Moisture Carryover Research Articles

The Role of Antecedent Winter Soil Moisture Carryover on Spring Runoff Predictability in Snow-Influenced Western U.S. Catchments

Abstract Spring runoff is critical to agricultural, industrial, and municipal water supply as well as environmental uses in the western United States. Although spring runoff in this region has long been predicted based on late winter and early spring montane snow water storage, the role of soil moisture carryover from the previous winter is less understood and utilized in forecasts. We quantify the relationship between antecedent winter soil moisture and spring runoff for 85 unmanaged catchments in the western United States. Using a regression-based approach, we estimate the proportional reduction in error in seasonal runoff forecasts associated with soil moisture. We classify the catchments into two regimes: interior (cold and relatively dry) and maritime (warmer and wetter), based on seasonal variations in soil moisture. Soil moisture generally is relatively unchanged through the winter period in interior catchments, whereas it increases (mostly gradually, but occasionally rapidly) in maritime catchments. We find that winter temperature dominates soil moisture variability in both types of catchments. We find two patterns in the predictability of spring runoff. First, including antecedent winter soil moisture as a predictor enhances forecast accuracy and variance explanation in spring runoff for both interior and maritime catchments, particularly and with greater significance in interior catchments. Second, spring runoff prediction skill from antecedent winter soil moisture increases with elevation. Overall, we find strong evidence that the use of antecedent soil moisture can improve spring runoff forecast skill for catchments in the western United States. Significance Statement Spring runoff forecasts are crucial for water supply in the western United States, but typically exclude information about soil moisture despite its key role in the water balance. Our study explores how and why incorporating information about winter’s soil moisture levels affects spring runoff forecasts across 85 catchments in the western United States. We find that doing so can produce modest improvements in the prediction skill of spring runoff for both interior and maritime catchments but is particularly noticeable in interior catchments and at higher elevations where temperatures are lower. Overall, our research strongly supports the idea that using information about soil moisture from the previous winter can improve accuracy in spring runoff forecasts for the western United States.

Stronger control of surface conductance by soil water content than vapor pressure deficit regulates evapotranspiration in an urban forest in Beijing, 2012–2022

With urbanization rapidly increasing, evapotranspiration (ET) in urban forests plays an increasingly important role in urban hydrology and climate. However, large uncertainty remains regarding the regulating factors of ET in urban area. Using the eddy-covariance technique, we investigated the temporal variations of ET in an urban forest park in Beijing for 2012–2022. Daily ET was close to zero during winter and reached 3–6 mm day−1 in summer. Daily ET increased with vapor pressure deficit (VPD) and soil water content (SWC). When binning daily data into 10 bins according to percentiles of either SWC or VPD, surface conductance (gs) increased with SWC for all VPD bins, but showed weak responses to VPD for SWC bins. Monthly ET increased linearly with normalized difference vegetation index, showed a strong correlation with gs, and exhibited saturated responses to increasing monthly precipitation (PPT). Annual ET ranged from 326 to 566 mm (with the eleven-year mean of 428.66 ± 83.83 mm; mean±SD), and varied from 55 % to 148 % of annual PPT. Aggregated ET over the eleven years (4715 mm) accounted for 82 % of the aggregated PPT. Soil water replenishment through PPT from mid-summer to late autumn of the previous year was responsible for the generally higher monthly ET in spring relative to PPT, resulting in a weak correlation between annual ET and PPT in the same calendar year (R2= 0.28). The PPT in the early growing season partly promoted annual ET through its effect on summer gs. Our results suggest that biotic factors and PPT seasonality played an essential role in regulating ET at the seasonal and interannual scales, respectively. Soil dryness imposed additional constraints on gs at the finer timescale (i.e., days). Urban land-surface models should adequately address the soil moisture carryover effect to improve simulations.

Interannual variation in evapotranspiration in an urban forest reserve with respect to drought

IntroductionA warming global climate is expected to perturb the hydrological cycle, resulting in deviations in both frequency and duration of drought and thus being hypothesized to lead to interannual variation in evapotranspiration (ET). Interannual variation in ET in urban forest ecosystems in response to drought remains poorly understood.MethodsHere, ET in an urban forest reserve in the megalopolis of Beijing was investigated using eddy-covariance measurements collected over six consecutive years (2012–2017).ResultsThe mean annual cumulative ET was 462 ± 83mm (±first standard deviation), with a coefficient of variation of 18%. Interannual variation in both annual and monthly ET was shown to be largely controlled by canopy conductance (gs), affected by environmental factors. The main factors affecting interannual variation in monthly ET varied seasonally, namely, soil volumetric water content (VWC) and normalized difference vegetation index (NDVI) in spring, precipitation and soil temperature in summer, and VWC and net radiation (Rn) in autumn. Interannual variation in annual ET was driven largely by spring and mid-summer droughts induced by insufficient precipitation during the non-growing and mid-growing seasons, respectively. Spring drought reduced annual ET by restricting leafing out, shortening growing season length (GSL), and reducing the normalized difference vegetation index (NDVI). The summer drought reduced annual ET by reducing stomatal conductance.Discussion and conclusionResults from this study point to the importance of precipitation timing and volume and the soil moisture carry-over effect in controlling interannual variation in ecosystem ET. Irrigation during the early spring and mid-summer is viewed as a practical management measure for sustaining growth and better ecosystem services in urban forests in Northern China.

Study on gravity separation of air-water from the upper part of UTSG full-scale swirl separator in pressurized water reactor

The steam separator is one of the most critical components in the U-tube steam generator (UTSG), which qualifies moisture carryover less than 0.1% to minimize the damage to turbines. Take both high separation efficiency and low manufacture cost into account, the height of the gravity separation space should be designed appropriately. Air-water separation experiments are carried out to study the effect of several different gravity heights on the separation performance. A droplet mathematical model is proposed and the experimental results are discussed based on it. The analysis indicated that (1) For Stokes flow, weather initial droplet velocity ud0 is bigger or smaller than vapor velocity ug, the analytical solution of the maximum height h for the droplet to reach can be calculated by the same formula. (2) From the numerical solutions of droplet mechanics model, it is found that separation height is related with all three factors (ug,ud0,D) for the small droplet, but is only related with ud for the big droplet. (3) Experimental results show that there exists a minimum gravity separation height to obtain the maximum separation efficiency under the given gas–water conditions. (4) Initial droplet velocity is the key parameter required for the engineering design of separation space height.

Hydrological losses and soil moisture carryover affected the relationship between evapotranspiration and rainfall in a temperate semiarid shrubland

Evapotranspiration (ET) represents a major pathway of water loss from terrestrial ecosystems. However, large uncertainty exists regarding the relationship between ET and precipitation at seasonal and interannual timescales in drylands. Using the eddy-covariance technique, we investigated temporal variations of ET in a semiarid shrubland of northern China during January 2012–December 2020. Daily ET was close to zero during winter and reached up to 2–4 mm day−1 in summer. Monthly ET was positively and linearly correlated with the normalized difference vegetation index and surface conductance (gs), and showed a saturating relationship with monthly rainfall. Analyses based on bin-averaged half-hourly values revealed increases in midday ET and gs with increasing soil water content, and decreases in midday gs and saturated ET with increasing vapor pressure deficit. Annual ET for ecohydrologic years (July 1–June 30) ranged 207–297 mm yr−1 (with a multi-year average of 242 mm yr−1), and accounted for 62%–105% of annual rainfall. Aggregated ET over the study period (2163 mm) accounted for 78% of total rainfall. Rainfall amount was a poor predictor of year-to-year differences in annual ET, wet-season (July 1–November 30) ET, and dry-season (December 1–June 30) ET. Wet-season ET (mm season−1) was generally lower than rainfall while dry-season ET tended to be higher than rainfall. Our results suggest that biotic factors played an essential role in regulating seasonal variations in ET, while air and soil dryness imposed additional constraints on ET at finer timescales. Moreover, hydrological losses (e.g., to subsurface runoff and/or deep drainage) during wet seasons and soil moisture carryover from wet to dry seasons may be nonnegligible in the studied semiarid shrubland, and thus affected seasonal and interannual relationships between ET and rainfall.

Experimental study on performance optimization for full-scale swirl separator of air-water in PWR UTSG

The separation of liquid water from the steam-water mixture is one of the key processes in U-tube steam generators, which is critical to assure the turbine safety by minimizing the water erosion damage. To develop a highly successful separator under actual operating conditions, air-water tests are carried out to study the effect of different separation heights above swirl vanes on the separation performance. The tests are based on a full-scale separator with the air superficial velocity ranging from 10 m/s to 19 m/s and the water superficial velocity including 0.127 m/s and 0.151 m/s. The moisture carryover in this work is in the range of 0.3%–0.6%, which increases with the air superficial velocity increasing. While the air velocity is under 13.8 m/s, the moisture carryover almost changes little with the increase of separation heights. Nevertheless, the moisture carryover decreases significantly with the increase of separation heights for the air velocity above 15.5 m/s. The pressure drop increases approximately linearly with the increase of the air superficial velocity, and almost remains unchanged for different separation heights. To obtain better separation performance in a wide range of operation conditions, the maximum separation height is recommended.

Development and Experimental Validation for Quantifying the Moisture Carryover in a Moisture Separator Using an Air/Water Test Facility

The moisture carryover (MCO) of the primary separator in a steam generator is the most important design parameter to ensure high efficiency in a steam generator. There is an inherent limitation to experimentally evaluate the MCO under the prototype conditions. In this study, the air/water test facility was constructed based on the similarity law, and a new isokinetic system was developed to quantify the MCO. Several experiments were performed for the mass quality ranging from 0.315 to 0.382. The accuracy and versatility of the experimental method was verified experimentally using a full and half scale of separators. The test results were compared with the prototype results. It was proved to be a reliable experimental method for evaluating the MCO of the moisture separator.

Moisture-carryover performance optimization using physics-constrained machine learning

A data-driven model for predicting moisture carryover (MCO) in the General Electric Type-4 boiling water reactor (BWR) was constructed using a physics-constrained artificial intelligence technique. An accurate prediction of the MCO is of great value for commercial BWR operators as it can be used to modify the operational plan during a power cycle to mitigate high MCO, thereby avoiding elevated dose to on-site personnel and damage to turbine components. Using data from operational plants and preliminary features selected through physics and engineering analyses, a neural network based model for predicting MCO was built. A final feature set was then obtained through a hyperspace optimization performed using a genetic algorithm. Multiple neural network models possessing good generalization were obtained, the best of these having a mean-square error (MSE) of 9.69E-5 for prediction of an un-seen cycle, which is in agreement with the uncertainty in the measured MCO data. This predictive capability is of great value for the planning of a power generation cycle, and for scheduling of operations for cycles already underway.

증기발생기 습분분리기 습분동반율에 대한 물/공기 실험적 연구

The separation efficiency of the moisture separator in a steam generator is the most important key parameter to ensure the safety of turbine and to obtain high efficiency in a nuclear power plant. The objective of this research is to investigate which experimental method can be used for evaluating the performance of the separator, namely moisture carry over (MCO), of the prototype separator. The air/water test facility based on the similarity law was constructed and developed an experimental method to quantify the MCO. For a various mass quality ranged from 0.277 to 0.382, several experiments were carried out to evaluate the MCO and to verify the experimental method. The obtained results were compared to data on the prototype condition and showed a good agreement with that of the prototype conditions.

Effect of water level on performance of swirl-vane separator and steam dryer in PWR SG

Swirl-vane separator and steam dryer work as primary and secondary separator in PWR SG to supply the dry-saturation steam for the turbines to generate electricity. In this paper, steam-water two-phase experiment is conducted to investigate the effect of water level on the separation efficiency, moisture carryover (MCO) and pressure drop of swirl-vane separator and steam dryer, respectively. The operation pressure is 6 MPa and the mass flowrate of steam and water are 3.81–11.73 kg/s and 7.62–70.40 kg/s, corresponding to 50–154% full power and 3–7 circulation ratio under prototypical conditions. For swirl-vane separator, the results indicate that the separation efficiency decreases (or MCO increases) with power load and circulation ratio at normal-water level, while it decreases more significantly with power load and the dependence on circulation ratio becomes complex at high-water level. The separator pressure drop increases with power load and circulation ratio increasing, but the influence of water level is minor. In terms of steam dryer, at both normal and high-water level, the separation efficiency and MCO exhibit minor change with power load and circulation ratio below the critical load (e.g. 120%–140%). Otherwise, MCO increases (or separation efficiency decreases) rapidly with power load and circulation ratio, and its value changes from 0.1% to 1.9% at normal-water level and from 1.0% to 22.4% at high-water level. The dryer pressure drop increases with power load while the influence of circulation ratio and water level is minor. Overall, the high-water level deteriorates the separation efficiency but has little influence on pressure drop of steam separator package in nuclear SG.

Effect of velocity and pressure on performance of a full-scale SG steam separator package

Steam separator package including swirl-vane separator, gravity and dryer is crucial for supplying the qualified steam for the turbines in nuclear steam generator (SG). In this paper, steam-water experiments are carried out to study the separation efficiency, moisture carryover (MCO) and pressure loss of a full-scale SG steam separator package of the GEN-III advanced PWR. The system pressure ranges from 2 to 6 MPa and the superficial velocities of the steam jg and water jl are 1.47–5.91 m/s and 0.18–1.05 m/s, respectively. At rated pressure of 6 MPa, the results indicate that the separation efficiency of swirl-vane separator is insensitive to jg at low jl but decreases with jg at high jl. Generally, a larger jl causes a higher efficiency. Nevertheless, both the influence of jg and jl on the separation efficiency of gravity and dryer is minor. The MCO of swirl-vane separator and gravity decreases with jg increasing or jl decreasing whereas the residual wetness at dryer exit exhibits minor change with jg and jl. The pressure loss of swirl-vane separator increases with both jg and jl increasing while it increases gradually with jg but shows slight change with jl in the dryer. Overall, a higher pressure leads to a lower separation efficiency of swirl-vane separator and gravity but a higher dryer efficiency, a lower MCO and a higher-pressure loss of the whole separator package. Considering the effect of velocity and pressure, empirical correlations are proposed to predict the performance of swirl vanes, which are the key components for the separation performance and pressure loss.

Experimental study on the separation performance of a full-scale SG steam-water separator

Steam separator package including swirl vane separator, gravity and dryer is crucial for guaranteeing steam humidity below 0.1% in SG. In this paper, a high-pressure flow system is designed to study the performance of a full-scale steam separator package at a rated pressure of 6 MPa and temperature of 275.6 °C. To obtain separation efficiency, moisture carryover and pressure drop of each stage, the Reynolds number steam and water are 1 × 106–6 × 106 and 8.27 × 105–3.2 × 106, corresponding to 25–145% load. Results indicate that the separation efficiency ranges from 97 to 99%, 0.5 to 2% and 0.2 to 0.75% for separator, gravity and dryer. The moisture carryover ranges from 2 to 16% and 1 to 4% for separator and gravity, and is below 0.1% at dryer outlet. The pressure drop ranges from 2 to 24 kPa and 0.3 to 3 kPa for separator and dryer. Empirical correlations for swirl vanes are proposed, which are responsible for more than 85% and 70% of total separation efficiency and pressure drop.

Machine-Learning Analysis of Moisture Carryover in Boiling Water Reactors

Moisture carryover (MCO) is modeled in the General Electric Type-4 boiling water reactor (BWR) using machine-learning methods and data from operating plants. Understanding MCO and the conditions that give rise to an elevated value is important since excessive MCO can damage critical turbine components, can result in elevated dose levels to on-site personnel, and can interfere with late-cycle power management. The analysis of MCO takes into account simplifying reactor symmetries and important geometric dependencies. The plant data are taken from several reactors and were collected over multiple years and multiple fuel cycles. A brief description of the origin of MCO in U.S. BWR plants is given. A machine-learning model is constructed from the data using applicable algorithms and data-reduction techniques. Matching model complexity with available data is one of the more challenging machine-learning tasks. Too many features and too little data will lead to overfitting. The data for each fuel cycle included over 6876 original features, 9 for each fuel bundle. Two approaches are used to reduce the data set into a manageable number of features. The first was an engineering analysis that resulted in the selection of steam quality Q and steam liquid phase velocity VL as the main features driving MCO. Using a Q and a VL for each fuel bundle gives 1528 Q and a VL feature describing the reactor behavior. An analysis of different functional forms of these two variables led to the actual inputs to the neural network model. The second approach involved the use of statistical techniques such as Pearson’s correlation and k-means analysis. The identified groupings of bundles behaved similarly. Treating each grouping as a single feature further reduced the input variable set to a manageable number. A model selection criterion is proposed, and results are presented along with a discussion of related issues.

A county‐level estimation of renewable surface water and groundwater availability associated with potential large‐scale bioenergy feedstock production scenarios in the United States

AbstractThis study examines fresh renewable water resources available for bioenergy feedstock production in the United States. The impacts of feedstock irrigation on surface and groundwater resources available to nonbioenergy sectors were quantified using a pair of water availability indexes: streamflow availability index and percolation flow availability index. The two metrics were applied to both historical (2008) and three possible future biomass production scenarios from the 2016 U.S. Billion‐Ton Report at the county level. For both historical and future scenarios, we found that the consumptive irrigation requirements for bioenergy feedstock account for <0.01% of annual streamflow in all but three counties in Nebraska. Results suggest that the irrigation demand of future biomass production could be supplied by annual renewable groundwater flow in about 94% of feedstock‐growing counties that use groundwater for irrigation, representing about 92% of production tonnage. Counties that require irrigation from nonrenewable groundwater resources are mostly located in the Northern Plains and Pacific regions. We also evaluated the sensitivity of crop water footprint estimation to soil moisture carryover by comparing blue water estimates from six different empirical and process‐based methods. Our findings suggest that accounting for preseason soil moisture is critical for representative blue water estimation, so that the irrigation water consumption is not overestimated. This is especially true in the Corn Belt region, where blue water estimates with and without preseason soil moisture would be about 1.9 versus 45.5 billion m3/year under the historical scenario. This difference is smaller in semiarid regions like the High Plains, but the blue water estimate can still triple if soil moisture is not considered. From the perspective of renewable surface water and groundwater resources, scaling feedstock production up in the High Plains and California will require careful planning integrated with water management strategies to improve water resource conservation.

Energy and water vapor exchange over a young plantation in northern China

Northern China’s plantations have long played a role in providing ecological services to the people of China. Reliable detection and attribution of ecosystem water and energy exchange is a precondition to the development of strategies for the sustainable management of these plantations. Here, the seasonal and interannual variability in surface energy exchange and evapotranspiration (ET) over a young pine plantation was investigated using eddy-covariance measurements collected over a four-year period (2012–2015). Seasonal patterns in net radiation (Rn), latent (LE) and sensible heat fluxes (H) were largely similar over the four years. H was the dominant energy component, with LE exceeding H only during the mid-growing season. A significant share of Rn was allocated to H during the 2014 summer drought. Energy exchange for the young pine plantation was characterized by high Bowen ratios (β = H/LE; 6.28, 6.42, 5.65, and 5.34 for the four years), high H/Rn (0.37, 0.36, 0.36, and 0.30), and low LE/Rn (0.15, 0.17, 0.17, and 0.16), with mean annual values of 5.92, 0.35, and 0.16 for β, H/Rn, and LE/Rn, respectively. Daily maximum and annual ET were 4.8, 4.5, 4.1, and 3.3 mm day−1 and 328, 371, 290, and 326 mm for the four years, with a mean annual value of 329 mm. Seasonal variation in ET was strongly controlled by biological factors (i.e., bulk surface conductance and vegetation greenness and density, as characterized by the normalized difference vegetation index) regulated by soil water availability and water vapor pressure deficit (VPD). Evapotranspiration varied interannually and the evapotranspiration-to-precipitation ratio (ET/P) ranged from 0.79 to 1.62. Soil water replenishment through precipitation during the non-growing period of the previous year and mid-growing season of the current year was responsible for the interannual variation observed in ET. These results clearly indicate the importance of precipitation timing and soil moisture carry-over from previous years in controlling ecosystem energy and water vapor exchange. Irrigation during the spring and dry periods of the year is highly favorable for growth of plantation trees in northern China.

Carbon and water exchange over a temperate semi-arid shrubland during three years of contrasting precipitation and soil moisture patterns

Water is considered a key factor affecting ecosystem carbon exchange in dryland regions. However, the relationship between inter-annual variations in precipitation and ecosystem productivity remains to be clarified for arid and semi-arid areas. Based on eddy-covariance measurements, we examined how ecosystem production in a shrubland of northern China varied over three years (2012–2014) with contrasting precipitation and soil moisture patterns. Net ecosystem production (NEP) was 77±10 (±standard deviation), −4±10 and −22±5gCm−2 in 2012–2014, respectively, indicating a rapid shift from an annual sink to a source of carbon. Gross ecosystem production (GEP), total ecosystem respiration (TER) and evapotranspiration (ET) also declined over the three years. Annual carbon and water fluxes appeared to be suppressed in years with low spring soil moisture, which declined dramatically from 2012 to 2014. GEP declined more than TER and ET, leading to reduced carbon sequestration capacity and water use efficiency (WUE=GEP/ET). Neither annual nor growing-season precipitation could explain the year-to-year variations in carbon fluxes, whereas at our site ET was a better proxy for water available to ecosystem carbon exchange on an annual basis. Autumn soil moisture levels were carried over winter to the following spring, and, thus, may affect the rates of leafout, plant growth and carbon uptake in the early- to mid-growing season. Our conclusions were drawn from only three years of measurements and are therefore preliminary. Longer timeseries encompassing a wider range of precipitation and soil moisture conditions are needed to confirm or refine these conclusions. Our findings highlight the importance of precipitation timing and soil moisture carry-over in controlling ecosystem productivity. Winter warming and decreases in autumn and winter precipitation may induce spring drought and thus impair the carbon sequestration potential of shrubland and steppe ecosystems in semi-arid and arid Eurasia.

Determine Recooling Plant’s Effectiveness in the Jet-Bubbling Contact Members

Recooling systems, and in particular, their kind, water recycling systems, are one of the most important elements of the technological complex of many industries. The performance of the process equipment, quality and production costs, the specific consumption of raw materials and energy depends on the quality and effectiveness of water recycling systems. Availability of a wide range of water cooling plants causes the need to develop criteria to assess their effectiveness in order to make informed choice of their type. It was proposed a jet-bubble device for improving the efficiency of industrial cooling tower, which is able to provide a minimum moisture carryover by gas flow, a large surface contact between the phases and minimal hydraulic resistnace. There were presented results of studies heat and mass transfer efficiency using contact members.

Interacting controls on productivity in a northern Great Plains grassland and implications for response to ENSO events

In this study we investigated the causes of annual variability in peak aboveground biomass production, net ecosystem productivity (NEP) and gross ecosystem productivity (GEP) during an 8-year period (1999–2006) in a northern Great Plains grassland near Lethbridge, Alberta, Canada. In particular, we tested for a significant relationship between growing season precipitation and productivity and determined whether soil moisture carry-over from the previous fall–winter could alter this relationship. We also investigated the interaction between soil moisture availability and temperature in controlling grassland productivity. There was a very strong correlation between total precipitation input and average soil moisture content during the May–October growing season. However, the growing season average soil moisture contents in 2003 and 2006 were very similar to those recorded in 1999, despite lower than normal precipitation occurring in these 2 years. This resulted from a positive difference between precipitation and evapo-transpiration that allowed significant soil moisture to be carried-over from the previous fall–winter during both 2003 and 2006. Strong logistic relationships were observed between soil moisture and annual productivity based on data from all years except 2003 and 2006, years which had higher productivity than was predicted from the logistic regression. Interaction between temperature and soil moisture explained this difference. Productivity values in 2003 and 2006 were high compared with 1999, a year with approximately the same soil moisture content, and this resulted from the higher average growing season temperatures that were apparent in 2003 and 2006. Analysis of weather records indicated that precipitation in the month of June was significantly higher during El Niño years than during La Niña years in Lethbridge. During the study period, aboveground biomass, NEP and GEP were generally higher in El Niño years and lower in La Niña years because of associated variation in summer precipitation.

Analytical derivation of the Budyko curve based on rainfall characteristics and a simple evaporation model

The Budyko curve is often used to estimate the actual evaporation as a function of the aridity index in a catchment. Different empirical equations exist to describe this relationship; however, these equations have very limited physical background. The model concept presented in this paper is physically based and uses only measurable parameters. It makes use of two types of evaporation: interception and transpiration. It assumes that interception can be modeled as a threshold process on a daily time scale. If multiplied with the rainfall distribution function, integrated, and multiplied with the expected number of rain days per month, the monthly interception is obtained. In a similar way, the monthly interception can be upscaled to annual interception. Analogous to the interception process, transpiration can be modeled as a threshold process at a monthly time scale and can be upscaled by integration and multiplication with the expected number of rain months. The expected rain days per month are modeled in two ways: as a fixed proportion of the monthly rainfall and as a power function based on Markov properties of rainfall. The latter is solved numerically. It appears that on an annual basis the analytical model does not differ much from the numerical solution. Hence, the analytical model is used and applied on 10 locations in different climates. This paper shows that the empirical Budyko curve can be constructed on the basis of measurable parameters representing evaporation threshold values and the expected number of rain days and rain months and, in addition, a monthly moisture carryover amount for semiarid zones.

Development and Application of an Entrainment Model for the PWR U-Tube Steam Generators for Main Steam Line Break Analysis

The purpose of this paper is to present the analyses that were performed to develop and use an entrainment model for pressurized water reactor U-tube steam generators (SG) for main steam line break (MSLB) analyses. The entrainment model was developed using the RETRAN-3D computer program, and the model was benchmarked against experimental data of moisture carryover during a simulated MSLB accident. The application methodology was also developed to incorporate entrainment into the MSLB mass and energy release calculations for Kori Unit 1. This methodology utilizes LOFTRAN and RETRAN-3D codes in an iterative sequence of cases in which the LOFTRAN nuclear steam supply system model provides boundary conditions for the RETRAN-3D broken loop steam generator model, and the RETRAN-3D model provides the entrainment data that is input back into the LOFTRAN model. FORTRAN programs were developed to facilitate the sequencing of these iterative calculations. As a result of applying the en-trainment model to Kori Unit 1, the temperature calculated inside Containment during MSLB accident using the CON-TEMPT-LT computer program decreased by about 25°C. Consequently this entrainment model provides a significant benefit by decreasing the temperature envelop for environment qualification as well as decreasing the peak Containment pressure.