Eric E. Small’s research while affiliated with University of Colorado Boulder and other places

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Publications (189)


Using a random forest model to combine airborne lidar and Snotel data for daily estimates of snow depth across mountain drainage basins of Colorado
  • Preprint

January 2025

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1 Read

Jordan Herbert

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Mark S. Raleigh

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Eric E. Small

A spatial comparison of (a) 3 km observed CYGNSS reflectivity, (b) 3 km interpolated CYGNSS reflectivity, and (c) 9 km SMAP brightness temperature. All data are from 31 March 2018. The spatial coverage of observed CYGNSS reflectivity over the displayed landmass is 10.9%.
Workflow depicting the steps required to calculate 3 km SMAP/CYGNSS soil moisture.
(a) Depiction of SMAP/CYGNSS temporal merging periods and brightness temperature time series from May 2020 to June 2020. Black lines denote the occurrence of a SMAP observation and alternating white and gray shaded regions denote the temporal merging periods of ±half the time between successive SMAP observations. Time series shows the increased temporal frequency of 3 km interpolated SMAP/CYGNSS brightness temperature compared to 3 km observed SMAP/CYGNSS brightness temperature. All data are from the 3 km grid cell at 33.194°N and 88.024°W, denoted with a red diamond in (b,d). Bottom row: the difference in spatial coverage for an example 33 × 33 km box (black square), centered on the 9 × 9 km grid cell (red square) at 33.166°N and 87.993°W, on 18 June 2020. (b) All observed CYGNSS reflectivity values (Γf) used to calculate (c) observed ΓC. (d) All interpolated CYGNSS reflectivity values (Γf) used to calculate (e) interpolated ΓC.
(a) Boxplots of the daily standard deviation of soil moisture over the continental United States (25–38°N, 75–125°E) for each day from April 2017 to December 2021. The comparison includes 3 km observed and interpolated SMAP/CYGNSS soil moisture, observed and interpolated SMAP/CYGNSS soil moisture upscaled to 9 km, and 9 km SMAP soil moisture. (b) Boxplots of the fractional spatial coverage of 3 km observed and interpolated SMAP/CYGNSS soil moisture, compared to 9 km SMAP soil moisture, calculated using all data within the latitudinal range of ±37° for each day during the year 2020. Blue boxes indicate the interquartile ranges, red lines indicate the medians, and black plus signs denote all values outside of the interquartile range.
All images and maps show a ~150 km × 100 km region of northwest Texas, USA (35.4°–36.4°N and 101°–102.5°W). (a) Terra/MODIS reflectance image on 20 August 2020 [50], showing areas with irrigated cropland adjacent to non-agricultural areas. (b) 3 km interpolated SMAP/CYGNSS soil moisture. (c) 3 km observed SMAP/CYGNSS soil moisture. (d) 3 km SMAP/Sentinel soil moisture [51]. (e) 9 km SMAP soil moisture [42]. All soil moisture maps are averaged or aggregated over two periods: 1–31 July 2020 and 1–31 August 2020.

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Spatially Interpolated CYGNSS Data Improve Downscaled 3 km SMAP/CYGNSS Soil Moisture
  • Article
  • Full-text available

August 2024

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37 Reads

Soil moisture data with both a fine spatial scale and a short global repeat period would benefit many hydrologic and climatic applications. Since the radar transmitter malfunctioned on NASA’s Soil Moisture Active Passive (SMAP) in 2015, SMAP soil moisture has been downscaled using numerous alternative fine-resolution data. In this paper, we describe the creation and validation of a new downscaled 3 km soil moisture dataset, which is the culmination of previous work. We downscaled SMAP enhanced 9 km brightness temperatures by merging them with L-band Cyclone Global Navigation Satellite System (CYGNSS) reflectivity data, using a modified version of the SMAP active–passive brightness temperature algorithm. We then calculated 3 km SMAP/CYGNSS soil moisture using the resulting 3 km SMAP/CYGNSS brightness temperatures and the SMAP single-channel vertically polarized soil moisture algorithm (SCA-V). To remedy the sparse daily coverage of CYGNSS data at a 3 km spatial resolution, we used spatially interpolated CYGNSS data to downscale SMAP soil moisture. 3 km interpolated SMAP/CYGNSS soil moisture matches the SMAP repeat period of ~2–3 days, providing a soil moisture dataset with both a fine spatial scale and a short repeat period. 3 km interpolated SMAP/CYGNSS soil moisture, upscaled to 9 km, has an average correlation of 0.82 and an average unbiased root mean square difference (ubRMSD) of 0.035 cm³/cm³ using all SMAP 9 km core validation sites (CVSs) within ±38° latitude. The observed (not interpolated) SMAP/CYGNSS soil moisture did not perform as well at the SMAP 9 km CVSs, with an average correlation of 0.68 and an average ubRMSD of 0.048 cm³/cm³. A sensitivity analysis shows that CYGNSS reflectivity is likely responsible for most of the uncertainty in downscaled SMAP/CYGNSS soil moisture. The success of 3 km SMAP/CYGNSS soil moisture demonstrates that Global Navigation Satellite System–Reflectometry (GNSS-R) observations are effective for downscaling soil moisture.

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Reanalyzing the spatial representativeness of snow depth at automated monitoring stations using airborne lidar data

August 2024

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32 Reads

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4 Citations

Automated snow station networks provide critical hydrologic data. Whether point observations represent snowpack at larger areas is an enduring question. Leveraging the recent proliferation of airborne lidar snow depth data, we revisit the question of snow station representativeness at multiple scales surrounding 111 stations in Colorado and California (USA) from 2021–2023 (n=476 total samples). In about 50 % of cases, station depths were at least 10 cm higher than areal-mean snow depth (from lidar) at 0.5 to 4 km scales. The nearest 50 m lidar pixels had lower bias and were more often representative of the areal-mean snow depth than coincident stations. The closest 3 m lidar pixel often agreed with station snow depth to within 10 cm, suggesting differences between station snow depth and the nearest 50 m lidar pixel result from highly localized conditions and not the measurement method. Representativeness decreased as scale increased up to ∼6 km, mainly explained by the elevation of a site relative to the larger area. Relative values of vegetation and southness did not have significant impacts on site representativeness. The sign of bias at individual snow stations is temporally consistent, suggesting the relationship between station depth and that of the surrounding area may be predictable. Improving understanding of snow station representativeness could allow for more accurate validation of modeled and remotely sensed data.


Evaluating Large‐Storm Dominance in High‐Resolution GCMs and Observations Across the Western Contiguous United States

June 2024

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91 Reads

Nels R. Bjarke

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[...]

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Eric E. Small

Extreme precipitation events are projected to increase in frequency across much of the land‐surface as the global climate warms, but such projections have typically relied on coarse‐resolution (100–250 km) general circulation models (GCMs). The ensemble of HighResMIP GCMs presents an opportunity to evaluate how a more finely resolved atmosphere and land‐surface might enhance the fidelity of the simulated contribution of large‐magnitude storms to total precipitation, particularly across topographically complex terrain. Here, the simulation of large‐storm dominance, that is, the number of wettest days to reach half of the total annual precipitation, is quantified across the western United States (WUS) using four GCMs within the HighResMIP ensemble and their coarse resolution counterparts. Historical GCM simulations (1950–2014) are evaluated against a baseline generated from station‐observed daily precipitation (4,803 GHCN‐D stations) and from three gridded, observationally based precipitation data sets that are coarsened to match the resolution of the GCMs. All coarse‐resolution simulations produce less large‐storm dominance than in observations across the WUS. For two of the four GCMs, bias in the median large‐storm dominance is reduced in the HighResMIP simulation, decreasing by as much as 62% in the intermountain west region. However, the other GCMs show little change or even an increase (+28%) in bias of median large‐storm dominance across multiple sub‐regions. The spread in differences with resolution amongst GCMs suggests that, in addition to resolution, model structure and parameterization of precipitation generating processes also contribute to bias in simulated large‐storm dominance.


Demonstrating a Hybrid Machine Learning Approach for Snow Characteristic Estimation Throughout the Western United States

June 2024

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75 Reads

Snow is a critical component of global climate and provides water resources to over 1 billion people worldwide. Yet current measurement methods and modeling techniques lack the ability to fully capture snow characteristics such as snow water equivalent (SWE) and density across variable landscapes. In recent years, physics‐informed machine learning (ML) methods have demonstrated promise for combining data‐driven learning and physical information. However, this capability has not been widely explored within snow hydrology. Here, we develop a “hybrid” model that applies ML informed by outputs from a physical model and assess whether it provides more accurate estimations of SWE and snow density. We trained and evaluated models at 49 SNOw TELemetry locations spanning a range of snow climates in the western US using 9 years of daily data. The research addressed two questions. In the first, the performance of the hybrid model was compared against a plain neural network (long short‐term memory, Long‐Short Term Memory), a high‐quality physical model, and a statistical snow density model. The second question focused on how regionally trained hybrid models compared to a westwide model as well as their transferability between multiple snow regions. The results showed that combining physical information and ML reduced SWE Root Mean Square Error by 35% compared to a physical model and 51% compared to a neural network. Additionally, regional training only provided minimal benefits compared with a westwide model. These findings indicate that a hybrid approach can yield more accurate snowpack characterization than either physical snow models or ML alone.



Reanalyzing the spatial representativeness of snow depth at automated monitoring stations using airborne Lidar data

November 2023

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22 Reads

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1 Citation

Automated snow station networks provide critical hydrologic data. Whether point observations represent snowpack at larger areas is an enduring question. Leveraging the recent proliferation of airborne Lidar snow depth data, we revisit the question of snow station representativeness at multiple scales surrounding 111 stations in Colorado and California (U.S.A.) from 2021–2023 (n= 476 total samples). In about 50 % of cases, station depths were at least 10 cm higher than areal-mean snow depth (from Lidar) at 0.5 to 4 km scales. The nearest 50 m Lidar pixels had lower bias and were more often representative than coincident stations. The closest 3 m Lidar pixel often agreed (within 10 cm) with station snow depth, suggesting differences between station snow depth and the nearest 50 m Lidar pixel result from highly localized conditions, not the measurement method. Representativeness decreased as scale increased up to 6 km, mainly explained by the elevation of a site relative to the larger area. The bias direction at individual snow stations is temporally consistent, suggesting the relationship between station depth and that of the surrounding area may be predictable. Improving understanding of snow station representativeness could allow for more accurate validation of modelled and remotely sensed data.



CYGNSS Handbook (2nd-ed.)

December 2022

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297 Reads

The CYGNSS Handbook was compiled in 2015 to serve as a source of information about the mission and its data products for potential data users. The handbook was updated to describe multiple changes to data processing and products in 2022. Chapter 1 describes the motivation for the project and includes a discussion about tropical cyclones and current technologies for observing and forecasting them, as well as the unique impact the CYGNSS mission will have on the advancement of our scientifc understanding in this field. Chapter 2 outlines the science objectives as well as the baseline mission requirements. Additionally, a mission synopsis explains the different phases of the mission and provides an overview of the flow of information, the ground data processing, and the fight segment hardware required to support the mission. Chapter 3 explains the mission design in detail, including the orbital elements, the observatory, and the science payload. Chapter 4 gives the reader an overview of the data products at each level of processing, including descriptions of their temporal and spatial resolutions. Chapters 5 through 10 provide relevant excerpts from the project Algorithm Theoretical Basis Documents (ATBDs). The ATBDs give the reader a more comprehensive explanation of each level of data product, including the physical and mathematical descriptions of the algorithms used in the generation of the Science Data Products, an explanation of uncertainty estimates, and considerations of calibration, validation, exception control, and diagnostics. Chapter 11 presents both a top-down and a bottom-up assessment of Level 1 (basic observable) and Level 2 (wind speed estimate) uncertainties. The handbook concludes with a list of project publications in Chapter 12 and a list of acronyms in Chapter 13. The document concludes with an appendix describing the ocean surface bistatic scattering forward model. The forward model relates the state of the ocean to the measurements made by CYGNSS and is a fundamental mathematical framework for the science behind the CYGNSS data products.


Figure 1. 9 km SMAP brightness temperatures (TBs) over (a) southern North America and (b) Australia, and CYGNSS reflectivity gridded at 3 × 3 km over (c) southern North America and (d) Australia on 9 March 2020.
Figure 2. We merged 9 km SMAP TBs with CYGNSS reflectivity data, gridded at 3 km, to create 3 km SMAP/CYGNSS TBs. 9 km SMAP TB data have a native resolution of approximately 33 km. To collocate SMAP and CYGNSS data, we derived 33 km boxes for each SMAP 9 km grid cell [2,3].
Figure 3. All displayed data falls within the 33 km box centered on the 9 km grid cell at [31.2N, 98.7W]. In (b-d), the black borders are the 33 km box and the red squares are the 9 km grid cell. (a): A month-long timeseries of collocated SMAP and CYGNSS data, where each temporal collocation period is ±half the time between successive SMAP observations. The black lines denote the time of each SMAP observation, and the alternating gray and white shaded regions show the temporal collocation periods. The blue shaded region shows the collocation period depicted in (b-d). The green squares are SMAP observations. The blue dots are CYGNSS observations. The red diamond is the í µí»¤ value shown in (c). (b): The í µí»¤ map shows all the CYGNSS reflectivity values collocated with the SMAP observation on 17 February 2020. (c): í µí»¤ is the median of all í µí»¤ and is used to calculate í µí±‡í µí°µ within the central 9 km grid cell. (d) The í µí±‡í µí°µ map shows the 3 km SMAP/CYGNSS TBs calculated using the displayed í µí»¤ and í µí»¤ values.
Figure 4. Examples of 45-day SMAP emissivity and CYGNSS reflectivity data pairs and their corresponding linear regressions in (a) India, (b) the United States, (c) China, (d) Australia, (e) Brazil (Amazon Rainforest), and (f) Mauritania (Sahara Desert). Geographic coordinates, landcover class, β value (slope), and correlation value (R) are provided for each.
Figure 8. A depiction of the effect that NSSM variability has on β values. All displayed data falls within the 33 km box centered on the 9 km grid cell at [36.1N, 119.6W]. (a) Bi-monthly SMAP emissivity and CYGNSS reflectivity data, collocated using ±half the time between successive SMAP observations, and their corresponding linear regressions. The seasonally varying β values are included in each plot. The SMAP/CYGNSS data points are colored to match the timeseries in (c). (b) 45-day SMAP emissivity and CYGNSS reflectivity data (as described in Section 2.2.2) and the corresponding β value. (c) SMAP NSSM timeseries with FLDAS monthly rainfall data. The NSSM data points are colored bi-monthly, to match the scatter plots in (a).
Downscaling SMAP Brightness Temperatures to 3 km Using CYGNSS Reflectivity Observations: Factors That Affect Spatial Heterogeneity

October 2022

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125 Reads

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3 Citations

NASA’s Soil Moisture Active Passive (SMAP) mission only retrieved ~2.5 months of 3 km near surface soil moisture (NSSM) before its radar transmitter malfunctioned. NSSM remains an important area of study, and multiple applications would benefit from 3 km NSSM data. With the goal of creating a 3 km NSSM product, we developed an algorithm to downscale SMAP brightness temperatures (TBs) using Cyclone Global Navigation Satellite System (CYGNSS) reflectivity data. The purpose of downscaling SMAP TB is to represent the spatial heterogeneity of TB at a finer scale than possible via passive microwave data alone. Our SMAP/CYGNSS TB downscaling algorithm uses β as a scaling factor that adjusts TB based on variations in CYGNSS reflectivity. β is the spatially varying slope of the negative linear relationship between SMAP emissivity (TB divided by surface temperature) and CYGNSS reflectivity. In this paper, we describe the SMAP/CYGNSS TB downscaling algorithm and its uncertainties and we analyze the factors that affect the spatial patterns of SMAP/CYGNSS β. 3 km SMAP/CYGNSS TBs are more spatially heterogeneous than 9 km SMAP enhanced TBs. The median root mean square difference (RMSD) between 3 km SMAP/CYGNSS TBs and 9 km SMAP TBs is 3.03 K. Additionally, 3 km SMAP/CYGNSS TBs capture expected NSSM patterns on the landscape. Lower (more negative) β values yield greater spatial heterogeneity in SMAP/CYGNSS TBs and are generally found in areas with low topographic roughness (<350 m), moderate NSSM variance (~0.01–0.0325), low-to-moderate mean annual precipitation (~0.25–1.5 m), and moderate mean Normalized Difference Vegetation Indices (~0.2–0.6). β values are lowest in croplands and grasslands and highest in forested and barren lands.


Citations (71)


... The harsh weather conditions of the remote areas where the snowpack is present complicate the installation of monitoring networks, with the number of automatic weather stations declining dramatically with higher elevation (Matthews et al., 2020). Given the considerable complexity of the spatial patterns of the seasonal snowpack, monitoring networks often suffer from a lack of representativity (Herbert et al., 2024). In addition, monitoring SWE, which is the key snow hydrological variable, is significantly more uncertain and costly to measure than other variables such as snow depth, and remains an active research topic (e.g., Gugerli et al., 2022;Orio-Alonso et al., 2023). ...

Reference:

Ensemble-based data assimilation improves hyperresolution snowpack simulations in forests
Reanalyzing the spatial representativeness of snow depth at automated monitoring stations using airborne lidar data

... Various regions are selected for study, and CYGNSS observations are aggregated at spatial resolutions ranging mainly from 3 to 36 km. Comparing a set of CYGNSS-based soil moisture algorithms, [33,34] showed that the performance of different approaches depends on the observational and environmental conditions and that none fully outperforms the others. They also demonstrated that approximate models based on linear regression exhibit strong performance in estimating soil moisture, comparable to more robust models. ...

A Blended CYGNSS Soil Moisture Product Partitioned with Ancillary Data
  • Citing Conference Paper
  • January 2024

... Moreover, synoptic weather station measurements are applied in the form of a prior field to optimize effGS in the HUT model. The representativeness of weather stations for satellite pixels is unknown or problematic because of the large disparity in resolution between point measurements and coarse satellite pixels (the so-called scale effect) [32]. In addition, the dependence on snow depth priors partially delays the real-time or near-real-time monitoring of the SWE. ...

Reanalyzing the spatial representativeness of snow depth at automated monitoring stations using airborne Lidar data

... Besides the above-mentioned observables directly derived from the CYGNSS, several previous studies coupled other observables from different satellite systems to these fundamental CYGNSS observables for improving SM retrieval capacity and accuracy. Typically, Wernicke et al., 2022 andYang et al., 2022b used brightness temperature (T B ) retrieved from the SMAP passive radiometer to enhance the CYGNSS SR measurements, while Zhu et al. (2022) and Zhang et al. (2023) considered the soil surface temperature (SST) as an ancillary variable to directly improve SM estimation. ...

Downscaling SMAP Brightness Temperatures to 3 km Using CYGNSS Reflectivity Observations: Factors That Affect Spatial Heterogeneity

... Since a dry period was intentionally chosen to test the SHADI and HADI, these discrepancies in the results were expected. The main purpose for the derivation and utilization of variable threshold levels in drought categorization is to fulfil the necessity of consideration of both spatial and temporal distributions of droughts [42]. Hence, different thresholds for each drought category would be expected if different periods were selected. ...

Investigating the Role of Snow Water Equivalent on Streamflow Predictability during Drought
  • Citing Article
  • August 2022

Journal of Hydrometeorology

... In forested environments, up to 60% of winter snowfall can be intercepted (Pomeroy & Schmidt, 1993), with sublimation from intercepted snow dominating over other alternate sublimation pathways such as from the snowpack or blowing snow (Frank et al., 2019;Molotch et al., 2007;Strasser et al., 2008). However, snow interception is difficult to measure in-situ beyond the point scale (i.e., a single tree) (Lundberg & Halldin, 1994;Montesi et al., 2004;Nakai et al., 1994;Raleigh et al., 2022), necessitating the development of models to simulate interception Lv & Pomeroy, 2019;Niu et al., 2011;Roesch et al., 2001;Strasser et al., 2008). Models can also be used to understand which processes influence snow interception and subsequent unloading via wind, melting, or sublimation Lumbrazo et al., 2022;Roesch et al., 2001). ...

Challenges and Capabilities in Estimating Snow Mass Intercepted in Conifer Canopies With Tree Sway Monitoring

... Data assimilation has found successful application in numerous snow modeling studies (e.g., Alonso-González et al., 2022;De Lannoy et al., 2022;Girotto et al., 2020;Helmert et al., 2018;Largeron et al., 2020). The applied assimilation schemes range from directly inserting observations into the modeled snow states (e.g., Hedrick et al., 2018) to interpolation schemes (e.g., Gichamo & Draper, 2022;Kongoli et al., 2019;Magnusson et al., 2014) and ensemble-based Bayesian filtering techniques (e.g., Aalstad et al., 2018;Gichamo & Tarboton, 2019;Magnusson et al., 2017;Smyth et al., 2019Smyth et al., , 2022. The choice of the most suitable assimilation scheme strongly depends on factors such as the complexity of the model, the intended application, and the type and frequency of available observations (Alonso-González et al., 2022;Largeron et al., 2020). ...

The Challenges of Simulating SWE Beneath Forest Canopies are Reduced by Data Assimilation of Snow Depth

... Forests challenge InSAR ΔSWE retrievals because trees attenuate the radar signal, and this effect increases as temperatures approach 0°C . Additionally, tree sway due to wind and snow loading and shifts in the branches can influence the location of the phase-center (e.g., Raleigh et al., 2022), reducing coherence and confounding the interferometric snow signal. The accumulation of snow in the forest canopy, which is common in many snow climates, causes additional attenuation . ...

Isolating Forest Process Effects on Modeled Snowpack Density and SWE
  • Citing Article
  • January 2022

Hydrological Processes

... Following this research, by incorporating SMAP data into a modified version of the Penman-Monteith equation, Kim et al. (2020) investigated the global ET a variations. Another example is E-SMAP, a soil evaporation model, derived from the SMAP satellite soil moisture product based on a soil water balance at 9 km spatial resolution (Abolafia-Rosenzweig et al., 2020). Via inversion of Warrick's (1975) analytical model, Sadeghi et al. (2019Sadeghi et al. ( , 2020 also showed that the land surface net water flux, including ET a , can be estimated from only surface soil moisture data (e.g., NASA's SMAP). ...

A continental-scale soil evaporation dataset derived from Soil Moisture Active Passive satellite drying rates

Scientific Data