Response of water and energy exchange to the environmental variable in a desert‐oasis wetland of Northwest China

A case study on a desert‐oasis wetland ecosystem in the arid region of Northwest China measured the seasonal and interannual variation in energy partitioning and evapotranspiration to analyse the response of water and energy exchange on soil moisture, groundwater, and environmental variables. Energy partitioning showed a clear seasonal and interannual variability, and the process of water and energy exchange differed significantly in the monthly and interannual scales. The net radiation was 7.31 MJ m^?2· day^?1, and sensible heat flux accounted for 50.42% of net radiation in energy fluxes, 40.56% for latent heat flux, and 9.02% for ground heat flux. The parameters in energy fluxes were best described by a unimodal curve, whereas sensible heat flux followed a bimodal curve. Variations in the daily evapotranspiration and crop evapotranspiration also exhibited a single peak curve with annual values of 569.84 and 644.47 mm, respectively. Canopy conductance averaged 20.77 ± 13.75 mm s^?1 and varied from 0.16 to 83.96 mm s^?1 during the two hydrological years. The variation in water and energy exchange reflected environmental conditions and depended primarily on vapour pressure deficit, net radiation, soil moisture, and water depth. Although the effects of precipitation on evapotranspiration showed that the response of this ecosystem to climate changes was not obvious, the variation of air temperatures had a strong influence on evapotranspiration, resulting in a significant increase in evapotranspiration (R = 0.730; P < 0.01). Copyright © 2013 John Wiley & Sons, Ltd.     

Hydrometeorological behaviour of pine and larch forests in eastern Siberia

Seasonal changes in the water and energy exchanges over a pine forest in eastern Siberia were investigated and compared with published data from a nearby larch forest. Continuous observations (April to August 2000) were made of the eddy‐correlation sensible heat flux and latent heat flux above the canopy. The energy balance was almost closed, although the sum of the turbulent fluxes sometimes exceeded the available energy flux (R_n ? G) when the latent heat flux was large; this was related to the wind direction. We examined the seasonal variation in energy balance components at this site. The seasonal variation and magnitude of the sensible heat flux (H) was similar to that of the latent heat flux (λE), with maximum values occurring in mid‐June. Consequently, the Bowen ratio was around 1·0 on many days during the study period. On some clear days just after rainfall, λE was very large and the sum of H and λE exceeded R_n ? G. The evapotranspiration rate above the dry canopy from May to August was 2·2 mm day^?1. The contributions of understory evapotranspiration (E_u) and overstory transpiration (E_o) to the evapotranspiration of the entire ecosystem (E_t) were both from 25 to 50% throughout the period analysed. These results suggest that E_u plays a very important role in the water cycle at this site. From snowmelt through the tree growth season (23 April to 19 August 2000), the total incoming water, comprised of the sum of precipitation and the water equivalent of the snow at the beginning of the melt season, was 228 mm. Total evapotranspiration from the forest, including interception loss and evaporation from the soil when the canopy was wet, was 208–254 mm. The difference between the incoming and outgoing amounts in the water balance was from +20 to ?26 mm. The water and energy exchanges of the pine and larch forest differed in that λE and H increased slowly in the pine forest, whereas λE increased rapidly in the larch forest and H decreased sharply after the melting season. Consequently, the shape of the Bowen ratio curves at the two sites differed over the period analysed, as a result of the differences in the species in each forest and in soil thawing. Copyright © 2003 John Wiley & Sons, Ltd.     

Energy flux partitioning and evapotranspiration in a sub‐alpine spruce forest ecosystem

In this study, we examined the year 2011 characteristics of energy flux partitioning and evapotranspiration of a sub‐alpine spruce forest underlain by permafrost on the Qinghai–Tibet Plateau (QPT). Energy balance closure on a half‐hourly basis was H + λE = 0.81 × (R_n ? G ? S) + 3.48 (W m^?2) (r² = 0.83, n = 14938), where H, λE, R_n, G and S are the sensible heat, latent heat, net radiation, soil heat and air‐column heat storage fluxes, respectively. Maximum H was higher than maximum λE, and H dominated the energy budget at midday during the whole year, even in summer time. However, the rainfall events significantly affected energy flux partitioning and evapotranspiration. The mean value of evaporative fraction (Λ = λE/(λE + H)) during the growth period on zero precipitation days and non‐zero precipitation days was 0.40 and 0.61, respectively. The mean daily evapotranspiration of this sub‐alpine forest during summer time was 2.56 mm day^?1. The annual evapotranspiration and sublimation was 417 ± 8 mm year^?1, which was very similar to the annual precipitation of 428 mm. Sublimation accounted for 7.1% (30 ± 2 mm year^?1) of annual evapotranspiration and sublimation, indicating that the sublimation is not negligible in the annual water balance in sub‐alpine forests on the QPT. The low values of the Priestley–Taylor coefficient (α) and the very low value of the decoupling coefficient (Ω) during most of the growing season suggested low soil water content and conservative water loss in this sub‐alpine forest. Copyright © 2013 John Wiley & Sons, Ltd.     

Surface energy balance at a tropical station

Summary Studies of various fluxes, namely net radiation, soil heat, sensible heat and latent heat observed at a tropical station are presented in this paper. The time variation of these fluxes are examined in relation to various meteorological parameters and atmospheric conditions. The turbulent transfer coefficients have been evaluated to examine the applicability of the classical theory or the non-equivalence theory for eddy transport in the lower layers of the atmosphere. The energy balance at a tropical station is evaluated. It is found over year there is a net surplus of 94,000 ly. A detailed discussion of the disposal of this energy by various consuming processes is given.Symbols and notation All the quantities represented by symbols in the text of the paper are defined below C _p specific heat at constant pressure in cal. g^–1 °K - E evaporation in g cm^–2 hr^–1 - E ^* evaporative heat flux cal. cm^–2 sec^–1 (in Eq. 10) - e vapour pressure in millibars - e _z ,e _2z vapour pressure at heightsz and 2z - g acceleration due to gravity - H sensible heat flux cal cm^–2 sec^–1 (in Eq. 12) - K _M ,K _H ,K _W coefficients of eddy diffusivities of momentum, heat, and water vapour respectively in cm² sec^–1 - k von Karman' constant=0.4 - L Monin-Obukhov length (according to Monin and Obukhov [53] the structure of the turbulent boundary layer is determined by the non-dimensional variableZ/L whereL is defined byL=–(u _* ³ C _p T)/(kgH) - ly langleys - Q _c Q—sensible heat flux in langleys (in Eqs. 3 and 4) - Q _e E—latent heat flux in langleys (in Eqs. 3 and 4) - Q _s S—soil heat flux in langleys (in Eqs. 3 and 4) - Q _i Q _c +Q _e +Q _s whenK _M K _H K _W , (in Eq. 6) - Q' _i Q' _c +Q' _e +Q _s whenK _M =K _H =K _W (in Eq. 7) - qq mean specific humidity g kg^–1     

Estimation of spatially distributed surface energy fluxes using remotely‐sensed data for agricultural fields

Land surface energy fluxes are required in many environmental studies, including hydrology, agronomy and meteorology. Surface energy balance models simulate microscale energy exchange processes between the ground surface and the atmospheric layer near ground level. Spatial variability of energy fluxes limits point measurements to be used for larger areas. Remote sensing provides the basis for spatial mapping of energy fluxes. Remote‐sensing‐based surface energy flux‐mapping was conducted using seven Landsat images from 1997 to 2002 at four contiguous crop fields located in Polk County, northwestern Minnesota. Spatially distributed surface energy fluxes were estimated and mapped at 30 m pixel level from Landsat Thematic Mapper and Enhanced Thematic Mapper images and weather information. Net radiation was determined using the surface energy balance algorithm for land (SEBAL) procedure. Applying the two‐source energy balance (TSEB) model, the surface temperature and the latent and sensible heat fluxes were partitioned into vegetation and soil components and estimated at the pixel level. Yield data for wheat and soybean from 1997 to 2002 were mapped and compared with latent heat (evapotranspiration) for four of the fields at pixel level. The spatial distribution and the relation of latent heat flux and Bowen ratio (ratio of sensible heat to latent heat) to crop yield were studied. The root‐mean‐square error and the mean absolute percentage of error between the observed and predicted energy fluxes were between 7 and 22 W m⁻² and 12 and 24% respectively. Results show that latent heat flux and Bowen ratio were correlated (positive and negative) to the yield data. Wheat and soybean yields were predicted using latent heat flux with mean R² = 0·67 and 0·70 respectively, average residual means of −4·2 bushels/acre and 0·11 bushels/acre respectively, and average residual standard deviations of 16·2 bushels/acre and 16·6 bushels/acre respectively (1 bushel/acre ≈ 0·087 m³ ha⁻¹). The flux estimation procedure from the SEBAL‐TSEB model was useful and applicable to agricultural fields. Copyright © 2005 John Wiley & Sons, Ltd.     

A simple method using climatic variables to estimate canopy temperature,sensible and latent heat fluxes in a winter wheat field on the North China Plain

Estimation of evapotranspiration from a crop field is of great importance for detecting crop water status and proper irrigation scheduling. The Penman–Monteith equation is widely viewed as the best method to estimate evapotranspiration but it requires canopy resistance, which is very difficult to determine in practice. This paper presents a simple method simplified from the Penman–Monteith equation for estimating canopy temperature (T_c). The proposed method is a biophysically‐sound extended version of that proposed by Todorovic. The estimated canopy temperature is used to calculate sensible heat flux, and then latent heat flux is calculated as the residual of the surface energy balance. An eddy covariance (EC) system and an infrared thermometer (IRT) were installed in an irrigated winter wheat field on the North China Plain in 2004 and 2005, to measure T_c, and sensible and latent heat fluxes were used to test the modified Todorovic model (MTD). The results indicate that the original Todorovic model (TD) severely underestimates T_c and sensible heat flux, and hence severely overestimates the latent heat flux. However, the MTD model has good capability for estimating T_c, and gives acceptable results for latent heat flux at both half‐hourly and daily scales. The MTD model results also agreed well with the evapotranspiration calculated from the measured T_c. Copyright © 2008 John Wiley & Sons, Ltd.     

A Comparative Study of Radiation Fog and Quasi-Fog Formation Processes During the ParisFog Field Experiment 2007

Fog is an atmospheric phenomenon that has important environmental consequences related to visibility, air quality and climate change on local and regional scales. The formation of radiation fog results from a complex balance between surface radiative cooling, turbulent mixing in the surface layer, aerosol growth by deliquescence and activation of fog droplets. During the ParisFog field experiment, out of 16 events forecasted for radiation fog, activated fog materialized in seven events, while in five other events the visibility dropped to 1–2 km but haze particle size remained below the critical size of activation. To better understand the conditions that lead to or do not lead to sustained fog droplet activation, we performed a comparative study of dynamic, thermal, radiative and microphysical processes occurring between sunset and fog (or quasi-fog) onset. We selected two radiation fog events and two quasi-radiation fog events that occurred under similar large-scale conditions for this comparative study. We identified that aerosol growth by deliquescence and droplet activation actually occurred in both quasi-fog events, but only during <1 h. Based on ParisFog measurements, we found that the main factors limiting sustained activation of droplets at fog onset in the Paris metropolitan area are (1) lack of mixing in the surface layer (typically wind speed <0.5 ms^?1), (2) relative humidity exceeding 90 % throughout the residual layer, (3) low cooling rate in the surface layer (typically less than ?1 °C per hour on average) due to weak radiative cooling (0 to ?30 Wm^?2) and near zero sensible heat fluxes, and (4) a combination of the three factors listed above during the critical phase of droplet activation preventing the transfer of cooling from the surface to the liquid layer. In addition, we found some evidence of contrasted aerosol growth by deliquescence under high relative humidity conditions in the four events, possibly associated with the chemical nature of the aerosols, which could be another factor impacting droplet activation.     

Energy budget above a temperate mixed forest in northeastern China

Components of the energy budget were measured continuously above a 300‐year‐old temperate mixed forest at the Changbaishan site, northeastern China, from 1 January to 31 December 2003, as a part of the ChinaFlux programme. The albedo values above the canopy were lower than most temperate forests, and the values for snow‐covered canopy were over 50% higher than for the snow‐free canopy. In winter, net radiation R_n was generally less than 5% of the summer value due to high albedo and low incoming solar radiation. The annual mean latent heat LE was 37·5 W m^?2, accounting for 52% of R_n. The maximum daily evaporation was about 4·6 mm day^?1 in summer. Over the year, the accumulated precipitation was 578 mm; this compares with 493 mm of evapotranspiration, which shows that more than 85% of water was returned to the atmosphere through evapotranspiration. The LE was strongly affected by the transpiration activity and increased quickly as the broadleaved trees began to foliate. The sensible heat H dropped at that time, although R_n increased. Consequently, the seasonal variation in the Bowen ratio β was clearly U‐shaped, and the minimum value (0·1) occurred on a sunny day just after rain, when most of the available energy was used for evapotranspiration. Negative β values occurred occasionally in the non‐growing season as a result of intensive radiative cooling and the presence of water on the surface. The β was very high (up to 13·0) in snow‐covered winter, when evapotranspiration was small due to low surface temperature and available soil water. Vegetation phenology and soil moisture were the key variables controlling the available energy partitioning between H and LE. Energy budget closure averaged better than 86% on a half‐hourly basis, with slightly greater closure on a daily basis. The degree of closure showed a dependence on friction velocity u*. Copyright © 2006 John Wiley & Sons, Ltd.     

Water and heat fluxes above a lowland dipterocarp forest in Peninsular Malaysia

We measured the fluxes of sensible and latent heat between a low‐land dipterocarp forest in Peninsular Malaysia and the atmosphere. No clear seasonal or interannual changes in latent heat flux were found from 2003 to 2005, while sensible heat flux sometimes fluctuated depending on the fluctuation of incoming radiation between wet and dry seasons. The evapotranspiration rates averaged for the period between 2003 and 2005 were 2·77 and 3·61 mm day^?1 using eddy covariance data without and with an energy balance correction, respectively. Average precipitation was 4·74 mm day^?1. Midday surface conductance decreased with an increasing atmospheric water vapour pressure deficit and thus restricted the excess water loss on sunny days in the dry season. However, the relationship between the surface conductance and vapour pressure deficit did not significantly decline with an increase in volumetric soil water content even during a period of extremely low rainfall. Copyright © 2009 John Wiley & Sons, Ltd.     

Treatment of anchor pixels in the METRIC model for improved estimation of sensible and latent heat fluxes

Abstract

Reliable estimation of sensible heat flux (H) is important in energy balance models for quantifying evapotranspiration (ET). This study was conducted to evaluate the value of adding the Priestley-Taylor (PT) equation to the METRIC (Mapping Evapotranspiration at high Resolution with Internalized Calibration) model. METRIC was used to estimate energy fluxes for 10 Landsat images from the 2005, 2006 and 2007 crop growing seasons in south-central Nebraska, USA, where each image owing to recent rainfall exhibited high residual moisture content even at the hot pixel. The METRIC model performed satisfactorily for net radiation (R_n ) and soil heat flux (G) estimation with a root mean square error (RMSE) of 52 and 24 W m^-2, respectively. A RMSE of 122 W m^-2 for H indicated the limitation of the METRIC model in estimating H for high residual moisture content of the hot pixel (Alfalfa reference ET fraction, ET _r F > 0.15). The modified METRIC model (wet METRIC or wMETRIC) incorporating the PT equation was applied to calculate H at the anchor pixels (hot and cold) for high residual moisture content of the hot pixel. The α coefficient of the PT equation was locally calibrated using hourly meteorological data from an automatic weather station and R_n and G data from a Bowen ratio flux tower. The mean α coefficient value was 1.14. The wMETRIC model reduced the RMSE of H from 122 to 64 W m^-2 and that of latent heat flux, LE, from 163 to 106 W m^-2. The RMSE of daily ET decreased from 1.7 to 1.1 mm d^-1 with wMETRIC. The results indicate that treatment of anchor pixels for high residual moisture content with the PT approach gives improved estimation of H, LE and daily ET. It is recommended that the wMETRIC model be used for estimating ET if the hot pixel has high residual moisture (i.e. reference ET fraction > 0.15).

Citation Singh, R. K. & Irmak, A. (2011) Treatment of anchor pixels in the METRIC model for improved estimation of sensible and latent heat fluxes. Hydrol. Sci. J. 56(5), 895–906.     

The impact of climate change on water fluxes in a Macaronesian cloud forest

Fog phenomena and their associated meteorological variables were continuously monitored during 4 years in an evergreen laurisilva cloud forest of the Anaga Massif Biosphere Reserve (Tenerife, Canary Islands), in order to establish its current dynamics. Fog was more frequent during night through early morning and in the afternoon, and particularly from May until September, coincidental with a frequent immersion of the 1025 m a.s.l. experimental site in the cloud layer of wind‐driven stratocumulus. The concomitant meteorological conditions during different fog regimes, characterized according to visibility (Ω) ranges, were compared with those when fog was absent. The presence of fog was associated with a significant reduction in global solar radiation, R_g, increased wind speed, and lower and more stable ambient temperatures. The foggy versus fog‐free hourly medians of R_g were found to be linearly related, whereas the proportion of median R_g reduction due to fog varied logarithmically with Ω. However, foggy versus fog‐free extreme values of the hourly R_g distributions departed from such a linear trend. By contrast, hourly temperatures during foggy versus fog‐free periods behaved linearly for most of the Ω range, except for very dense fog, Ω ≤ 100 m. Transpiration of the canopy, intermittently wetted due to interception of both rain and fog water droplets, was determined by quantifying the water balance at leaf scale with a mathematical model for the two representative hypostomatous species present at the site: the arboreal shrub Erica platycodon, with needle‐like leaves, and the laurophyll tree Myrica faya. Both tree transpiration and evaporation of the intercepted fog water were predictively higher during summer. By contrast, transpiration was reduced during February, in agreement with a 1 year period of sap velocity measurements, and was not appreciably affected by soil moisture content. The consequences of an anticipated downward shift of the stratocumulus cloud layer and of various projected Representative Concentration Pathways (RCPs) scenarios in the Macaronesian area were simulated, yielding in all cases a significant rise in transpiration for both species. Particularly, the simulated RCPs scenarios implied 29%–73% increments in transpiration from the actual values. Because fog is concomitant with lower temperatures and vapour pressure deficit, the modification of its current distribution as a consequence of climate change may have a direct effect on such associated meteorological variables, and therefore a meaningful impact in the water relations of the laurel cloud forests.     

Forest water use in the initial stages of reclamation in the Athabasca Oil Sands Region

Following large‐scale surface oil sands mining, large tracts of the boreal forest in the Athabasca Oil Sands Region of Western Canada are legally required to be reclaimed. A greater understanding of how these novel ecosystems function and develop with regard to water use is crucial to aid in the development of regulatory practices and protocols based on information from ecosystem recovery. In this paper, a 12‐year (2003–2014) eddy covariance measurement record of latent and sensible heat fluxes and gross ecosystem productivity of carbon dioxide is analysed to evaluate how a reclaimed boreal forest has developed during its initial growth period. The study site is a reclaimed oil sands saline‐sodic clay shale overburden deposit that was topped with 100 cm of glacial till and 20 cm of peat mineral mix. The site was seeded with barley (Hordeum spp.) in 2001 to reduce erosion of the soil cover whereas aspen (Populus tremuloides Michx.) and spruce (Picea glauca [Moench] Voss) boreal tree species were planted in 2004. Changes in structure and function corresponded to the transition of dominant vegetation cover from early successional species to forest. Leaf area index increased from a growing season peak of 0.9 in 2003 to 4.0 in 2014 and was associated with an increased growing season gross ecosystem productivity (4.9 to 8.9 g C m^?2 day^?1), an increased evapotranspiration (1.6 to 3.4 mm day^?1), and a decreased partitioning of energy to sensible heat (Bowen's ratio decreased from 1.1 to 0.4). Although canopy conductance increased throughout the 12 years, the shift from early successional species to trees with more conservative water use resulted in a decrease in conductance normalized by leaf area. Water use efficiency has increased slightly since 2008 with an average of 10.0 g CO₂ kg^?1 H₂O for the last 6 years. No prolonged dry periods were observed during the study period. The functioning of this novel ecosystem is evolving as expected on the basis of the trends observed for other natural and disturbed boreal forests.     

Effects of the introduction of rice on evapotranspiration in seasonal wetlands

Land use changes in wetland areas can alter evapotranspiration, a major component of the water balance, which eventually affects the water cycle and ecosystem. This study assessed the effect of introduced rice‐cropping on evapotranspiration in seasonal wetlands of northern Namibia. By using the Bowen ratio–energy balance method, measurements of evapotranspiration were performed over a period of 2.5 years at two wetland sites—a rice field (RF) and a natural vegetation field (NVF)—and at one upland field (UF) devoid of surface water. The mean evapotranspiration rates of RF (1.9 mm daytime^?1) and NVF (1.8 mm daytime^?1) were greater than that in UF (1.0 mm daytime^?1). RF and NVF showed a slight difference in seasonal variations in evapotranspiration rates. During the dry season, RF evapotranspiration was less than the NVF evapotranspiration. The net radiation in RF was less in this period because of the higher albedo of the non‐vegetated surface after rice harvesting. In the early growth period of rice during the wet season, evapotranspiration in RF was higher than that in NVF, which was attributed to a difference in the evaporation efficiency and the transfer coefficient for latent heat that were both affected by leaf area index (LAI). Evapotranspiration sharply negatively responded to an increase in LAI when surface water is present according to sensitivity analysis, probably because a higher LAI over a surface suppresses evaporation. The control of LAI is therefore a key for reducing evaporation and conserving water. Copyright © 2013 John Wiley & Sons, Ltd.     

An Analysis of Turbulent Heat Fluxes and the Energy Balance During the REFLEX Campaign

Three eddy covariance stations were installed at the Barrax experimental farm during the Land-Atmosphere Exchanges (REFLEX) airborne training and measurement campaign to provide ground truth data of energy balance fluxes and vertical temperature and wind profiles. The energy balance closure ratio (EBR) was 105% for a homogeneous camelina site, 86% at a sparse reforestation site, and 73% for a vineyard. We hypothesize that the lower closure in the last site was related to the limited fetch. Incorporating a vertical gradient of soil thermal properties decreased the RMSE of the energy balance at the camelina site by 16 W m^?2. At the camelina site, eddy covariance estimates of sensible and latent heat fluxes could be reproduced well using mean vertical profiles of wind and temperature, provided that the Monin—Obukhov length is known. Measured surface temperature and sensible heat fluxes suggested high excess resistance for heat (kB^?1 = 17).     

Seasonal variation in the energy and water exchanges above and below a larch forest in eastern Siberia

The water and energy exchanges in forests form one of the most important hydro‐meteorological systems. There have been far fewer investigations of the water and heat exchange in high latitude forests than of those in warm, humid regions. There have been few observations of this system in Siberia for an entire growing season, including the snowmelt and leaf‐fall seasons. In this study, the characteristics of the energy and water budgets in an eastern Siberian larch forest were investigated from the snowmelt season to the leaf‐fall season. The latent heat flux was strongly affected by the transpiration activity of the larch trees and increased quickly as the larch stand began to foliate. The sensible heat dropped at that time, although the net all‐wave radiation increased. Consequently, the seasonal variation in the Bowen ratio was clearly ‘U’‐shaped, and the minimum value (1·0) occurred in June and July. The Bowen ratio was very high (10–25) in early spring, just before leaf opening. The canopy resistance for a big leaf model far exceeded the aerodynamic resistance and fluctuated over a much wider range. The canopy resistance was strongly restricted by the saturation deficit, and its minimum value was 100 s m^?1 (10 mm s^?1 in conductance). This minimum canopy resistance is higher than values obtained for forests in warm, humid regions, but is similar to those measured in other boreal conifer forests. It has been suggested that the senescence of leaves also affects the canopy resistance, which was higher in the leaf‐fall season than in the foliated season. The mean evapotranspiration rate from 21 April 1998 to 7 September 1998 was 1·16 mm day^?1, and the maximum rate, 2·9 mm day^?1, occurred at the beginning of July. For the growing season from 1 June to 31 August, this rate was 1·5 mm day^?1. The total evapotranspiration from the forest (151 mm) exceeded the amount of precipitation (106 mm) and was equal to 73% of the total water input (211 mm), including the snow water equivalent. The understory evapotranspiration reached 35% of the total evapotranspiration, and the interception evaporation was 15% of the gross precipitation. The understory evapotranspiration was high and the interception evaporation was low because the canopy was sparse and the leaf area index was low. Copyright © 2001 John Wiley & Sons, Ltd.     

River flux uncertainties predicted by hydrological variability and riverine material behaviour

Data on riverine fluxes are essential for calculating element cycles (carbon, nutrients, pollutants) and erosion rates from regional to global scales. At most water‐quality stations throughout the world, riverine fluxes are calculated from continuous flow data (q) and discrete concentration data (C), the latter being the main cause of sometimes large uncertainties. This article offers a comprehensive approach for predicting the magnitude of these uncertainties for water‐quality stations in medium to large basins (drainage basin area > 1000 km²) based on the commonly used discharge‐weighted method. Uncertainty levels – biases and imprecisions – for sampling intervals of 3 to 60 days are correlated first through a nomograph with a flux variability indicator, the quantity of riverine material discharged in 2% of time (M_2%). In turn, M_2% is estimated from the combination of a hydrological reactivity index, W_2% (the cumulative flow volume discharged during the upper 2% of highest daily flow) and the truncated b_50sup exponent, quantifying the concentration versus discharge relationship for the upper half of flow values (C = a q ^b50sup, for q > q₅₀, where q₅₀ is the median flow): M_2% = W_2% + 27.6b_50sup. W_2% can be calculated from continuous flow measurements, and the b_50sup indicator can be calculated from infrequent sampling, which makes it possible to predict a priori the level of uncertainty at any station, for any type of riverine material either concentrated (b_50sup > 0) or diluted (b_50sup > 0) with flow. A large data base of daily surveys, 125 station variables of suspended particulate matter (SPM), total dissolved solids (TDS) and dissolved and particulate nutrients, was used to determine uncertainties from simulated discrete surveys and to establish relationships between indicators. Results show, for example, that for the same relatively reactive basin (W_2% > 25%), calculated fluxes from monthly sampling would yield uncertainties approaching ±100% for SPM (b_50sup > 1.4) fluxes and ±10% for TDS (b_50sup = ?0.2). The application to the nitrate survey of the river Seine shows significant trends for the 1972–2009 records. Copyright © 2012 John Wiley & Sons, Ltd.     

A detailed energy budget analysis of river supercooling and the importance of accurately quantifying net radiation to predict ice formation

River supercooling and ice formation is a regular occurrence throughout the winter in northern countries. The resulting frazil ice production can obstruct the flow through intakes along the river, causing major problems for hydropower and water treatment facilities, among others. Therefore, river ice modellers attempt to calculate the river energy budget and predict when supercooling will occur in order to anticipate and mitigate the effects of potential intake blockages. Despite this, very few energy budget studies have taken place during freeze-up, and none have specifically analysed individual supercooling events. To improve our understanding of the freeze-up energy budget detailed measurements of air temperature, relative humidity, barometric pressure, wind speed and direction, short- and longwave radiation, and water temperature were made on the Dauphin River in Manitoba. During the river freeze-up period of late October to early November 2019, a total of six supercooling events were recorded. Analysis of the energy budget throughout the supercooling period revealed that the most significant heat source was net shortwave radiation, reaching up to 298 W/m², while the most significant heat loss was net longwave radiation, accounting for losses of up to 135 W/m². Longwave radiation was also the most significant heat flux overall during the individual supercooling events, accounting for up to 84% of the total heat flux irrespective of flux direction, highlighting the importance of properly quantifying this flux during energy budget calculations. Five different sensible (Q_h) and latent (Q_e) heat flux calculations were also compared, using the bulk aerodynamic method as the baseline. It was found that the Priestley and Taylor method most-closely matched the bulk aerodynamic method on a daily timescale with an average offset of 8.5 W/m² for Q_h and 10.1 W/m² for Q_e, while a Dalton-type equation provided by Webb and Zhang was the most similar on a sub-daily timescale with average offsets of 20.0 and 14.7 W/m² for Q_h and Q_e, respectively.     

On the heat and mass transfer from an ascending magma

The maximum heat transfer possible from a sphere of magma ascending through a viscous lithosphere is estimated using a Nusselt number formulation. An upper bound is found for the Nusselt number by using the characteristics of a potential flow which, it is argued, is similar in the limit to a non-isothermal Stokes-flow in which the fluid (wall rock) viscosity is sensitive to temperature. A set of cooling curves are calculated for a magma ascending at a constant velocity beneath an island arc. If the magma is to arrive at the surface without solidifying its ascent velocity must be greater than about 5.8 × 10^?3 cm s^?1, for a magma radius of 1 km, and greater than about 2.7 × 10^?5 cm s^?1, for a magma radius of 6 km. If the magma begins its ascent crystal free it will generally become superheated over most of its ascent. Using essentially the same formulation as for heat transfer the mass transfer to or from a spherical body of magma ascending at these velocities is given approximately by ΔC ? ΔW/10, where ΔC is the change in weight percent of a component in the magma during ascent and ΔW is the compositional contrast of that component between the magma and its wall rock.     

Energy balance and evaporation loss of an agricultural reservoir in a semi‐arid climate (south‐eastern Spain)

A typical agricultural water reservoir (AWR) of 2400 m² area and 5 m depth, located in a semi‐arid area (southern Spain), was surveyed on a daily basis for 1 year. The annual evaporation flux was 102·7 W m^?2, equivalent to an evaporated water depth of 1310 mm year^?1. The heat storage rate G exhibited a clear annual cycle with a peak gain in April (G ～ 45 W m^?2) and a peak loss in November (G ～ 40 W m^?2), leading to a marked annual hysteretic trend when evaporation (λE) was related to net radiation (R_n). λE was strongly correlated with the available energy A, representing 91% of the annual AWR energy loss. The sensible heat flux H accounted for the remaining 9%, leading to an annual Bowen ratio in the order of 0·10. The equilibrium and advective evaporation terms of the Penman formula represented 76 and 24%, respectively, of the total evaporation, corresponding to a annual value of the Priestley–Taylor (P–T) coefficient (α) of 1·32. The P–T coefficient presented a clear seasonal pattern, with a minimum of 1·23 (July) and a maximum of 1·65 (December), indicating that, during periods of limited available energy, AWR evaporation increased above the potential evaporation as a result of the advection process. Overall, the results stressed that accurate prediction of monthly evaporation by means of the P–T formula requires accounting for both the annual cycle of storage and the advective component. Some alternative approaches to estimating R_n, G and α are proposed and discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Prediction of concentrated flow width in ephemeral gully channels

Empirical prediction equations of the form W = aQ^b have been reported for rills and rivers, but not for ephemeral gullies. In this study six experimental data sets are used to establish a relationship between channel width (W, m) and flow discharge (Q, m³ s^?1) for ephemeral gullies formed on cropland. The resulting regression equation (W = 2·51 Q^0·412; R² = 0·72; n = 67) predicts observed channel width reasonably well. Owing to logistic limitations related to the respective experimental set ups, only relatively small runoff discharges (i.e. Q < 0·02 m³s^?1) were covered. Using field data, where measured ephemeral gully channel width was attributed to a calculated peak runoff discharge on sealed cropland, the application field of the regression equation was extended towards larger discharges (i.e. 5 × 10^?4m³s^?1 < Q < 0·1 m³s^?1). Comparing W–Q relationships for concentrated flow channels revealed that the discharge exponent (b) varies from 0·3 for rills over 0·4 for gullies to 0·5 for rivers. This shift in b may be the result of: (i) differences in flow shear stress distribution over the wetted perimeter between rills, gullies and rivers, (ii) a decrease in probability of a channel formed in soil material with uniform erosion resistance from rills over gullies to rivers and (iii) a decrease in average surface slope from rills over gullies to rivers. The proposed W–Q equation for ephemeral gullies is valid for (sealed) cropland with no significant change in erosion resistance with depth. Two examples illustrate limitations of the W–Q approach. In a first example, vertical erosion is hindered by a frozen subsoil. The second example relates to a typical summer situation where the soil moisture profile of an agricultural field makes the top 0·02 m five times more erodible than the underlying soil material. For both cases observed W values are larger than those predicted by the established channel width equation for concentrated flow on cropland. For the frozen soils the equation W = 3·17 Q^0·368 (R² = 0·78; n = 617) was established, but for the summer soils no equation could be established. Copyright © 2002 John Wiley & Sons, Ltd.