Estimates Of Turbulent Heat Fluxes Research Articles

Assessment of radiative heating errors in Tropical Atmosphere Ocean array marine air temperature measurements

We assess the radiative heating error affecting marine air temperature (MAT) measurements in the Tropical Atmosphere Ocean array. The error in historical observations is found to be ubiquitous across the array, spatially variable and approximately stationary in time. The error induces spurious warming during daytime hours, but does not affect night-time temperatures. The range encompassing the real, unknown daily- and monthly-mean values is determined using daytime and night-time mean temperatures as upper and lower limits. The uncertainty in MAT is less than or equal to 0.5 °C and 0.2 °C for 95% of daily and monthly estimates, respectively. Uncertainties impact surface turbulent heat flux estimates, with potentially significant influences on the quantification of coupled ocean-atmosphere processes.

Improving Soil Moisture and Surface Turbulent Heat Flux Estimates by Assimilation of SMAP Brightness Temperatures or Soil Moisture Retrievals and GOES Land Surface Temperature Retrievals

AbstractSurface heat fluxes are vital to hydrological and environmental studies, but mapping them accurately over a large area remains a problem. In this study, brightness temperature (TB) observations or soil moisture retrievals from the NASA Soil Moisture Active Passive (SMAP) mission and land surface temperature (LST) product from the Geostationary Operational Environmental Satellite (GOES) are assimilated together into a coupled water and heat transfer model to improve surface heat flux estimates. A particle filter is used to assimilate SMAP data, while a particle smoothing method is adopted to assimilate GOES LST time series, correcting for both systematic biases via parameter updating and for short-term error via state updating. One experiment assimilates SMAP TB at horizontal polarization and GOES LST, a second experiment assimilates SMAP TB at vertical polarization and GOES LST, and a third experiment assimilates SMAP soil moisture retrievals along with GOES LST. The aim is to examine if the assimilation of physically consistent TB and LST observations could yield improved surface heat flux estimates. It is demonstrated that all three assimilation experiments improved flux estimates compared to a no-assimilation case. Assimilating TB data tends to produce smaller bias in soil moisture estimates compared to assimilating soil moisture retrievals, but the estimates are influenced by the respective bias correction approaches. Despite the differences in soil moisture estimates, the flux estimates from different assimilation experiments are in general very similar.

Mapping Regional Turbulent Heat Fluxes via Assimilation of MODIS Land Surface Temperature Data into an Ensemble Kalman Smoother Framework

AbstractEstimation of turbulent heat fluxes via variational data assimilation (VDA) approaches has been the subject of several studies. The VDA approaches need an adjoint model that is difficult to derive. In this study, remotely sensed land surface temperature (LST) data from the Moderate Resolution Imaging Spectroradiometer (MODIS) are assimilated into the heat diffusion equation within an ensemble Kalman smoother (EnKS) approach to estimate turbulent heat fluxes. The EnKS approach is tested in the Heihe River Basin (HRB) in northwest China. The results show that the EnKS approach can estimate turbulent heat fluxes by assimilating low temporal resolution LST data from MODIS. The findings indicate that the EnKS approach performs fairly well in various hydrological and vegetative conditions. The estimated sensible (H) and latent (LE) heat fluxes are compared with the corresponding observations from large aperture scintillometer systems at three sites (namely, Arou, Daman, and Sidaoqiao) in the HRB. The turbulent heat flux estimates from EnKS agree reasonably well with the observations, and are comparable to those of the VDA approach. The EnKS approach also provides statistical information on the H and LE estimates. It is found that the uncertainties of H and LE estimates are higher over wet and/or densely vegetated areas (grassland and forest) compared to the dry and/or slightly vegetated areas (cropland, shrubland, and barren land).

Evaluation of the Weak Constraint Data Assimilation Approach for Estimating Turbulent Heat Fluxes at Six Sites

A number of studies have estimated turbulent heat fluxes by assimilating sequences of land surface temperature (LST) observations into the strong constraint-variational data assimilation (SC-VDA) approaches. The SC-VDA approaches do not account for the structural model errors and uncertainties in the micrometeorological variables. In contrast to the SC-VDA approaches, the WC-VDA approach (the so-called weak constraint-VDA) accounts for the effects of structural and model errors by adding a model error term. In this study, the WC-VDA approach is tested at six study sites with different climatic and vegetative conditions. Its performance is also compared with that of SC-VDA at the six study sites. The results show that the WC-VDA produces 10.16% and 10.15% lower root mean square errors (RMSEs) for sensible and latent heat flux estimates compared with the SC-VDA approach. The model error term can capture errors in the turbulent heat flux estimates due to errors in LST and micrometeorological measurements, as well as structural model errors, and does not allow those errors to adversely affect the turbulent heat flux estimates. The findings also indicate that the estimated model error term varies reasonably well, so as to capture the misfit between predicted and observed net radiation in different hydrological and vegetative conditions. Finally, synthetically generated positive (negative) noises are added to the hydrological input variables (e.g., LST, air temperature, air humidity, incoming solar radiation, and wind speed) to examine whether the WC-VDA approach can capture those errors. It was found that the WC-VDA approach accounts for the errors in the input data and reduces their effect on the turbulent heat flux estimates.

Variability of Internal Wave‐Driven Mixing and Stratification in Canadian Arctic Shelf and Shelf‐Slope Waters

AbstractOur understanding of ocean mixing is challenged by its patchy, episodic nature and a scarcity of direct measurements, especially in the Arctic Ocean. In this study, we exploit a historical record of nearly 3,000 conductivity‐temperature‐depth profiles collected in the shelf and shelf‐slope waters of the Canadian Arctic Ocean from 2002 to 2016 to characterize the variability of 28,872 internal wave‐driven turbulent dissipation and mixing rate estimates from a finescale parameterization. We find that these estimates of wave‐driven dissipation rates and associated diapycnal diffusivities are generally low, but exhibit wide variability, each spanning several orders of magnitude. We further find that stratification plays a significant role in modulating the mixing rate both vertically and regionally within the study domain. Dissipation rate and diffusivity estimates display a weak seasonal cycle, but no evidence of statistically significant interannual trends over this period. Exceptionally large localized temporal variability appears to dominate other potential underlying patterns. The presence of strong upper ocean stratification combined with predominately weak dissipation rate estimates implies that many regions in the Canadian Arctic Ocean are likely in a molecular or buoyancy‐controlled mixing regime. Even when the concept of a turbulent‐enhanced diffusivity is potentially relevant, most turbulent heat flux estimates out of the Atlantic Water thermocline are smaller than the average value required to close the standardly assumed Arctic Ocean heat budget. In contrast, we find evidence for isolated occurrences of anomalously large heat fluxes, which may disproportionately contribute to the liberation of Atlantic Water heat toward the surface sea ice pack.

Spatial Distribution of Sensible and Latent Heat Flux in the City of Basel (Switzerland)

Urban surfaces are a complex mixture of different land covers and surface materials; the relative magnitudes of the surface energy balance components therefore vary widely across a city. Eddy covariance (EC) measurements provide the best estimates of turbulent heat fluxes but are restricted to the source area. Land surface modeling with earth observation (EO) data is beneficial for extrapolation of a larger area since citywide information is possible. Turbulent sensible and latent heat fluxes are calculated by a combination of micrometeorological approaches (the aerodynamic resistance method, ARM), EO data, and GIS techniques. Input data such as land cover fractions and surface temperatures are derived from Landsat 8 OLI and TIRS, urban morphology was calculated from high-resolution digital building models and GIS data layers, and meteorological data were provided by flux tower measurements. Twenty-two Landsat scenes covering all seasons and different meteorological conditions were analyzed. Sensible heat fluxes were highest for industrial areas, railway stations, and areas with high building density, mainly corresponding to the pixels with highest surface-to-air temperature differences. The spatial distribution of latent heat flux is strongly related to the saturation deficit of vapor and the (minimum) stomatal resistance of vegetation types. Seasonal variations are highly dependent on meteorological conditions, i.e., air temperature, water vapor saturation deficit, and wind speed. Comparison of measured fluxes with modeled fluxes in the weighted source area of the flux towers is moderately accurate due to known drawbacks in the modeling approach and uncertainties inherent to EC measurements, particularly in urban areas.

Review and assessment of latent and sensible heat flux accuracy over the global oceans

For over a decade, several research groups have been developing air-sea heat flux information over the global ocean, including latent (LHF) and sensible (SHF) heat fluxes over the global ocean. This paper aims to provide new insight into the quality and error characteristics of turbulent heat flux estimates at various spatial and temporal scales (from daily upwards). The study is performed within the European Space Agency (ESA) Ocean Heat Flux (OHF) project. One of the main objectives of the OHF project is to meet the recommendations and requirements expressed by various international programs such as the World Research Climate Program (WCRP) and Climate and Ocean Variability, Predictability, and Change (CLIVAR), recognizing the need for better characterization of existing flux errors with respect to the input bulk variables (e.g. surface wind, air and sea surface temperatures, air and surface specific humidities), and to the atmospheric and oceanic conditions (e.g. wind conditions and sea state). The analysis is based on the use of daily averaged LHF and SHF and the associated bulk variables derived from major satellite-based and atmospheric reanalysis products. Inter-comparisons of heat flux products indicate that all of them exhibit similar space and time patterns. However, they also reveal significant differences in magnitude in some specific regions such as the western ocean boundaries during the Northern Hemisphere winter season, and the high southern latitudes. The differences tend to be closely related to large differences in surface wind speed and/or specific air humidity (for LHF) and to air and sea temperature differences (for SHF). Further quality investigations are performed through comprehensive comparisons with daily-averaged LHF and SHF estimated from moorings. The resulting statistics are used to assess the error of each OHF product. Consideration of error correlation between products and observations (e.g., by their assimilation) is also given. This reveals generally high noise variance in all products and a weak signal in common with in situ observations, with some products only slightly better than others. The OHF LHF and SHF products, and their associated error characteristics, are used to compute daily OHF multiproduct-ensemble (OHF/MPE) estimates of LHF and SHF over the ice-free global ocean on a 0.25°×0.25° grid. The accuracy of this heat multiproduct, determined from comparisons with mooring data, is greater than for any individual product. It is used as a reference for the anomaly characterization of each individual OHF product.

Estimating spatially distributed turbulent heat fluxes from high-resolution thermal imagery acquired with a UAV system

ABSTRACTIn this study, high-resolution thermal imagery acquired with a small unmanned aerial vehicle (UAV) is used to map evapotranspiration (ET) at a grassland site in Luxembourg. The land surface temperature (LST) information from the thermal imagery is the key input to a one-source and two-source energy balance model. While the one-source model treats the surface as a single uniform layer, the two-source model partitions the surface temperature and fluxes into soil and vegetation components. It thus explicitly accounts for the different contributions of both components to surface temperature as well as turbulent flux exchange with the atmosphere. Contrary to the two-source model, the one-source model requires an empirical adjustment parameter in order to account for the effect of the two components. Turbulent heat flux estimates of both modelling approaches are compared to eddy covariance (EC) measurements using the high-resolution input imagery UAVs provide. In this comparison, the effect of different methods for energy balance closure of the EC data on the agreement between modelled and measured fluxes is also analysed. Additionally, the sensitivity of the one-source model to the derivation of the empirical adjustment parameter is tested. Due to the very dry and hot conditions during the experiment, pronounced thermal patterns developed over the grassland site. These patterns result in spatially variable turbulent heat fluxes. The model comparison indicates that both models are able to derive ET estimates that compare well with EC measurements under these conditions. However, the two-source model, with a more complex treatment of the energy and surface temperature partitioning between the soil and vegetation, outperformed the simpler one-source model in estimating sensible and latent heat fluxes. This is consistent with findings from prior studies. For the one-source model, a time-variant expression of the adjustment parameter (to account for the difference between aerodynamic and radiometric temperature) that depends on the surface-to-air temperature gradient yielded the best agreement with EC measurements. This study showed that the applied UAV system equipped with a dual-camera set-up allows for the acquisition of thermal imagery with high spatial and temporal resolution that illustrates the small-scale heterogeneity of thermal surface properties. The UAV-based thermal imagery therefore provides the means for analysing patterns of LST and other surface properties with a high level of detail that cannot be obtained by traditional remote sensing methods.

A Simple Scheme for Estimating Turbulent Heat Flux over Landfast Arctic Sea Ice from Dry Snow to Advanced Melt

We describe a dynamic-parameter aggregation scheme to estimate hourly turbulent heat fluxes over landfast sea ice during the transition from winter to spring. Hourly albedo measurements are used to track the morphology of the surface as it evolved from a fairly smooth homogeneous dry snow surface to a rougher heterogeneous surface with spatially differential melting and melt ponds. The estimates of turbulent heat fluxes for 928 h are compared with eddy-covariance measurements. The model performance metrics (W m $$^{-2}$$ ) for sensible heat flux were found to be: mean bias $$=$$ $$-3$$ , root-mean-square error $$=$$ 6 and absolute accuracy $$=$$ 4, and for latent heat flux near zero, 3 and 2, respectively. The correlation coefficient between modelled and measured sensible heat fluxes was 0.82, and for latent heat fluxes 0.88. The turbulent heat fluxes were estimated more accurately without adjustments than with adjustments for atmospheric stability based on the bulk Richardson number. Overall, and across all metrics for both sensible and latent heat fluxes, the dynamic-parameter aggregation scheme outperformed the static Community Ice (C-ICE) scheme, part of the Community Climate System model, applied to the same winter-to-spring transition period.

Surface heat flux estimation with the ensemble Kalman smoother: Joint estimation of state and parameters

The estimation of surface heat fluxes based on the assimilation of land surface temperature (LST) has been achieved within a variational data assimilation (VDA) framework. Variational approaches require the development of an adjoint model, which is difficult to derive and code in the presence of thresholds and discontinuities. Also, it is computationally expensive to obtain the background error covariance for the variational approaches. Moreover, the variational schemes cannot directly provide statistical information on the accuracy of their estimates. To overcome these shortcomings, we develop an alternative data assimilation (DA) procedure based on ensemble Kalman smoother (EnKS) with the state augmentation method. The unknowns of the assimilation scheme are neutral turbulent heat transfer coefficient (that scales the sum of turbulent heat fluxes) and evaporative fraction, EF (that represents partitioning among the turbulent fluxes). The new methodology is illustrated with an application to the First International Satellite Land Surface Climatology Project Field Experiment (FIFE) that includes areal average hydrometeorological forcings and flux observations. The results indicate that the EnKS model not only provides reasonably accurate estimates of EF and turbulent heat fluxes but also enables us to determine the uncertainty of estimations under various land surface hydrological conditions. The results of the EnKS model are also compared with those of an optimal smoother (a dynamic variational model). It is found that the EnKS model estimates are less than optimal. However, the degree of suboptimality is small, and its outcomes are roughly comparable to those of an optimal smoother. Overall, the results from this test indicate that EnKS is an efficient and flexible data assimilation procedure that is able to extract useful information on the partitioning of available surface energy from LST measurements and eventually provides reliable estimates of turbulent heat fluxes.

Assessing the potential of the Atmospheric Infrared Sounder (AIRS) surface temperature and specific humidity in turbulent heat flux estimates in the Southern Ocean

Surface air temperature (TA), sea surface temperature (TO), and surface specific humidity (qa) satellite retrievals from the Atmospheric Infrared Sounder (AIRS) are compared with shipboard measurements across Drake Passage for the period from September 2002 to June 2007. The objective is to evaluate whether AIRS retrievals, in conjunction with microwave sea surface temperatures from the Advanced Microwave Scanning Radiometer (AMSRE), can provide sufficiently accurate parameters to estimate sensible and latent heat fluxes in the data‐limited Southern Ocean. The collocated data show that both AIRS TA and TO are colder than those from shipboard measurements, with a time mean bias of −2.03°C for TA and −0.22°C for TO. Results show that air‐sea temperature difference (TA − TO), qa, and relative humidity (RH) are the major factors contributing to the differences between satellite and shipboard temperature measurements. Differences in AIRS and shipboard TA (ΔTA) decrease with increasing TA − TO, and ΔTA increases with increasing RH, whereas differences in AIRS and shipboard TO (ΔTO) increase with both increasing TA − TO and increasing qa. The time mean qa from AIRS is lower than the shipboard qa by 0.69 g/kg. Statistical analyses suggest that TA − TO, cloud, and qa are the major contributors to the qa difference (Δqa). Δqa becomes more negative with increasing TA − TO and increasing cloud fraction. Δqa also becomes more negative as qa increases. Compared with TA, TO, and TA − TO, from the National Centers for Environmental Prediction/National Center for Atmospheric Research Reanalysis (NCEP), AIRS‐derived and AMSRE‐derived variables show more small‐scale spatial structure, as is also typical of the ship observations. Although AIRS qa gives a better representation of the full range of values of shipboard qa, its deviation from shipboard qa is relatively large compared to NCEP qa. Compared with several existing gridded flux products, turbulent fluxes estimated from AIRS and AMSRE data using bulk algorithms are better able to represent the full range of flux values estimated from shipboard parameters.

Surface energy budget over the South Pole and turbulent heat fluxes as a function of an empirical bulk Richardson number

Routine radiation and meteorological data at South Pole Station are used to investigate historical discrepancies of up to 50 W m−2 in the monthly mean surface energy budget and to investigate the behavior of turbulent heat fluxes under stable atmospheric temperature conditions. The seasonal cycles of monthly mean net radiation and turbulent heat fluxes are approximately equal, with a difference of 40 W m−2 between summer and winter, while the seasonal cycle of subsurface heat fluxes is only a few W m−2. For an 8‐month period (the winter of 2001), we calculate two estimates of turbulent heat fluxes, one from Monin‐Obukhov (MO) similarity theory and one as the residual of the surface energy budget (i.e., subsurface heat fluxes minus net radiation, where all fluxes toward the snow surface are positive). The turbulent fluxes from MO theory agree well with the residual of the energy budget under lapse conditions. However, under stable conditions MO theory underestimates turbulent fluxes by approximately 40–60%. The relationship between turbulent heat fluxes as a residual of the energy budget, temperature inversion strength, and wind shear as a function of the bulk Richardson number (Rib) is examined under stable conditions (i.e., positive Rib). The Rib used here is calculated from 10‐m wind speeds and 0‐ to 2‐m temperature inversion strength. No critical value of Rib is found where the turbulent heat fluxes drop to zero. However, a threshold (Rib = 0.05) exists below which 70% of the turbulent energy fluxes can be explained by only the temperature inversion strength. For Rib > 0.05, the relationship between turbulent heat fluxes and temperature inversion strength decreases, while the importance of wind shear to turbulent heat transfer increases. Above Rib = 0.05, a growing linear correlation also exists between atmospheric temperature inversion strength and wind shear. Thus, inversion strength and wind shear are not independent predictors of turbulent heat flux for extremely stable conditions. The exact values of the correlation coefficients and Rib threshold are likely specific to the experimental conditions; however, their implications are probably valid for all stable flows. Knowledge of the time‐varying surface characteristics would help to generalize these parameters.

Assessment of global annual atmospheric energy balance from satellite observations

Global atmospheric energy balance is one of the fundamental processes for the earth's climate system. This study uses currently available satellite data sets of radiative energy at the top of atmosphere (TOA) and surface as well as latent and sensible heat over the oceans for the year 2000 to assess the global annual energy budget. Over land, surface radiation data are used to constrain assimilated results and to force the radiation, turbulent heat, and heat storage into balance due to a lack of observation‐based turbulent heat flux estimates. Global annual means of the TOA net radiation obtained from both satellite direct measurements and calculations are close to zero. The net radiative energy fluxes into the surface and the surface latent heat transported into the atmosphere are about 113 and 86 W/m2, respectively. The estimated atmospheric and surface heat imbalances are about −8 and 9 W/m2, respectively, values that are within the uncertainties of surface radiation and sea surface turbulent flux estimates and the likely systematic biases in the analyzed observations. The potential significant additional absorption of solar radiation within the atmosphere suggested by previous studies does not appear to be required to balance the energy budget: the spurious heat imbalances in the current data are much smaller (about half) than those obtained previously and debated about a decade ago. Progress in surface radiation and oceanic turbulent heat flux estimations from satellite measurements has significantly reduced the bias errors in the observed global energy budgets of the climate system.

The relationship between synoptic weather systems and meteorological forcing on the North Carolina inner shelf

A strong relationship is observed between synoptic weather systems and atmospheric forcing of the ocean as estimated from buoy measurements made on the North Carolina inner shelf during August and October‐November 1994 as part of the Coastal Ocean Processes (CoOP) Inner Shelf Study. Synoptic variation (timescales of days to weeks) in the meteorological time series was primarily associated with the passage of atmospheric frontal systems. The most common synoptic weather pattern observed was the passage of a low‐pressure center to the north of the study site, which caused the associated cold front to pass over the study region. Before passage of the cold front, warm, moist northeastward winds increased the heat flux into the ocean, whereas after the cold front passed, cold, dry southwestward winds decreased the heat flux into the ocean. In addition, in the presence of oceanic stratification, northeastward winds drove coastal upwelling, bringing colder water to the surface, further increasing the air‐sea temperature contrast and hence the heat flux into the ocean inshore of the surface front between cool upwelled water and warmer water offshore. The decrease in surface heat flux during the passage of a cold front was of order 400 W m−2, due primarily to a decrease in latent heat flux. Although other synoptic patterns were observed, including one warm front passage and two tropical storm systems, the dominance of cold fronts as a source of variability resulted in a strong positive correlation between the along‐shelf component of wind stress and the surface heat flux. To address the issue of spatial variation in the surface heat fluxes, data from several different sources located along a cross‐shelf transect were analyzed. This analysis suggests that the temperature of the atmospheric boundary layer undergoes adjustment when warm air blows over cold water but not when cold air blows over warm water. This produces cross‐shelf gradients in the bulk estimates of turbulent heat fluxes during offshore winds but not during onshore winds.

Seasonal variations between sampling and classical mean turbulent heat flux estimates in the eastern North Atlantic

Abstract. The two commonly used statistical measures of the air-sea heat flux, the sampling and classical means, have been compared using hourly reports over a 7-year-period from a weather ship stationed in the NE Atlantic. The sampling mean is the average over all flux estimates in a given period, where individual flux estimates are determined from ship reports of meteorological variables using the well-known bulk formulae. The classical mean is the flux derived by substituting period-averaged values for each of the meteorological variables into the bulk formula (where the averaging period employed is the same as that over which the fluxes are to be determined). Monthly sampling and classical means are calculated for the latent and sensible heat fluxes. The monthly classical mean latent heat flux is found to overestimate the sampling mean by an amount which increases from 1–2 W m–2 in summer to 7 W m–2 in winter, on average, over the 7-year-period. In a given winter month, the excess may be as great as 15 W m–2, which represents about 10% of the latent heat flux. For the sensible heat flux, any seasonal variation between the two means is of the order of 1 W m–2 and is not significant compared to the interannual variation. The discrepancy between the two means for the latent heat flux is shown to arise primarily from a negative correlation between the wind speed and sea-air humidity difference, the effects of which are implicitly included in the sampling method but not in the classical. The influence of the dominant weather conditions on the sign and magnitude of this correlation are explored, and the large negative values that it takes in winter are found to depend on the typical track of the mid-latitude depressions with respect to the position sampled. In conclusion, it is suggested that sampling means should be employed where possible in future climatological studies.

Seasonal variations between sampling and classical mean turbulent heat flux estimates in the eastern North Atlantic

<strong class="journal-contentHeaderColor">Abstract.</strong> The two commonly used statistical measures of the air-sea heat flux, the sampling and classical means, have been compared using hourly reports over a 7-year-period from a weather ship stationed in the NE Atlantic. The sampling mean is the average over all flux estimates in a given period, where individual flux estimates are determined from ship reports of meteorological variables using the well-known bulk formulae. The classical mean is the flux derived by substituting period-averaged values for each of the meteorological variables into the bulk formula (where the averaging period employed is the same as that over which the fluxes are to be determined). Monthly sampling and classical means are calculated for the latent and sensible heat fluxes. The monthly classical mean latent heat flux is found to overestimate the sampling mean by an amount which increases from 1–2 W m^–2 in summer to 7 W m^–2 in winter, on average, over the 7-year-period. In a given winter month, the excess may be as great as 15 W m^–2, which represents about 10% of the latent heat flux. For the sensible heat flux, any seasonal variation between the two means is of the order of 1 W m^–2 and is not significant compared to the interannual variation. The discrepancy between the two means for the latent heat flux is shown to arise primarily from a negative correlation between the wind speed and sea-air humidity difference, the effects of which are implicitly included in the sampling method but not in the classical. The influence of the dominant weather conditions on the sign and magnitude of this correlation are explored, and the large negative values that it takes in winter are found to depend on the typical track of the mid-latitude depressions with respect to the position sampled. In conclusion, it is suggested that sampling means should be employed where possible in future climatological studies.