Steven A. Margulis

Quantifying Uncertainty in Modeling Snow Microwave Radiance for a Mountain Snowpack at the Point-Scale, Including Stratigraphic Effects

Merging microwave radiances and modeled estimates of snowpack states in a data assimilation scheme is a potential method for snowpack characterization. A radiance assimilation scheme for snow requires a land surface model (LSM) coupled to a radiative transfer model (RTM). In this paper, we explore the degree of model fidelity required in order for radiance assimilation to yield benefits for snowpack characterization. Specifically, we characterize the uncertainty of Microwave Emission Model for Layered Snowpacks (MEMLS) radiance predictions by quantifying model accuracy and sensitivity to the following: (1) the LSM snowpack layering scheme and (2) the properties of the snow layers, including melt-refreeze ice layers. MEMLS was consistent with the measured brightness temperatures at 18.7 and 36.5 GHz with a bias (mean absolute error) of 0.1 K (3.1 K) for the vertical polarization and 3.4 K (9.3 K) for the horizontal polarization. An error in the predictions at horizontal polarization is due to uncertainty in ice-layer properties. It was found that in order for predicted brightness temperatures from the coupled LSM and RTM to be adequate for radiance assimilation purposes, the following must be satisfied: (1) the LSM snowpack layering scheme must accurately represent the stratigraphic snowpack layers; (2) dynamics of melt-refreeze ice layers must be modeled explicitly, and the predicted density of melt-refreeze layers must be accurate within ; and (3) the MEMLS correlation length must be predicted within 0.016 mm, or effective optical grain diameter must be predicted within 0.045 mm. Recommendations for future field measurements are made.

Correcting first‐order errors in snow water equivalent estimates using a multifrequency, multiscale radiometric data assimilation scheme

A season-long, multiscale, multifrequency radiometric data assimilation experiment is performed to test the feasibility of snow water equivalent (SWE) estimation. Synthetic passive microwave (PM) observations at Advanced Microwave Scanning Radiometer-Earth Observing System frequencies and 25 km resolution and synthetic near infrared (NIR) narrowband albedo observations corresponding to Moderate Resolution Imaging Spectroradiometer band 5 (1230–1250 μm) and 1 km resolution are assimilated into a land surface model snow scheme using the ensemble Kalman filter. First-order sources of model uncertainty, including error in precipitation quantity, grain size evolution, precipitation spatial distribution, and vegetation leaf area index are modeled. SWE remote sensing retrieval schemes would be of limited value for these scenarios where snow depth ranged between 1.0 and 2.0 m, grain size varied in space, significant vegetation was present, and the snowpack sometimes contained liquid water. Nevertheless, the true basinwide SWE is recovered, in general, within a root-mean-square error (RMSE) of approximately 2 cm. Synergy is observed between the PM and NIR measurements because of the complementary nature of the multiscale, multifrequency measurements. Results from the assimilation are compared to those from a pure modeling approach and from a remote sensing retrieval approach. The effects of model uncertainty, measurement error, and ensemble size are investigated.

Feasibility Test of Multifrequency Radiometric Data Assimilation to Estimate Snow Water Equivalent

Abstract A season-long, point-scale radiometric data assimilation experiment is performed in order to test the feasibility of snow water equivalent (SWE) estimation. Synthetic passive microwave observations at Special Sensor Microwave Imager (SSM/I) and Advanced Microwave Scanning Radiometer-Earth Observing System (AMSR-E) frequencies and synthetic broadband albedo observations are assimilated simultaneously in order to update snowpack states in a land surface model using the ensemble Kalman filter (EnKF). The effects of vegetation and atmosphere are included in the radiative transfer model (RTM). The land surface model (LSM) was given biased precipitation to represent typical errors introduced in modeling, yet was still able to recover the true value of SWE with a seasonally integrated rmse of only 2.95 cm, despite a snow depth of around 3 m and the presence of liquid water in the snowpack. This ensemble approach is ideal for investigating the complex theoretical relationships between the snowpack proper...

Variational Assimilation of Radiometric Surface Temperature and Reference-Level Micrometeorology into a Model of the Atmospheric Boundary Layer and Land Surface

Abstract Data assimilation provides a useful framework that allows us to combine measurements and models, by appropriately weighting the sources of error in both, to produce a statistically optimal and dynamically consistent estimate of the evolving state of the system. In this paper a variational approach is used to estimate regional land and atmospheric boundary layer states and fluxes via the assimilation of standard reference-level temperature and humidity and radiometric surface temperature measurements into a coupled land surface–atmospheric boundary layer model. Results from an application to a field experiment site show that using both surface temperature and reference-level micrometeorology measurements allows for the accurate and robust estimation of land surface fluxes even during nonideal conditions, where the evaporation rate is atmospherically controlled and processes that are not parameterized in the model (i.e., advection) are important. The assimilation scheme is able to provide estimates...

A Landsat-Era Sierra Nevada Snow Reanalysis (1985–2015)

AbstractA newly developed state-of-the-art snow water equivalent (SWE) reanalysis dataset over the Sierra Nevada (United States) based on the assimilation of remotely sensed fractional snow-covered area data over the Landsat 5–8 record (1985–2015) is presented. The method (fully Bayesian), resolution (daily and 90 m), temporal extent (31 years), and accuracy provide a unique dataset for investigating snow processes. The verified dataset (based on a comparison with over 9000 station years of in situ data) exhibited mean and root-mean-square errors less than 3 and 13 cm, respectively, and correlation greater than 0.95 compared with in situ SWE observations. The reanalysis dataset was used to characterize the peak SWE climatology to provide a basic accounting of the stored snowpack water in the Sierra Nevada over the last 31 years. The pixel-wise peak SWE volume over the domain was found to be 20.0 km3 on average with a range of 4.0–40.6 km3. The ongoing drought in California contains the two lowest snowpack...

A Coupled Land Surface–Boundary Layer Model and Its Adjoint

Abstract In this paper, a simple coupled land surface–boundary layer model and its adjoint are presented. The primary goal is to demonstrate the capabilities of the adjoint model as a general tool for sensitivity analysis and data assimilation. The adjoint method was chosen primarily for two reasons: 1) the adjoint model can be used not only to obtain parameter sensitivities with greater efficiency but, more important, to provide added insight into the sensitivities as compared with that obtained with traditional simulation techniques (e.g., pathways, time variations in sensitivity) and 2) the adjoint model can be used in a variational data assimilation framework to combine measurements and the model of the physical system optimally in order to estimate state variables and fluxes. Two simple examples are presented to illustrate how the framework can be used for performing both diagnostic sensitivity experiments and hydrologic data assimilation. In the sensitivity experiment, temporal patterns and total in...

A Particle Batch Smoother Approach to Snow Water Equivalent Estimation

AbstractThis paper presents a newly proposed data assimilation method for historical snow water equivalent SWE estimation using remotely sensed fractional snow-covered area fSCA. The newly proposed approach consists of a particle batch smoother (PBS), which is compared to a previously applied Kalman-based ensemble batch smoother (EnBS) approach. The methods were applied over the 27-yr Landsat 5 record at snow pillow and snow course in situ verification sites in the American River basin in the Sierra Nevada (United States). This basin is more densely vegetated and thus more challenging for SWE estimation than the previous applications of the EnBS. Both data assimilation methods provided significant improvement over the prior (modeling only) estimates, with both able to significantly reduce prior SWE biases. The prior RMSE values at the snow pillow and snow course sites were reduced by 68%–82% and 60%–68%, respectively, when applying the data assimilation methods. This result is encouraging for a basin like...

Temporal disaggregation of satellite-derived monthly precipitation estimates and the resulting propagation of error in partitioning of water at the land surface

Abstract. Global estimates of precipitation can now be made using data from a combination of geosynchronous and low earth-orbit satellites. However, revisit patterns of polar-orbiting satellites and the need to sample mixed-clouds scenes from geosynchronous satellites leads to the coarsening of the temporal resolution to the monthly scale. There are prohibitive limitations to the applicability of monthly-scale aggregated precipitation estimates in many hydrological applications. The nonlinear and threshold dependencies of surface hydrological processes on precipitation may cause the hydrological response of the surface to vary considerably based on the intermittent temporal structure of the forcing. Therefore, to make the monthly satellite data useful for hydrological applications (i.e. water balance studies, rainfall-runoff modelling, etc.), it is necessary to disaggregate the monthly precipitation estimates into shorter time intervals so that they may be used in surface hydrology models. In this study, two simple statistical disaggregation schemes are developed for use with monthly precipitation estimates provided by satellites. The two techniques are shown to perform relatively well in introducing a reasonable temporal structure into the disaggregated time series. An ensemble of disaggregated realisations was routed through two land surface models of varying complexity so that the error propagation that takes place over the course of the month could be characterised. Results suggest that one of the proposed disaggregation schemes can be used in hydrological applications without introducing significant error. Keywords: precipitation, temporal disaggregation, hydrological modelling, error propagation

Validation and Error Characterization of the GPCP-1DD Precipitation Product over the Contiguous United States

Abstract A validation and error characterization study of the Global Precipitation Climatology Project, 1 degree daily (GPCP-1DD) precipitation product over the contiguous United States is presented. Daily precipitation estimates over a 1° grid are compared against aggregated precipitation values obtained from the forcing field of the North American Land Data Assimilation System (LDAS). LDAS daily values are consistent with the National Centers for Environmental Prediction Climate Prediction Center (CPC) gauge-based daily precipitation product and hence are regarded as realistic ground-truth values with full coverage of the United States. Continuous and categorical measures of skill are presented, so that both the ability of GPCP-1DD to identify a precipitation event and its accuracy in determining cumulative precipitation amounts are evaluated. Daily values are aggregated into seasonal averages, and spatial averages are computed for five arbitrarily defined zones that cover most of the study area. Result...

A Case Study of Using a Multilayered Thermodynamical Snow Model for Radiance Assimilation

A microwave radiance assimilation (RA) scheme for the retrieval of snow physical state variables requires a snowpack physical model (SM) coupled to a radiative transfer model. In order to assimilate microwave brightness temperatures (Tbs) at horizontal polarization (h-pol), an SM capable of resolving melt-refreeze crusts is required. To date, it has not been shown whether an RA scheme is tractable with the large number of state variables present in such an SM or whether melt-refreeze crust densities can be estimated. In this paper, an RA scheme is presented using the CROCUS SM which is capable of resolving melt-refreeze crusts. We assimilated both vertical (v) and horizontal (h) Tbs at 18.7 and 36.5 GHz. We found that assimilating Tb at both h-pol and vertical polarization (v-pol) into CROCUS dramatically improved snow depth estimates, with a bias of 1.4 cm compared to -7.3 cm reported by previous studies. Assimilation of both h-pol and v-pol led to more accurate results than assimilation of v-pol alone. The snow water equivalent (SWE) bias of the RA scheme was 0.4 cm, while the bias of the SWE estimated by an empirical retrieval algorithm was -2.9 cm. Characterization of melt-refreeze crusts via an RA scheme is demonstrated here for the first time; the RA scheme correctly identified the location of melt-refreeze crusts observed in situ.