Vertical Polarization Brightness Temperature Research Articles

A novel global snow depth retrieval method considering snow metamorphism and forest influence

Accurate snow depth (SD) information at global scales is highly important for validation and calibration of hydrological model, snowmelt runoff prediction, and global water supplies estimation. Passive microwave remote sensing has been proven to be an efficient method to detect SD at regional or global scales. However, numerous heterogeneous snow property parameters and forest parameters affect the microwave radiation characteristics, which is a great challenge for SD retrieval. In this study, a novel SD retrieval algorithm that comprehensively considered the multiple sensitive factors was developed at global scales by coupling the Microwave Emission Model of Layered Snowpacks (MEMLS) model and machine learning (ML) technique. The exponential correlation length (Pec), snow density (ρ), and forest cover fraction (fforest) are three sensitive parameters for retrieving SD from passive microwave observations based on the extended Fourier amplitude sensitivity test (EFAST) algorithm. The key parameter Pec, which characterizes the snow microstructure information inside snowpacks, was optimized by minimizing the brightness temperature between satellite observations and microwave radiative transfer model simulations by integrating the MEMLS, forest impact, and atmospheric radiation attenuation. The random forest (RF) ML technique was used, and the optimal combination of independent variables was selected by correlation heatmap and importance ranking of variables. Six selected essential parameters, including Pec, vertical polarized brightness temperature differences between 18.7 and 36.5 GHz, ρ from ERA5, fforest, elevation, and longitude together with target SD output were used to train the RF model. Seventy percent of the entire data at meteorological stations were randomly chosen to train the RF model, and the remaining 30% were adopted as the validation data from 2013 to 2020 to ensure the mutual independence of training data and validation data. Compared with independent in situ measurements, the overall RMSE of SD is 13.6 cm, which was noticeably lower than those of the international SD remote sensing products and reanalysis datasets, including AMSR2 (36.2 cm), GlobSnow 3.0 (25.3 cm), ERA5 (38.2 cm), and ERA5-land (29.9 cm). The results demonstrated that the new proposed algorithm, by coupling the MEMLS model with the ML technique, could significantly enhance the overall performance in SD retrieval at global scales.

A Soil Moisture Retrieval Method for Reducing Topographic Effect: A Case Study on the Qinghai–Tibetan Plateau With SMOS Data

The topography can be very important for passive microwave remote sensing of soil moisture due to its complex influence on the emitted brightness temperature observed by a satellite microwave radiometer. In this study, a methodology of using the first brightness Stokes parameter (i.e., the sum of vertical and horizontal polarization brightness temperature) observed by the Soil Moisture and Ocean Salinity (SMOS) was proposed to improve the soil moisture retrieval under complex topographic conditions. The applicability of the proposed method is validated using in-situ soil moisture measurements collected at four networks (Pali, Naqu, Maqu and Wudaoliang) on the Qinghai-Tibetan Plateau. The results over Pali, which is a typical mountainous area, showed that soil moisture retrievals using the first brightness Stokes parameter are in better agreement with the in-situ measurements (the correlation coefficient R >0.75 and unbiased root mean square error < 0.04 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> /m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) compared with that using the single-polarization brightness temperature. At the other three networks with relatively flatter terrains, soil moisture retrievals using the first brightness Stokes parameter are found to be comparable to the single-polarization retrievals. On the contrary, the maximum bias of the retrieved soil moisture caused by topographic effects exceeds 0.1 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> /m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> when using vertical or horizontal polarization alone, which is far beyond the expected accuracy (0.04 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> /m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) of SMOS satellite. In the regions on the Qinghai-Tibetan Plateau where the vegetation effect can be ignored, soil moisture retrieved using horizontal polarization brightness temperature is generally underestimated, overestimated when using vertical polarization brightness temperature. It is reasonable due to the polarization rotation effect (depolarization) caused by the topographic effects. It is concluded that the proposed method for soil moisture retrieval using the first brightness Stokes parameter has a great potential in reducing the influence of topographic effects.

Detection of soil freeze/thaw states in the Arctic region based on combined SMAP and AMSR-2 radio brightness observations

ABSTRACT In this study, a new approach to identify the freeze/thaw states of tundra topsoil was developed based on the polarization ratio index, which was calculated from the reflectivity values of soil. Reflectivity was estimated from radiometric measurements of the SMAP satellite using the values of vertical polarization brightness temperature measured by the AMSR-2 radiometer at 6.9 GHz; this value was used to characterize the effective temperature of the soil. The proposed approach was tested using weather station data on soil surface temperatures for six test sites located in the North Slope of Alaska and the Yamal Peninsula collected from April 2015 to June 2018. The modified polarization ratio index, calculated from values of reflectivity rather than from brightness temperatures, significantly improved the possibility of determining the reference values of the index in the winter and in the summer. During testing, the modified index showed a good correlation between the dates of transition through the threshold level and soil temperature transition through 0ºC, as recorded at meteorological stations.

Modeling the microwave emission of a moist granular medium

Based on the Mie Scattering Theory and the Dense Medium Radiative Transfer (DMRT) Theory, this paper analyze the electromagnetic scattering properties of particles under different humidity and temperature, and discusse the polarization brightness temperature of moist granular layer. The numerical calculation results show that when the particle temperature is over 273 K, the particle humidity has more obviously influence on the electromagnetic scattering properties of sand particles than its temperature. When the temperature is below 273 K, the optical properties of particles are mainly affected by the humidity of particles, and with the increase of humidity, the extinction efficiency of particle shows a trend of increasing initially and decreasing afterwards, and the maximum value appears when the humidity of the wet ice is 0.2. In addition, with the increase of particle temperature and humidity, the microwave brightness temperature of particle layer significantly increases, and its vertical polarization brightness temperature is greater than the horizontal polarization brightness temperature, the maximum difference appears near the observation angle of 55°. However, it is more sensitive to the thickness of sand layer when the observation angle is below 30° and the thickness does not exceed 30 cm.

Examination of the impacts of vegetation on the correlation between snow water equivalent and passive microwave brightness temperature

Snow accumulation, ablation, and runoff in mountainous areas are critical components of the hydrologic cycle, but are poorly known. Passive microwave (PM) measurements are sensitive to snow water equivalent (SWE), even in mountain regions, but vegetation masks the microwave signals and reduces this sensitivity. This study examines how the PM snow signal is affected by the forest density in fourteen basins in the Sierra Nevada, USA, and in a series of sixteen subsets of the Kern basin that have varied vegetation density. 36.5GHz vertical polarization brightness temperature (Tb) time series for each basin were produced from the spaceborne AMSR-E operational period (water year (WY) 2003 to WY2011). For each basin, the coefficient of determination (R2) between the annual minimum Tb and the concurrent SWE was calculated to evaluate the sensitivity of the PM to SWE. The relationship between the R2 values and the forest density was then analyzed to assess how vegetation affect the SWE information in the observed Tb. Mean forest coverage from MODIS was used to represent forest density. The R2 between the annual minimum Tb and concurrent SWE was >0.6 for three of the basins. Consistent with previous studies, WY2006 demonstrated anomalous Tb values for many basins, apparently due to anomalous warm winter rainfall. Excluding WY2006, R2 is significantly higher in all basins: eight of fourteen basins have R2 >0.6. For basins with average elevation >2500m, SWE correlates well with Tb. The R2 decreases monotonically with decreasing elevation. Basin elevation and forest cover are highly correlated in the Sierra; a basin elevation of 2500m generally coincides with forest cover of 20%. A total of 42% of Sierra Nevada has <20% forest cover; this corresponds to an estimated 34% of the total SWE in the Sierra. Thus, SWE and Tb are empirically correlated for over a third of the SWE in the Sierra, typically at high elevations and above treeline.

A Method to Determine the Margins of High Sea Ice Concentration Using AMSR-E Passive Microwave Imagery

The margin of the sea ice with high sea ice concentration is a principal feature in microwave image and a hotspot in image recognition. A method for determining the margins is developed using the feature of dual-polarized brightness temperatures at 36.5 GHz and a new parameter (contrast ratio) is used in this paper. For the microwaves, the ratio of the horizontal-polarized emissivity to the vertical-polarized emissivity is approximately equal to the ratio between horizontal-polarized and vertical-polarized brightness temperatures of sea surface, which called as the dual-polarized emissivity ratio in this study. It is found that the dual-polarized emissivity ratio of sea ice with nearly 100% sea ice concentration in Arctic at 36.5 GHz band has a value ranged between 0.92 and 0.96, as shown by satellite-observed data in figure of horizontal-po-larized brightness temperature versus vertical-polarized brightness temperature. From open water to sea ice covered area, the contrast-ratio can show the changing features of the dual-polarized brightness temperature at 36.5 GHz. The contrast ratio rapidly changes at the ice margins and its gradient appears an extreme value when the ratio changes around 0.92. This extreme value is examined by the ice concentration calculated by the MODIS data. And the results indicate that the threshold ratio coincides with the contour line of 96% sea ice concentration. So the parameter of contrast ratio could be used to determine the position of margins in microwave image.

Mapping Surface Soil Freeze-Thaw Cycles in China Based on SMMR and SSM/I Brightness Temperatures from 1978 to 2008

This paper aims to provide a long time-series data set documenting the surface soil freeze-thaw cycles in China over a period of more than 30 years. The remote sensing data are from the daily brightness temperatures recorded by the Scanning Multichannel Microwave Radiometer (SMMR, 1978–1987) and Special Sensor Microwave Imager (SSM/I, 1987–2008), which have a 25 km spatial resolution. The classification method used to identify the surface soil freeze-thaw states is a dual-indices algorithm based on the 37 GHz vertical polarization brightness temperature and spectral gradient between the 37 GHz and 18/19 GHz brightness temperatures. This algorithm has been recalibrated for SMMR and SSM/I using the in situ daily minimal ground surface temperatures observed at 77 meteorological stations covering the dominant land surface types of China. The daily classifications of surface soil freeze-thaw states were validated by observations from an additional 273 meteorological stations. The classification accuracy of the frozen and thawed soils as well as the total accuracy exceed 80%. Based on this data set, we analyzed the seasonal and interannual variations across the areal extent and timing of surface soil freezing, trend of the onset date of surface soil freezing and thawing, and duration of surface soil thawing in China. The results showed that the maximum frozen extent during 1978–1987 was 6.93 × 106 km2 or 72.8% of the area, and it generally occurred in late December and January. The minimum frozen extent was 0.26 × 106 km2 or 3.0% of the area, and it occurred in late July and August. The first day of soil freezing occurred between September and November, whereas the first day of soil thawing occurred between March and May. The trend analysis demonstrated that from 1978 to 2008, the onset date of surface freezing was postponed by 19.6 ± 14.6 days, whereas the onset of surface thawing was advanced by -19.0 ± 9.4 days, and the thawing period was prolonged by 34.3 ± 16.5 days. These trends revealed a pattern of earlier thawing, later freezing, and longer growing seasons because of climate warming, especially in the seasonally frozen ground and permafrost regions with high ground temperatures.

Model for microwave emission of a snow-covered ground with focus on L band

Passive L-band (1–2GHz) observables are sensitive to surface soil moisture and ocean salinity, which is the core of the “soil moisture and ocean salinity” (SMOS) mission of the European Space Agency (ESA). This work investigates microwave emission processes that are important to link L-band brightness temperatures with soil freeze/thaw states and the presence and the state of snow. To this end, a ground snow radiative transfer (GS RT) model has been developed on the basis of the “Microwave Emission Model of Layered Snowpacks” (MEMLS). Our model sensitivity study revealed that L-band emission of a freezing ground can be affected significantly by dry snow, which has been mostly disregarded in previous studies. Simulations suggest that even dry snow with mostly negligible absorption at the L-band can impact L-band emission of winter landscapes significantly. We found that impedance matching and refraction caused by a dry snowpack can increase or decrease L-band emission depending on the polarization and the observation angle. Based on the performed sensitivity study, these RT processes can be compensatory at vertical polarization and the observation angle of 50°. This suggests the use of vertical polarized brightness temperatures measured at around 50° in order to achieve segregated information on soil-frost. Furthermore, our simulations demonstrate a significant sensitivity of L-band emission at horizontal polarization with respect to the density of the lowest snow layer as the result of refraction and impedance matching by the snowpack.

Antenna cross-polarization correction for spaceborne polarimetric microwave correlation radiometer (II): Correction experiment

In this paper, we simulated the earth scene brightness temperature by creating the earth scene data sets and using polarimetric microwave radiative transfer model. On the basis of the fully polarized antenna temperature equation we have derived, the radiometer antenna temperature was also simulated by generating antenna pattern through GRASP9 software. Then by using multiple linear regression method, the M matrix was calculated and the antenna cross-polarization correction for spaceborne polarimetric microwave correlation radiometer was realized. The correction results show that the antenna temperature and earth scene brightness temperature have a linear relationship. Antenna cross-polarization influences the orthogonal channels brightness temperature seriously, especially the vertical polarization brightness temperature. The antenna cross-polarization for each channel has been effectively reduced. Residual cross-polarization is better than -23 dB and the polarization purity is greater than 99.5%. Correction of using M matrix to eliminate the antenna cross-polarization is feasible. It has been proved that this technique is most appropriate for the final correction of antenna cross-polarization for the spaceborne polarimetric microwave correlation radiometer on orbit.

Soil moisture estimation over an arid environment in Mongolia from passive microwave remote sensing based on a simplified parameterization method

Satellite passive microwave remote sensing provides a major basis for the analysis of temporal and spatial variation of top soil moisture at large scales. A global soil moisture data product is currently released by the National Aeronautics and Space Administration (NASA) of USA based on AMSR-E (the Advanced Microwave Scanning Radiometer for the Earth Observing System onboard the NASA EOS Aqua satellite) global dual-polarization brightness temperature observations of the Earth. But the accuracy of this soil moisture product is not satisfactory in arid Mongolian regions. Based on a simplified parameterization method for characterizing the effects of the sparse vegetation cover and surface roughness on surface microwave emission, the estimation of daytime (local noon) and nighttime (local midnight) top soil moisture during a near two-year period from October 1, 2005 to September 20, 2007 over the arid CEOP(The Coordinated Energy and Water Cycle Observations Project)-Mongolia experiment area was conducted based on a multifrequency algorithm by mainly using AMSR-E 6.9 GHz, 10.7 GHz and 18.7 GHz vertical-polarized brightness temperature data. In the inversion model, the only model parameter asking for experimental calibration, i. e., the vegetation single scattering albedo, could be achieved through optimization technique by using in-situ soil moisture measurements. The results showed that the root mean square error (RMSE) between satellite estimated soil moisture and ground-measured soil moisture was close to 0.030 cm(3)/cm(3). Without other supplementary data else, the retrieval algorithm proposed in this paper may be applied to near real-time monitoring of the dynamic variation in top soil moisture at large scales, in an all-weather working manner, over arid and or semiarid environments characterized by natural sparse vegetation conditions. Therefore, it will be promising to provide sustaining and reliable initial near-surface soil moisture information for the long term study of climate change and water cycle over arid and or semiarid regions.

A new approach of dynamic monitoring of 5‐day snow cover extent and snow depth based on MODIS and AMSR‐E data from Northern Xinjiang region

AbstractTaking the Northern Xinjiang region as an example, we develop a snow depth model by using the Advanced Microwave Scanning Radiometer‐Earth Observing System (AMSR‐E) horizontal and vertical polarization brightness temperature difference data of 18 and 36 GHz bands and in situ snow depth measurements from 20 climatic stations during the snow seasons November–March) of 2002–2005. This article proposes a method to produce new 5‐day snow cover and snow depth images, using Terra and Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) daily snow cover products and AMSR‐E snow water equivalent and daily brightness temperature products. The results indicate that (1) the brightness temperature difference (Tb18h–Tb36h) provides the most accurate and precise prediction of snow depth; (2) the snow, land and overall classification accuracies of the new images are separately 89.2%, 77.7% and 87.2% and are much better than those of AMSR‐E or MODIS products (in all weather conditions) alone; (3) the snow classification accuracy increases as snow depth increases; and (4) snow accuracies for different land cover types vary as 88%, 92.3%, 79.7% and 80.1% for cropland, grassland, shrub, and urban and built‐up, respectively. We conclude that the new 5‐day snow cover–snow depth images can provide both accurate cloud‐free snow cover extent and the snow depth dynamics, which would lay a scientific basis for water management and prevention of snow‐related disasters in this dry and cold pastoral area. After validations of the algorithms over other regions with different snow and climate conditions, this method would also be used for monitoring snow cover and snow depth elsewhere in the world. Copyright © 2011 John Wiley &amp; Sons, Ltd.

Shortwave broadband black-sky surface albedo estimation for Arctic sea ice using passive microwave radiometer data

[1] A new remote sensing method to estimate the optical broadband black-sky surface albedo using passive microwave radiometer data has been developed. In this research, the Advanced Very High Resolution Radiometer (AVHRR) based shortwave broadband black-sky albedos processed using the algorithms of the new surface broadband albedo CM-SAF product SAL, and the Advanced Microwave Scanning Radiometer (AMSR-E) microwave data from the National Snow and Ice Data Center, Boulder, Colorado, have been employed. To analyze the correspondence between AVHRR-based optical albedo and microwave brightness temperature, AMSR-E frequencies of 6.9, 18.7, and 36.5 GHz have been tested by fitting a third-degree polynomial curve to the SAL albedo and the AMSR-E data points. The best correlation occurs in 6.9 GHz vertical polarization brightness temperature (R2 = 0.92). To illustrate and compare the spatial variabilities of the SAL and AMSR-E albedos of the sea ice during the melting and refreezing period, maps of 13 weeks have been prepared of both albedos from June to August 2007. The albedo time series from AMSR-E and AVHRR data are calculated for the combined sea ice and open water cover for the Northern Hemisphere as a whole, and for six specific sea ice regions: the Arctic Ocean, the Kara and Barents Seas, the Greenland Sea, the Labrador Sea, Hudson Bay, and the Canadian Archipelago. The standard errors between the optical and passive microwave estimates varied from about 0.001 (Greenland Sea) to 0.04 (Canadian Archipelago) being 0.013 on the average in absolute units. The relative standard errors are then smaller than 5% in most of the regions.

A decision tree algorithm for surface soil freeze/thaw classification over China using SSM/I brightness temperature

This paper reports the development of a decision tree algorithm to classify the surface soil freeze/thaw states. The algorithm uses SSM/I brightness temperatures recorded in the early morning. Three critical indices are used as classification criteria—the scattering index (SI), the 37 GHz vertical polarization brightness temperature ( T 37V), and the 19 GHz polarization difference (PD 19). The thresholds of these criteria were obtained from samples of frozen soil, thawed soil, desert, and snow. The algorithm is capable of distinguishing between frozen soil, thawed soil, desert, and precipitation. In-situ 4-cm deep soil temperatures on the Qinghai–Tibetan Plateau were used to validate the classification results, and the average classification accuracy was found to be 87%. Regarding the misclassified pixels, about 40% and 73% of them appeared when the surface soil temperature ranged from − 0.5 °C to 0.5 °C and from − 2.0 °C to 2.0 °C, respectively, which means that most misclassifications occurred near the soil freezing point. In addition, misclassifications mainly occurred from April to May and September to October, the transition periods between warm and cold seasons. A grid-to-grid Kappa analysis was also conducted to evaluate the consistency between the map of the actual number of frozen days obtained using the decision tree classification algorithm and the reference map of geocryological regionalization and classification in China. The overall classification accuracy was 91.7%, and the Kappa index was 80.5%. The boundary between the frozen and thawed soil was consistent with the southern limit of seasonally frozen ground from the reference map. The statistics show that the maximum area of frozen soil is about 6.82 × 10 6 km 2 in late January, accounting for 69% of total Chinese land area.

Land surface temperature from Ka band (37 GHz) passive microwave observations

An alternative to thermal infrared satellite sensors for measuring land surface temperature (Ts) is presented. The 37 GHz vertical polarized brightness temperature is used to derive Ts because it is considered the most appropriate microwave frequency for temperature retrieval. This channel balances a reduced sensitivity to soil surface characteristics with a relatively high atmospheric transmissivity. It is shown that with a simple linear relationship, accurate values for Ts can be obtained from this frequency, with a theoretical bias of within 1 K for 70% of vegetated land areas of the globe. Barren, sparsely vegetated, and open shrublands cannot be accurately described with this single channel approach because variable surface conditions become important. The precision of the retrieved land surface temperature is expected to be better than 2.5 K for forests and 3.5 K for low vegetation. This method can be used to complement existing infrared derived temperature products, especially during clouded conditions. With several microwave radiometers currently in orbit, this method can be used to observe the diurnal temperature cycles with surprising accuracy.

Further validation of a new methodology for surface moisture and vegetation optical depth retrieval

A series of validation studies for a recently developed soil moisture and optical depth retrieval algorithm is presented. The approach is largely theoretical, and uses a non-linear iterative optimization procedure to solve a simple radiative transfer equation for the two parameters from dual polarization satellite microwave brightness temperatures. The satellite retrievals were derived from night-time 6.6 GHz Nimbus Scanning Multichannel Microwave Radiometer (SMMR) observations, and were compared to soil moisture data sets from the USA, Mongolia, Turkmenistan and Russia. The surface temperature, which is also an unknown parameter in the model, is derived off-line from 37 GHz vertical polarized brightness temperatures. The new theoretical approach is independent of field observations of soil moisture or canopy biophysical measurements and can be used at any wavelength in the microwave region. The soil moisture retrievals compared well with the surface moisture observations from the various locations. The vegetation optical depth also compared well to time series of Normalized Difference Vegetation Index (NDVI) and showed similar seasonal patterns. From a global perspective, the satellite-derived surface soil moisture was consistent with expected spatial patterns, identifying both known dry areas such as deserts and semi-arid areas and moist agricultural areas very well. Spatial patterns of vegetation optical depth were found to be in agreement with NDVI. The methodology described in this study should be directly transferable to the Advanced Microwave Scanning Radiometer (AMSR) on the recently launched AQUA satellite.

Soil freeze/thaw cycles over snow‐free land detected by passive microwave remote sensing

The timing, duration, and areal extent of the near‐surface soil freeze/thaw status were investigated using passive microwave satellite remote sensing data for the 1997/98 winter over the contiguous United States. A frozen soil algorithm was validated using soil temperature data at 0 cm and 5 cm depths from more than 20 sites over the study area. Results indicated that a negative spectral gradient and a cut‐off 37‐GHz vertical polarized brightness temperature of 258.2K can be used to determine near‐surface soil freeze/thaw status with confidence. The microwave freeze/thaw boundary generally agreed with −5.0°C isotherm of air temperature although frozen soils occurred sporadically between 0°C and −5.0°C isotherms. The maximum frozen soil area over snow‐free land surface was about 3.75 × 106 km² or about 37% of the total study area during the 1997/98 winter. The near‐surface soils often froze before snow covered the land surface, but soil freeze/thaw status under snow cover cannot be detected using this microwave technique. The onset of soil freeze mainly occurred in October and November, while the last days of soil freeze occurred in March and April, resulting in the duration of soil freezing varying from five to seven months over the majority of the study areas. The number of days of surface soil freezing varied from several days to longer than five months.

On the relationship between thermodynamic surface temperature and high-frequency (37 GHz) vertically polarized brightness temperature under semi-arid conditions

A method to estimate surface temperature from high-frequency microwave observations is presented. Microwave brightness temperature is a function of the emissivity and the physical temperature of the emitting layer, and therefore possesses a strong physical basis for the estimation of surface temperature. Field observations have shown that maximum and minimum daily air temperatures are strongly related to daytime (1200h) and night-time (2400h) surface temperature. Field measurements of surface temperature are also compared to METEOSAT thermal observations. Long-term daily maximum and minimum air temperatures are then used to derive datasets of daytime and night-time surface temperatures. The results indicate that 37 GHz vertical polarization brightness temperature provides a reasonable estimate of spatially averaged surface temperature. This approach could provide a useful tool for climate modelling, land surface processes investigations, and other energy balance applications by providing consistent and independent long-term estimates of daily global surface temperature.