Artificial neural network-based techniques for the retrieval of SWE and snow depth from SSM/I data

The retrieval of snow water equivalent (SWE) and snow depth is performed by inverting Special Sensor Microwave Imager (SSM/I) brightness temperatures at 19 and 37 GHz using artificial neural network ANN-based techniques. The SSM/I used data, which consist of Pathfinder Daily EASE-Grid brightness temperatures, were supplied by the National Snow and Ice Data Centre (NSIDC). They were gathered during the period of time included between the beginning of 1996 and the end of 1999 all over Finland. A ground snow data set based on observations of the Finnish Environment Institute (SYKE) and the Finnish Meteorological Institute (FMI) was used to estimate the performances of the technique. The ANN results were confronted with those obtained using the spectral polarization difference (SPD) algorithm, the HUT model-based iterative inversion and the Chang algorithm, by comparing the RMSE, the R², and the regression coefficients. In general, it was observed that the results obtained through ANN-based technique are better than, or comparable to, those obtained through other approaches, when trained with simulated data. Performances were very good when the ANN were trained with experimental data.     

Development of a winter snow water equivalent algorithm using in situ passive microwave radiometry over snow-covered first-year sea ice

A snow water equivalent (SWE) algorithm has been developed for thin and thick snow using both in situ microwave measurements and snow thermophysical properties, collected over landfast snow covered first-year sea ice during the Canadian Arctic Shelf Exchange Study (CASES) overwintering mission from December 2003 to May 2004. Results showed that the behavior of brightness temperatures (T_bs) in thin snow covers was very different from those in a thick snowpack. Microwave SWE retrievals using the combination of T_b 19 GHz and air temperature (multiple regression) over thick snow are quite accurate, and showed very good agreement with the physical data (R² = 0.94) especially during the cooling period (i.e., from freeze up to the minimum air temperature recorded) where the snow is dry and cold. Thin snow SWE predictions also showed fairly good agreement with field data (R² = 0.70) during the cold season. The differences between retrieved and in situ SWE for both thin and thick snow cover are mainly attributable to the variations in air temperature, snow wetness and spatial heterogeneity in snow thickness.     

Quantifying the uncertainty in passive microwave snow water equivalent observations

Passive microwave sensors (PM) onboard satellites have the capability to provide global snow observations which are not affected by cloudiness and night condition (except when precipitating events are occurring). Furthermore, they provide information on snow mass, i.e., snow water equivalent (SWE), which is critically important for hydrological modeling and water resource management. However, the errors associated with the passive microwave measurements of SWE are well known but have not been adequately quantified thus far. Understanding these errors is important for correct interpretation of remotely sensed SWE and successful assimilation of such observations into numerical models.This study uses a novel approach to quantify these errors by taking into account various factors that impact passive microwave responses from snow in various climatic/geographic regions. Among these factors are vegetation cover (particularly forest cover), snow morphology (crystal size), and errors related to brightness temperature calibration. A time-evolving retrieval algorithm that considers the evolution of snow crystals is formulated. An error model is developed based on the standard error estimation theory. This new algorithm and error estimation method is applied to the passive microwave data from Special Sensor Microwave/Imager (SSM/I) during the 1990-1991 snow season to produce annotated error maps for North America. The algorithm has been validated for seven snow seasons (from 1988 to 1995) in taiga, tundra, alpine, prairie, and maritime regions of Canada using in situ SWE data from the Meteorological Service of Canada (MSC) and satellite passive microwave observations. An ongoing study is applying this methodology to passive microwave measurements from Scanning Multichannel Microwave Radiometer (SMMR); future study will further refine and extend the analysis globally, and produce an improved SWE dataset of more than 25 years in length by combining SSMR and SSM/I measurements.     

Snowpack and runoff generation using AMSR-E passive microwave observations in the Upper Helmand Watershed, Afghanistan

Passive microwave estimates of snow water equivalent (SWE) were examined to determine their usefulness for evaluating water resources in the remote Upper Helmand Watershed, central Afghanistan. SWE estimates from the Advanced Microwave Scanning Radiometer-Earth Observing System (AMSR-E) and the Special Sensor Microwave/Imager (SSM/I) passive microwave data were analyzed for six winter seasons, 2004-2009. A second, independent estimate of SWE was calculated for these same time periods using a hydrologic model of the watershed with a temperature index snow model driven using the Tropical Rainfall Measuring Mission (TRMM) gridded estimates of precipitation. The results demonstrate that passive microwave SWE values from SSM/I and AMSR-E are comparable. The AMSR-E sensor had improved performance in the early winter and late spring, which suggests that AMSR-E is better at detecting shallow snowpacks than SSM/I. The timing and magnitude of SWE values from the snow model and the passive microwave observations were sometimes similar with a correlation of 0.53 and accuracy between 55 and 62%. However, the modeled SWE was much lower than the AMSR-E SWE during two winter seasons in which TRMM data estimated lower than normal precipitation. Modeled runoff and reservoir storage predictions improved significantly when peak AMSR-E SWE values were used to update the snow model state during these periods. Rapid decreases in passive microwave SWE during precipitation events were also well aligned with flood flows that increased base flows by 170 and 940%. This finding supports previous northern latitude studies which indicate that the passive microwave signal's lack of scattering can be used to detect snow melt. The current study's extension to rain on snow events suggests an opportunity for added value for flood forecasting.     

Development of a tundra-specific snow water equivalent retrieval algorithm for satellite passive microwave data

Airborne and satellite brightness temperature (T_B) measurements were combined with intensive field observations of sub-Arctic tundra snow cover to develop the framework for a new tundra-specific passive microwave snow water equivalent (SWE) retrieval algorithm. The dense snowpack and high sub-grid lake fraction across the tundra mean that conventional brightness temperature difference approaches (such as the commonly used 37 GHz-19 GHz) are not appropriate across the sub-Arctic. Airborne radiometer measurements (with footprint dimensions of approximately 70 × 120 m) acquired across sub-Arctic Canada during three field campaigns during the 2008 winter season were utilized to illustrate a slope reversal in the 37 GHz T_B versus SWE relationship. Scattering by the tundra snowpack drives a negative relationship until a threshold SWE value is reached near 130 mm at which point emission from the snowpack creates a positive but noisier relationship between 37 GHz T_B and SWE.The change from snowpack scattering to emission was also evident in the temporal evolution of 37 GHz T_B observed from satellite measurements. AMSR-E brightness temperatures (2002/03-2006/07) consistently exhibited decreases through the winter before reaching a minimum in February or March, followed by an increase for weeks or months before melt. The cumulative absolute change (Σ|Δ37V|) in vertically polarized 37 GHz T_B was computed at both monthly and pentad intervals from a January 1 start date and compared to ground measured SWE from intensive and regional snow survey campaigns, and climate station observations. A greater (lower) cumulative change in |Δ37V| was significantly related to greater (lower) ground measured SWE (r² = 0.77 with monthly averages; r² = 0.67 with pentad averages). Σ|Δ37V| was only weakly correlated with lake fraction: monthly r² values calculated for January through April 2003-2007 were largely less than 0.2. These results indicate that this is a computationally straightforward and viable algorithmic framework for producing tundra-specific SWE datasets from the complete satellite passive microwave record (1979 to present).     

Estimation of snow water equivalent over first-year sea ice using AMSR-E and surface observations

A SWE retrieval algorithm developed in-situ using passive microwave surface based radiometer data is applied to the Advanced Microwave Scanning Radiometer for Earth Observation System (AMSR-E). Snow water equivalent is predicted from two pixels located in Canadian Arctic Shelf Exchange Study (CASES) overwintering study area in Franklin Bay, N.W.T., Canada. Results show that the satellite SWE predictions are statistically valid with measured in-situ snow thickness data in both smooth and rough ice environments where predicted values range from 15 to 25 mm. Stronger correlation between measured and predicted data is found over smooth ice with R² value of 0.75 and 0.73 for both pixels respectively. Furthermore, a qualitative study of sea ice roughness using both passive and active microwave satellite data shows that the two pixels are rougher than the surrounding areas, but the SWE predictions do not seem to be affected significantly.     

Retrieving seawater turbidity from Landsat TM data by regressions and an artificial neural network

The radiance reflected at the sea surface (R_W (λ)) of the Ariake Sea, Japan, was first estimated by subtracting Lowtran 7 estimated Rayleigh and aerosol scattered radiances from Landsat Thematic Mapper measured radiance. Then R_W (λ) was averaged from 4×4 pixel windows centred at 33 sampling sites of the Ariake Sea and the data calibrated against the observed Secchi disk depth (SDD) using linear (LR) and nonlinear (NLR) regressions, and an artificial neural network (ANN) algorithm called the Modified Counter Propagation Network (MCPN). We found that at the validation stage, multi-date R_W (λ) data that are mainly based on the visible channels of Landsat Thematic Mapper (TM) predict more accurate and dependable SDDs than single-date R_W (λ) data. Furthermore, the NLR describes the SDD/R_W (λ) relationship more closely than the LR. As an ANN, MCPN possesses non-linearity, inter-connectivity, and an ability to learn and generalize information from complex or poorly understood systems, which enables it to even better represent the SDD/R_W (λ) relationship than the NLR. Our study confirms the feasibility of retrieving SDD (or turbidity) from Landsat TM data, and it seems that the calibrated MCPN and possibly NLR are portable temporally within the Ariake Sea. Lastly, the coefficient of efficiency E_f is a more stringent and probably a more accurate statistical measure than the popular coefficient of determination R ².     

Mapping of snow water equivalent and snow depth in boreal and sub-arctic zones by assimilating space-borne microwave radiometer data and ground-based observations

The monitoring of snow water equivalent (SWE) and snow depth (SD) in boreal forests is investigated by applying space-borne microwave radiometer data and synoptic snow depth observations. A novel assimilation technique based on (forward) modelling of observed brightness temperatures as a function of snow pack characteristics is introduced. The assimilation technique is a Bayesian approach that weighs the space-borne data and the reference field on SD interpolated from discrete synoptic observations with their estimated statistical accuracy. The results obtained using SSM/I and AMSR-E data for northern Eurasia and Finland indicate that the employment of space-borne data using the assimilation technique improves the SD and SWE retrieval accuracy when compared with the use of values interpolated from synoptic observations. Moreover, the assimilation technique is shown to reduce systematic SWE/SD estimation errors evident in the inversion of space-borne radiometer data.     

Bare surface soil moisture retrieval from the synergistic use of optical and thermal infrared data

Land surface soil moisture (SSM) is crucial to research and applications in hydrology, ecology, and meteorology. To develop a SSM retrieval model for bare soil, an elliptical relationship between diurnal cycles of land surface temperature (LST) and net surface shortwave radiation (NSSR) is described and further verified using data that were simulated with the Common Land Model (CoLM) simulation. In addition, with a stepwise linear regression, a multi-linear model is developed to retrieve daily average SSM in terms of the ellipse parameters x₀ (horizontal coordinate of the ellipse centre), y₀ (vertical coordinate of the ellipse centre), a (semi-major axis), and θ (rotation angle), which were acquired from the elliptical relationship. The retrieval model for daily average SSM proved to be independent of soil type for a given atmospheric condition. Compared with the simulated daily average SSM, the proposed model was found to be of higher accuracy. For eight cloud-free days, the root mean square error (RMSE) ranged from 0.003 to 0.031 m³ m^?3, while the coefficient of determination (R²) ranged from 0.852 to 0.999. Finally, comparison and validation were conducted using simulated and measured data, respectively. The results indicated that the proposed model showed better accuracy than a recently reported model using simulated data. A simple calibration decreased RMSE from 0.088 m³ m^?3 to 0.051 m³ m^?3 at Bondville Companion site, and from 0.126 m³ m^?3 to 0.071 m³ m^?3 at the Bondville site. Coefficients of determination R² = 0.548 and 0.445 were achieved between the estimated daily average SSM and the measured values at the two sites, respectively. This paper suggests a promising avenue for retrieving regional SSM using LST and NSSR derived from geostationary satellites in future developments.     

Comparison of artificial neural network and combined models in estimating spatial distribution of snow depth and snow water equivalent in Samsami basin of Iran

Snow water equivalent (SWE) is a key parameter in hydrological cycle, and information on regional SWE is required for various hydrological and meteorological applications, as well as for hydropower production and flood forecasting. This study compares the snow depth and SWE estimated by multivariate linear regression (MLR), discriminant function analysis, ordinary kriging, ordinary kriging-multivariate linear regression, ordinary kriging-discriminant function analysis, artificial neural network (ANN) and neural network-genetic algorithm (NNGA) models. The analysis was performed in the 5.2 km² area of Samsami basin, located in the southwest of Iran. Statistical criteria were used to measure the models’ performances. The results indicated that NNGA, ANN and MLR methods were able to predict SWE at the desirable level of accuracy. However, the NNGA model with the highest coefficient of determination (R ² = 0.70, P value < 0.05) and minimum root mean square error (RMSE = 0.202 cm) provided the best results among the other models. The lower SWE values were registered in the east of study area and higher SWE values appeared in the west of study area where altitude was higher.     

An improved look-up table technique for geophysical parameters from SSM/I

An improved look-up table technique is developed to calculate meteorological parameters from Special Sensor Microwave/Imager (SSM/I) measurements. The method, which is based on a look-up table and an extrapolation and interpolation technique used in the weather prediction model, gives results comparable to or better than the regression method for the total precipitable water (TPW), surface wind speed (V), and cloud liquid water path (LWP). Applied to a noise-free data set (dependent test) TPW, V and LWP are retrieved with a rms. accuracy of 0.26 kg m^-2, 0.28 m s^-1 and 0.002 kg m^-2, respectively. If the random noise of the SSM/I radiometer is taken into account in the retrieval, the r.m.s. increases to 0.84 kg m^-2, 1.08 m s^-1 and 0.013 kg m^-2, respectively. The method is applied to a set of over 520 SSM/I measurements from the DMSP-F8 satellite for which collocated radiosondes launched from ships are available. The rms. (bias) of TPW and V was 2.91 (-0.61) kg m^-2 and 2.75 (-0.13) m s^-1, respectively. We use the improved look-up table technique to calculate the monthly mean global distribution of surface wind for August 1989 and compare the results with the Comprehensive Ocean-Atmosphere Data Set (COADS) for the same month. The rms. error and mean differences for the monthly mean values of sea surface wind speed between the retrievals and COADS data are 1.01 m s^-1 and 0.03 m s^-1, respectively. We also calculate LWP for October 1987 and compare it with the LWP derived from cloud optical thicknesses of International Satellite Cloud Climatology Project (ISCCP) dataset. Good agreement is obtained. The extension of the method to calculate cloud water and water vapour profiles is discussed.     

Estimating east Mediterranean forest parameters using Landsat ETM

The conservation of Jordan's Mediterranean forest requires the use of remote sensing. Among the most important parameters needed are the crown-cover percentage (C) and above-ground biomass (A). This study aims to: (1) identify the best predictor(s) of C using Landsat Enhanced Thematic Mapper (ETM) bands and the derived transformed normalized difference vegetation index (TNDVI); (2) determine if C is a good predictor of A, volume (V), Shannon diversity index (S) and basal area (B); and (3) generate maps of all these parameters. A Landsat ETM image, aerial photographs and ground surveys are used to model C using multiple regression. C is then modelled to A, V, S and B using linear regression. The relationship between C and Landsat ETM bands (1 and 7) plus the TNDVI is significantly high (coefficient of determination R ² = 0.8) and is used to produce the C map. The generated C map is used to predict A (R ² = 0.56), V (R ² = 0.58), S (R ² = 0.50) and B (R ² = 0.43). Cross validation for the predicted C map (cross-validation error = 5.3%) and for the predicted forest-parameter maps (cross-validation error = 13.7%–19.9%) shows acceptable error levels. Results indicate that Jordan's east Mediterranean forest parameters can be mapped and monitored for biomass accumulation and carbon dioxide (CO₂) flux using Landsat ETM images.     

A comparison of 18 winter seasons of in situ and passive microwave-derived snow water equivalent estimates in Western Canada

The Meteorological Service of Canada (MSC) has developed an operational snow water equivalent (SWE) retrieval algorithm suite for western Canada that can be applied to both Scanning Multichannel Microwave Radiometer (SMMR) and Special Sensor Microwave/Imager (SSM/I) data. Separate algorithms derive SWE for open environments, deciduous, coniferous, and sparse forest cover. A final SWE value represents the area-weighted average based on the proportional land cover within each pixel. The combined SSM/I and SMMR time series of dual polarized, multichannel, spaceborne passive microwave brightness temperatures extends back to 1978, providing a lengthy time series for algorithm assessment. In this study, 5-day average (pentad) passive microwave-derived SWE imagery for 18 winter seasons (December, January, February 1978/79 through 1995/96) was compared to SWE estimates taken from a distributed network of surface measurements throughout western Canada.Results indicated both vegetative and snowpack controls on the performance of MSC algorithms. In regions of open and low-density forest cover, the in situ and passive microwave SWE data exhibited both strong agreement and similar levels of interannual variability. In locations where winter season SWE typically exceeded 75 mm, and/or dense vegetative cover was present, dataset agreement weakened appreciably, with little interannual variability in the passive microwave SWE retrievals. These results have important implications for extending the SWE monitoring capability of the MSC algorithm suite to northern regions such as the Mackenzie River basin.     

Evaluation of passive microwave snow water equivalent algorithms in the depth hoar-dominated snowpack of the Kuparuk River Watershed, Alaska, USA

This research investigates the utility of passive microwave remote sensing instruments to accurately determine snow water equivalent (SWE) over large spatial extents. Three existing Special Sensor Microwave Imager (SSM/I) snow water equivalent algorithms produced by Chang, Tait and Goodison were evaluated for their ability to determine snow water equivalent in a snowpack containing substantial depth hoar, large faceted snow crystals. The Kuparuk River Watershed (8140 km²) test site on the North Slope of Alaska was chosen for its snowpack containing a think depth hoar layer and long history of ground truth data. A new regional snow water equivalent algorithm was developed to determine if it could produce better results than the existing algorithms in an area known to contain significant depth hoar. The four algorithms were tested to see how well they could determine snow water equivalent: (1) on a per pixel basis, (2) across swath-averaged spatial bands of approximately 850 km², and (3) on a watershed scale. The algorithms were evaluated to see if they captured the annual spatial distribution in snow water equivalent over the watershed. Results show that the algorithms developed by Chang and from this research are generally within 3 cm of the spatially averaged snow water equivalents over the entire watershed. The algorithms produced by Chang, Tait, and in this research were able to predict the basin-wide ground measured snow water equivalent value within a percent error range from −32.4% to 24.4% in the years with a typical snowpack. None of the algorithms produce accurate results on a pixel-by-pixel scale, with errors ranging from −26% to 308%.     

Effects of vegetation and soil texture on surface soil moisture retrieval using multi-temporal optical and thermal infrared observations

To retrieve surface soil moisture (SSM) content over natural surfaces quantitatively, the effects of vegetation and soil texture on a previously developed bare SSM retrieval model are evaluated using simulated data from the common land model (CoLM). The results indicate that (1) both the accuracy and the five model parameters of the previous SSM retrieval model show relatively consistent variations when the fractional vegetation cover (FVC) varies from 0 to 0.7; and (2) the SSM exhibits a generally significant and exponential relationship with the rotation angle when the clay content is lower than 30%, with the FVC ranging from 0 to 0.7. These findings make it possible to estimate SSM directly under the conditions that the underlying surface is in the presence of spatially variable FVC and soil texture. On this basis, we further confirm the feasibility of using the previous bare SSM retrieval model to estimate SSM for FVC varying from 0 to 0.7 with a clay content lower than 30%. For the simulated data on eight cloud-free days, the total root mean square error (RMSE) of the retrieved SSM and the coefficient of determination (R²) are 0.033 m³m^?3 and 0.758, respectively. Ultimately, a preliminary validation is conducted using the ground measurements at the Bondville site; an R² = 0.328 and a RMSE = 0.058 m³m^?3 are obtained for 14 cloud-free days.     

Regularity for nonlinear variational inequalities of hyperbolic type

In this paper, we deal with the regularity for nonlinear variational inequalities of second order in Hilbert spaces with more general conditions on the nonlinear terms and without condition of the compactness of the principal operators. We also obtain the norm estimate of a solution of the given nonlinear equation on C([0,T];V)∩C¹((0,T];H)∩C²((0,T];V^∗) by using the results of its corresponding hyperbolic semilinear part.     

Correcting for the influence of frozen lakes in satellite microwave radiometer observations through application of a microwave emission model

The spatial resolution of passive microwave observations from space is of the order of tens of kilometers with currently available instruments, such as the Special Sensor Microwave/Imager (SSM/I) and Advanced Microwave Scanning Radiometer (AMSR-E). The large field of view of these instruments dictates that the observed brightness temperature can originate from heterogeneous land cover, with different vegetation and surface properties.In this study, we assess the influence of freshwater lakes on the observed brightness temperature of AMSR-E in winter conditions. The study focuses on the geographic region of Finland, where lakes account for 10% of the total terrestrial area. We present a method to mitigate for the influence of lakes through forward modeling of snow covered lakes, as a part of a microwave emission simulation scheme of space-borne observations. We apply a forward model to predict brightness temperatures of snow covered sceneries over several winter seasons, using available data on snow cover, vegetation and lake ice cover to set the forward model input parameters. Comparison of model estimates with space-borne observations shows that the modeling accuracy improves in the majority of examined cases when lakes are accounted for, with respect to the case where lakes are not included in the simulation. Moreover, we present a method for applying the correction to the retrieval of Snow Water Equivalent (SWE) in lake-rich areas, using a numerical inversion method of the forward model. In a comparison to available independent validation data on SWE, also the retrieval accuracy is seen to improve when applying the influence of snow covered lakes in the emission model.     

Merging complementary remote sensing datasets in the context of snow water equivalent reconstruction

Time series of snow covered area (SCA) estimates from the Moderate Resolution Imaging Spectroradiometer (MODIS) and Landsat Enhanced Thematic Mapper (ETM+) were merged with a spatially explicit snowmelt model to reconstruct snow water equivalent (SWE) in the Rio Grande headwaters (3419 km²). A linear optimization scheme was used to derive SCA estimates that preserve the statistical moments of the higher spatial resolution (i.e. 30 m) ETM+ data and resolve the superior temporal signal (i.e. ∼ daily) of the MODIS data. It was found that merging the two SCA products led to an 8% decrease and an 18% increase in the basinwide SWE in 2001 and 2002, respectively, compared to the SWE estimated from ETM+ only. Relative to SWE simulations using only ETM+ data, the hybrid SCA estimates reduced the mean absolute SWE error by 17 and 84% in 2001 and 2002, respectively; errors were determined using intensive snow survey data and two separate methods of scaling snow survey field measurements of SWE to the 1-km model pixel resolution. SWE bias for both years was reduced by 49% and skewness was reduced from − 0.78 to 0.49. These results indicate that the hybrid SWE was closer to being an unbiased estimate of the measured SWE and errors were distributed more normally. The accuracy of the SCA estimates is likely dependent on the vegetation fraction.     

Estimating northern hemisphere snow water equivalent for climate research through assimilation of space-borne radiometer data and ground-based measurements

The key variable describing global seasonal snow cover is snow water equivalent (SWE). However, reliable information on the hemispheric scale variability of SWE is lacking because traditional methods such as interpolation of ground-based measurements and stand-alone algorithms applied to space-borne observations are highly uncertain with respect to the spatial distribution of snow mass and its evolution. In this paper, an algorithm assimilating synoptic weather station data on snow depth with satellite passive microwave radiometer data is applied to produce a 30-year-long time-series of seasonal SWE for the northern hemisphere. This data set is validated using independent SWE reference data from Russia, the former Soviet Union, Finland and Canada. The validation of SWE time-series indicates overall strong retrieval performance with root mean square errors below 40 mm for cases when SWE < 150 mm. Retrieval uncertainty increases when SWE is above this threshold. The SWE estimates are also compared with results obtained by a typical stand-alone satellite passive microwave algorithm. This comparison demonstrates the benefits of the newly developed assimilation approach. Additionally, the trends and inter-annual variability of northern hemisphere snow mass during the era of satellite passive microwave measurements are shown.