate Q), and seasonal ice cover (freeze-up timing F, and break-up timing B) are crucial observables for hydrology and water cycle science.&#160; In-situ river gauging measurements of H, Q, F, and B are laborious and costly to install and maintain at a limited number of locations.&#160; It will be a breakthrough to use satellite data for global river measurements on a nearly-daily basis with multi-decadal data records.&#160; Passive microwave radiometer (PMR) data have been collected from space globally since the 1980s.&#160; Nevertheless, the typical satellite PMR resolution is coarse (10s km), which is much larger than general river widths.&#160; The key question is how PMR can possibly measure the river parameters.&#160;The answer is physically founded on the first principle of Maxwell equations to derive vector wave equations for all polarization combinations in heterogeneous multi-layered geophysical media.&#160; The wave equations are solved with dyadic Green&#8217;s functions subject to boundary conditions. The renormalization method is applied to determine the effective permittivity in each layer while all multiple wave-boundary interactions are included. To circumvent the limitation of the isothermal condition in the Kirchhoff approach, the fluctuation-dissipation theorem is used to calculate the brightness temperatureTb(h) for the horizontal polarization (the first modified Stoke parameter), Tb(v) for the vertical polarization (the second parameter), the polarization cross-correlation amplitude U (the third parameter), and the phase V (the fourth parameter).Based on this physical foundation, a protocol to derive the river observables (H, Q, F, and B) is developed due to the high sensitivity of microwave emissivity of water versus ice and soil conveyed in the brightness temperatures. This overcomes and renders the high spatial resolution requirement unnecessary for river remote sensing by wide-swath PMR for global river observations on a daily or near-daily basis. The PMR method relies on the total areal change of river water within the footprint rather than depending on the river width per se.&#160; As such, PMR can measure a narrow river when its meandering makes a sufficient total surface area in the PMR footprint.&#160; The PMR method is also robust against short-term river channel migration and in-stream sand bars that can be changed by river sedimentation and dynamic processes.To demonstrate the PMR capability for river monitoring, examples of satellite results for river measurements are compared and validated with in-situ river gauging time-series data records for various rivers from the tropics to cold land regions using PMR data at Ka-band such as AMSR-E, AMSR2, TRMM, and GPM and at L-band such as SMOS and SMAP.&#160; The capability to measure global rivers allows PMR satellite missions to address hydrology and water cycle science as a key contribution, including the future Copernicus Imaging Microwave Radiometer (CIMR) to be launched in the 2025+ time frame, further extending the existing long-term data records for river measurements. Moreover, a significant advance of water cycle science is expected with the synergy of PMR together with SWOT successfully launched by NASA in December 2023.