Water Balance Equation Research Articles

Water-balanced inlet and outlet boundary conditions of the lattice Boltzmann method for shallow water equations

Conservation of mass or water balance is important for the simulation of shallow water projects. The traditional treatment of discharge and water level boundary conditions ignores it in the lattice Boltzmann model for shallow water equations (LABSWE). In this paper, we introduced the water balance equation at these boundary conditions and proposed a universal treatment for the straight boundary of any direction. Six schemes on the unknown particle distribution functions (PDFs) at boundary lattices for given macroscopic quantities (h,u,v) were compared in terms of accuracy and stability, and the nonequilibrium extrapolation (NEQ) scheme and full link nonequilibrium extrapolation (Ful-NEQ) scheme were finally adopted in the proposed treatment. The numerical tests show that the proposed treatment fully satisfies the specified boundary conditions and conservation of mass. Moreover, the distribution of the velocities at the boundaries is consistent along downstream which can reduce the artificial influence length of the boundary.

The reallocation of water and ecosystem service values in arid ecosystems with the implementation of an ecological water diversion project

The rational allocation of the water resources in drylands and the scientific evaluation of their values are important for the regional sustainable development. We estimated the water consumption of each ecosystem in Ejina Oases in the arid area in northwest China based on the water balance equation, then assessed their ecosystem service values (ESVs) using the value per unit area method and the value equivalent factor per unit area method considering the cost of water consumption, respectively, and calculated their water productivities from 1990 to 2015. With the implementation of the ecological water diversion project (EWDP) in 2000, the deciduous broadleaf forest dominated by Populus euphratica had an increasing trend, meanwhile, lakes had a changing process from shrinking and drying up to recovery and expansion from 1990 to 2015. The total water consumption in Ejina Oases decreased from 5.26*108 m3 in 1990 to 4.79*108 m3 in 2000, and then increased continually to 5.97*108 m3 in 2015. The water consumption of forest, grassland and cultivated land hardly changed, while the water consumption of water or wetland changed obviously. The total ESVs estimated using the value per unit area method in Ejina Oases decreased from 1052.6 to 787.3 million ¥ in the period of 1990–2000, then increased to 1500.6 million ¥ in 2015, while the ESVs estimated using the value equivalent factor per unit area method decreased from 6368.7 million ¥ in 1990 to 5892.0 million ¥ in 2000, then increased to 7139.9 million ¥ in 2015, and the latter method was more reasonable. The results showed that the EWDP started in 2000 led to the reallocation of water resources and transfer of ESVs among ecosystems, which had obvious performance in the ecological environment and social economy. This study provided a comprehensive view of water use and management, ecological restoration and socio-economic development in this key ecological function zone, and will help decision-makers to formulate the scheme of rational allocation and efficient utilization of water resources in the basin.

Current Changes in the Major Water Balance Components of the Pechora and Kolyma Deltas under Warming Climate

Long-term variations of water balance components are compared for the deltas of the Pechora and Koluma rivers, flowing in the occurrence area of discontinuous and continuous permafrost rocks. Trends in the variations in the major components of water balance equation (river water flow, precipitation, and losses or increment of runoff in the delta) are considered for the conditions of climate warming (the late XX–early XXI centuries). A distinct increase, most pronounced in 2008–2018, was recorded in the major components of water balance.

Geographically-weighted water balance approach for satellite-hydrologic runoff estimation in Mekong Basin under ENSO

Total basin runoff has been estimated via satellite-hydrologic observations since 2000 due to the high maintenance cost of in situ runoff measurements and the existence of many ungauged river basins. Previous estimates of the satellite-hydrologic basin runoff have been done by simply averaging each gridded runoff within a river basin generated from satellite-hydrologic data products via the water balance equation. Nonetheless, geographical heterogeneities within the river basin are present, which should be considered when estimating satellite-hydrologic runoff. This study proposes a novel geographically-weighted water balance approach to estimate the satellite-hydrologic basin runoff. Our runoff estimates in the Mekong Basin show an improvement of 50–60 % (by means of reducing a root-mean-square error) when compared with published results, which is also consistent with other evaluation statistics. Despite hydrological characteristics for the floodplain of Tonlé Sap Lake in Cambodia differing from the mainstream of Mekong Basin, the runoff basin-averaged, including those areas, also reveal a comparable result against in situ runoff located at the Mekong delta based on the proposed method. We also acquire that the impact of ENSO variability on satellite-hydrologic runoff estimates is substantial, which has not previously been reported. Our error analysis indicates that space-borne water storage is one of the critical remaining error sources. We also anticipate that the runoff estimates could further be improved by combining different versions of space-borne water storage datasets.

Assessing the groundwater loss risk in Beijing based on ecosystem service supply and demand and the influencing factors

Incorporating ecosystem service supply and demand into ecological risk assessment can overcome the limitations of the traditional assessment framework. However, most previous studies are about theoretical discussions and applications of the assessment frameworks are very limited. In this study, we proposed an ecological risk assessment framework based on the supply and demand of ecosystem services and applied this framework to assess groundwater loss risk in Beijing. We calculated the water conservation service supply using the water balance equation and estimated the demand of the service using socioeconomic data from multiple sources. Moreover, the risk characterized by the risk probability of groundwater loss based on the budget of water conservation service was quantified. Furthermore, we delineated the spatial distribution characteristics of groundwater loss risk and analyzed natural and socio-economic factors affecting the risk using the geographically weighted regression (GWR). We found that the spatial distribution of water conservation supply and demand showed a mismatch. Moreover, high and very high groundwater loss risks were mainly distributed in the urban areas and on the cropland, and the very low risks were mainly located in the mountainous areas of Beijing. The average risk values in more than half of the administrative districts were >0.75 and parts of the new urban development areas displayed high groundwater loss risks. According to the GWR model, the impacts of the natural factors on the groundwater loss risk displayed larger spatial variations than those of the socioeconomic factors. Among the factors, population density exhibited a positive effect in most areas of Beijing and mainly affected the groundwater loss risk by influencing the water conservation service demand. Our study can provide a new perspective for ecological risk assessment in social-ecological systems and may provide scientific basis for the reduction of groundwater loss risk in Beijing.

How far are groundwater resource assessments in India reliable?

AbstractThe article critically reviews the methodology adopted by the Central Ground Water Board (CGWB) for the assessment of groundwater resources in India. The authors developed a water balance equation that simulates the changes in annual and seasonal groundwater storages of an agricultural region, using a water accounting framework; they solved the developed equation using the data of annual and seasonal water level fluctuations for a wet year for Ludhiana district of Punjab to estimate different components of the water balance. The estimated values are used to test the robustness of the CGWB methodology for monsoon recharge. The annual groundwater storage change obtained from solving the water balance equation was compared with the observed change in annual groundwater storage and was found to closely tally. As per the water balance equation, the CGWB estimates of rainfall recharge conform to the annual water level fluctuations recorded by the agency and therefore are not reliable. Hence, we could infer that our methodology is superior to that of CGWB for estimating monsoon recharge. The validated equation was also used to estimate the recharge from rainfall during a dry year. Using these outputs in a simple groundwater balance equation, irrigation return flows were estimated for the wet and dry years. The equation was then extended to the Ahmednagar district of Maharashtra, a hard rock area, for estimating the surface water import during a wet year, the key unknown in the region's water balance. Hence, our methodology can be employed to estimate rainfall recharge for dry years using annual changes in groundwater storage and estimated consumptive uses of water, when the “WLF approach,” used by CGWB, fails, owing to the presence of an additional variable, that is, monsoon draft. For wet years, it can be used to arrive at the consumptive use of water for various purposes.

Joint inversion of GNSS and GRACE/GFO data for terrestrial water storage changes in the Yangtze River Basin

SUMMARYSatellite geodetic technologies, such as the Global Navigation Satellite System (GNSS), Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GFO), have complementary advantages in inferring terrestrial water storage (TWS) changes at regional and basin scales. We introduced a joint inversion strategy to infer TWS changes using GNSS- and GRACE/GFO-derived vertical displacements based on Green's function theory in the Yangtze River Basin (YRB) from January 2011 to December 2020. Additionally, we investigated the performance of variance component estimation (VCE) and Akaike's Bayesian Information Criterion (ABIC) to determine the optimal relative weights of different observation data. The performance of our joint inversion strategy was verified through a closed-loop simulation and multi-source hydrometeorological data [i.e. the time derivative of TWS changes (${\rm d}S/{\rm d}t$) from precipitation (P), evapotranspiration (ET) and run-off (R) based on the water balance equation, called P-ET-R]. The closed-loop simulation shows that the TWS changes from joint inversion have better consistencies with the synthetic signals than those of GNSS- and GRACE-only estimates, and the corresponding root mean square error (RMSE) decreased 1.43−6.28 mm and correlation coefficient (CC) increased 3−10 per cent. The ABIC was more suitable for the joint inversion of measured GRACE/GFO and GNSS data for TWS changes in the YRB. Analysis from the measured data shows that the spatial patterns and seasonal characteristics in TWS changes derived from GNSS, GRACE/GFO and their joint inversion are in good agreement in the YRB. The contribution of GNSS observations to the joint inversion in the upstream of the YRB is greater than that of GRACE/GFO due to the relatively densely distributed GNSS stations, but the opposite is true in the downstream. Furthermore, the joint inversion results have better agreements with P and P-ET-R compared to GNSS- and GRACE/GFO-only estimates in the upstream, and the corresponding CCs increased 5−7 per cent (for P) and 2−5 per cent (for P-ET-R), respectively, which further demonstrates the effectiveness of our joint inversion strategy. Our estimation strategy provides a new insight for joint inversion of GNSS and GRACE/GFO data to obtain more reliable TWS changes.

A Soil Moisture Prediction Model, Based on Depth and Water Balance Equation: A Case Study of the Xilingol League Grassland.

Soil moisture plays an important role in ecology, hydrology, agriculture and climate change. This study proposes a soil moisture prediction model, based on the depth and water balance equation, which integrates the water balance equation with the seasonal ARIMA model, and introduces the depth parameter to consider the soil moisture at different depths. The experimental results showed that the model proposed in this study was able to provide a higher prediction accuracy for the soil moisture at 40 cm, 100 cm and 200 cm depths, compared to the seasonal ARIMA model. Different models were used for different depths. In this study, the seasonal ARIMA model was used at 10 cm, and the proposed model was used at 40 cm, 100 cm and 200 cm, from which more accurate prediction values could be obtained. The fluctuation of the predicted data has a certain seasonal trend, but the regularity decreases with the increasing depth until the soil moisture is almost independent of the external influence at a 200 cm depth. The accurate prediction of the soil moisture can contribute to the scientific management of the grasslands, thus promoting ecological stability and the sustainable development of the grasslands while rationalizing land use.

Имитационная модель для анализа и оценки многолетнего и сезонного колебания элементов водного баланса бассейна реки Волги

The purpose of the study is to improve the method of water balance of the river basin in terms of difficult-to-measure elements of water balance, such as total evaporation from the land surface and change in basin moisture reserves. For these purposes, the water balance equation of the river basin and the correlation equation connecting the patterns of formation of the river flow of the current period with the flow of previous years have been modified. A simulation model is presented, the structure of which includes systems of water balance equations and a correlation equation of a river basin. As a result of the joint use of these reference hydrological and meteorological stations, the results of simulation modeling were obtained and, on this basis, fairly long time series of water balance elements (EVB) of the Volga River basin in the formation zone to Volgograd were organized. Based on the obtained long series of EVB of the Volga River basin, a conjugate retrospective analysis of the interannual and seasonal variability of the EVB of the Volga River basin in the formation zone up to Volgograd was carried out.

ВОЗМОЖНЫЕ СЦЕНАРИИ ФОРМИРОВАНИЯ МАТЕРИКОВОГО СТОКА И СОЛЕНОСТИ ВОД АЗОВСКОГО МОРЯ С УЧЕТОМ СОВРЕМЕННЫХ И ПЕРСПЕКТИВНЫХ ТЕНДЕНЦИЙ ИЗМЕНЕНИЯ КЛИМАТА

Introduction. The ongoing climate changes have a significant impact on the formation of the habitat conditions for the aquatic biological resources of the Azov Sea. Salinity of the Azov Sea waters and continental runoff, which role in maintaining the ecological well-being of the habitat of aquatic biological resources is paramount, has underwent particularly noticeable transformations. Relevance. Assessment of the degree of influence of ongoing and expected climate changes on the formation of abiotic parameters of the marine ecosystem is a prerequisite for planning the successful development of the fisheries industry of the Azov Sea Basin. The aim of this work is to assess the current and expected changes in the hydrometeorological parameters of the Azov Sea ecosystem, as well as to identify the most probable scenarios of changes in the Azov Sea salinity depending on the annual volume of continental runoff. Methods. The study is based on the data from AzNIIRKH database for the time range 1960–2020 collected over the course of the expedition surveys examining the Azov Sea hydrological regime and the data of the reference observation network of the Russian Federal Service for Hydrometeorology and Environmental Monitoring (Roshydromet). Methods of mathematical statistics, graphoanalytical construction, mapping and analogy have been used for the data analysis. Results. This paper assesses the changes in the hydrological regime of the Azov Sea based on the annual monitoring of the habitat of aquatic biological resources. Preliminary calculations have been performed, and new data on the changes in the parameters of the sea water balance equation not covered by monitoring over the past forty-five years have been presented. The most probable formation scenarios for the continental runoff and the Azov Sea water salinity for the future up to 2030 are considered, with the observed trend of climate warming taken into account. Conclusions. Both the climatic and anthropogenic factors have contributed to considerable changes in the current hydrometeorological regime of the Azov Sea. These changes have mainly been manifested in an increase in air and water temperatures, a decrease in wind activity, and in a reduced continental runoff, in the formation of which, since 2006, a prolonged low water content cycle has been observed. The shortage of river runoff and increased water evaporation rate, along with other factors, have induced an unprecedented increase in the Azov Sea salinity, the average annual value of which in 2021 reached a record high (14.97 %). In the most probable scenario (60 %) with the continuation of the low water content period and the continental runoff into the Azov Sea of about 22 km3 in volume, the average annual salinity of the Azov Sea, including Taganrog Bay, can reach 15±0.40 ‰ with a variation range from 14.5 to 16.5 ‰ in the sea itself (excluding Taganrog Bay). 2021 can serve as an analogous year in terms of salinity formation and its spatial distribution.

INFLUENCE OF IRRIGATION SYSTEMS AND COVER CROP ON WATER PRODUCTIVITY, AND MAIZE GROWTH

A field experiment was carried out to assess the effect of different irrigation systems, which included surface drip irrigation, sub-surface drip irrigation, surface irrigation in basins and cover crop on water productivity, growth and yield of maize in a silty clay loam soil in the Nile sub-district of Babil Governorate, in the fall season 2020. The experiment was designed using the split plot arrangement according to a complete randomized block design (RCBD) with three replications. The experiment treatments included two factors: cover crop (C) includes cover crop (C1) and without the cover crop (C0), and irrigation systems (I): includes surface drip irrigation (I1) subsurface drip irrigation (I2) and surface irrigation in basins (I3). Scheduling Irrigation was applied after 50% depletion of the plant available water. The water balance equation was used to determine the water consumption of maize. The results showed that C1I3 treatment was highest mean of plant height 235 cm, grain yield 11236 kg ha-1, leaf area 6076 cm2 plant-1, and leaf area index 4.05. Whereas, C0I1 was the lowest values for the previous traits, 183 cm, 5200 kg ha-1, 3997 cm2 plants-1, and 2.67 respectively. Treatment C1I2 was superior in the value of field water use efficiency and crop water use efficiency, which reached 3.49 kg m-3 and 3.05 kg m-3, respectively. Whereas, treatment C0I1 gave the lowest value for field and crop water use efficiency, which was 1.11 kg m-3 and 1.05 kg m-3, respectively. The highest water consumption of maize was 709 mm season-1 was for treatment C0I3, and the lowest water consumption was 362 mm season-1 for the treatment C1I2. It is clear that surface drip irrigation in the presence of cover crop contributed to saving irrigation water by reducing water consumption of maize.

Identifying driving factors of the runoff coefficient based on the geographic detector model in the upper reaches of Huaihe River Basin

Abstract Various climate and watershed characteristics determine the runoff coefficient (RC), and their interactions are complicated. Understanding the driving factors of the RC is important for understanding the long-term water balance and how it might change. Using the upper reaches of the Huaihe River Basin as the study area, remote sensing data were used to produce a RC map. The geographical detector was selected to quantify the individual and interactive influences of 13 driving factors on the RC. The results revealed that moderate resolution imaging spectroradiometer evapotranspiration (ET) data can be used to produce a mean average RC map based on the water balance equation. The dominant factors influencing the RC were found to vary at different scales. Precipitation had the largest correlation coefficient with the RC at the watershed scale. For the pixel scale, results from the geographical detector indicated that actual evapotranspiration (AET) and precipitation had the highest explanatory rate for the RC in the small watershed region and the whole study area (0.785 and 0.248, respectively). Climate factors, elevation, and normalized difference vegetation index had a substantial influence on the RC. Any two factors exhibited bilinear or nonlinear enhanced relationships in their interactions. The largest interactions between the factors were AET and precipitation, which exceeded 0.900. This study serves to better understand and explain runoff’s complex interrelationships.

Study on the effect of different grazing strategies on soil moisture and vegetation biomass

A reasonable grazing policy of "returning grazing to grass" is the key to boosting the regional economy, preventing desertification of grasslands and safeguarding people's livelihoods. In this paper, the Woodward model is used to establish the quantitative relationship between grazing and plant growth from the perspective of mechanistic analysis. To analyse the effects of different grazing strategies on the physical properties of Xilinguole grassland, this paper establishes a water balance equation for the soil-vegetation-atmosphere system and obtains a mathematical model for the effects of the physical properties of soil and vegetation biomass in Xilinguole grassland. Finally, on the basis of keeping the current grazing strategy unchanged, a model is developed to predict the future soil moisture.

Linking evapotranspiration seasonal cycles to the water balance of headwater catchments with contrasting land uses

AbstractLand use affects evapotranspiration rates and is a primary driver of the catchment water balance. The water balance of two catchments in southeastern Australia dominated by either grazed pasture or blue gum (Eucalyptus globulus) plantation was studied, focusing on the patterns of evapotranspiration (ET) throughout the year. Rainfall, streamflow, and groundwater levels measured between 2015 and 2019 were combined to estimate annual ET using a water balance equation. In the pasture, eddy covariance was used to measure ET from the catchment. Sap flow measurements were used to estimate tree transpiration in May 2017–May 2018 and Feb 2019–Feb 2021 in two different plots within the plantation. The tree transpiration rates were added to interception, estimated as a percentage of annual rainfall, to calculate ET from the plantation catchment. ET in the pasture showed strong seasonal cycles with very low ET rates in summer and ET rates in spring that were larger than the transpiration rates in the plantation, where trees transpired consistently throughout the year. The estimated annual ET from the water balance equation was comparable to ET estimated from other measurements. In the pasture, ET on average accounted for 88% of annual rainfall, while ET in the plantation was on average 93% of rainfall, exceeding it in the years with annual rainfall lower than about 500 mm. The difference between the ET rates in the plantation and the pasture was approximately 30–50 mm y−1. The larger ET rates in the plantation were reflected in a gradual decrease in the groundwater storage. The larger ET rates were enough to cause a decrease in groundwater storage in the plantation but not in the pasture, where groundwater levels remained stable.

Unsustainable use of surface water due to water balance miscalculation: the Culiacán River basin, Mexico

ABSTRACT The development of instruments for the administration of water use is a pending issue in both developing and developed countries. UNESCO has published guidance on determining water availability in Latin American and Caribbean countries. We applied this method to the Culiacán River basin, the most significant basin in Mexico for agricultural productivity. We find that surface water availability has been overestimated due to the inclusion of non-physical terms in the water balance equation, miscalculation of natural runoff and the omission of ecological water flow. Thus, unsustainable surface water use is allowed based on a miscalculation of physical water availability.

Application of a multiple model integration framework for mapping evapotranspiration with high spatial–temporal resolution in the Haihe River Basin, China

Evapotranspiration (ET) is a key component of the water and carbon cycles. Because it cannot be observed directly on large regional scales at present, many satellite-based ET datasets have been widely used for different purposes. However, their use has been limited at regional and field scales because of their coarse spatial and temporal resolution. In this study, the Bayesian model averaging (BMA) method was used to simulate daily ET values with 500 m spatial resolution in the Haihe River Basin (HRB) from 2000 to 2019. Validation performed with the in-situ observations showed that the BMA ET values had higher accuracy (R2 = 0.69, RMSE = 1.15 mm/day) than those found with individual models. The BMA ET values also had higher accuracy and more credibility based on a water balance equation validation in the HRB. We used interpolated meteorological datasets, reanalysis net radiation products, and remote-sensing datasets to drive the BMA ET model. The mean annual BMA ET in the HRB from 2000 to 2019 was about 601.8 mm/year. The monthly change characteristics of this BMA ET product reflected water consumption characteristics and irrigation regularity of the winter wheat and summer maize rotation system. The BMA ET in the HRB showed a significant increasing trend from 2000 to 2019 of 3.39 mm/y2. The BMA ET values showed a strong positive trend at 80 % of HRB areas. The increasing trend of the BMA ET values was mainly attributed to an increase in the leaf area index. The high spatiotemporal resolution product showed variations in ET trends more accurately than the coarse resolution products. This high spatiotemporal product has great potential for applications in studies of regional microclimate change, interactions between human activities and climate change, drought disaster monitoring, agricultural policy making, and water security.

Irrigation water use driving desiccation of Earth’s endorheic lakes and seas

ABSTRACT Through 2019, the Caspian Sea excluded, the majority (54–60%) of Earth’s irrigation-impacted endorheic lake and sea (ELS) areal extent has been lost in basins that contain as much as 20% of global irrigated agricultural land. Estimates of irrigated agriculture contribution to ELS desiccation based on a steady-state water balance equation for endorheic basins generally agree that this contribution is on the order of 70–90% at the global scale. However, large uncertainties or errors in attribution – as large as 100% – are observed with respect to particular ELS, suggesting that attributions based on a single irrigated agriculture dataset, should be treated cautiously. The observed areal contraction in ELS attributed to irrigated agriculture corresponds to an estimated one-third decrease in ELS volume, excluding the Caspian Sea. Such volumetric decrease is expected to at least double solute concentration in 40–47% of Earth’s ELS.

Assessment of crop evapotranspiration and deep percolation in a commercial irrigated citrus orchard under semi-arid climate: Combined Eddy-Covariance measurement and soil water balance-based approach

An accurate estimate of crop coefficient (Kc) values at different development stages (Kcini, Kcmid, and Kcend) is crucial for assessing crop water requirements in semi-arid regions. The objectives of this study were first to quantify the reference evapotranspiration (ETo) and to calculate the actual evapotranspiration (ETa) over citrus in a semi-arid climate under drip irrigation. For this purpose, a site of a citrus orchard in Souss-Massa, planted with the Esbal variety of clementine, was equipped with an Eddy-Covariance (EC) system, and sensors to measure radiation, soil heat flux, and micrometeorological forcing data, during 2020 and 2021 seasons. Also, the soil moisture content at various soil depths in the root zone near the EC tower was monitored. The energy balance closure (EBC) approach was adopted for flux assessment to ensure a quality check for the EC measurements. The obtained EBCs were about 82% and 79% for the daily measurements in 2020 and 2021, respectively, which can be considered acceptable considering the nature of the citrus orchard (relatively tall and sparse). Second, the study aimed to estimate actual Kc act values for citrus under the same irrigation strategy. The derived values were compared to different recommended Kc values in the literature. In the third stage, this work aimed to offer an alternative plan to sustainable irrigation management by elaborating an irrigation schedule for citrus crops in the region using the FAO-56 simple approach to avoid water stress and deep percolation (i.e., Ks = 1 and DP = 0). Eventually, an irrigation schedule was drawn following the crop’s phenological stages. The seasonal mean citrus evapotranspiration (ETa) values are 1.68, 3.02, and 1.86 mm/day for the initial, mid, and end-season. The seasonal actual Kc act values were 0.64, 0.58, and 0.64 for Kcini, Kcmid, and Kcend, respectively. Additionally, the application of the water balance equation revealed that a large quantity of water is lost through deep percolation (52% of total water supplied). The study focuses on Citrus trees being a strategic crop with important socio-economic values in the Souss-Massa region. Thus, the results should support both scientists and farmers in planning and strategy development.

Integration of Satellite-Derived and Ground-Based Soil Moisture Observations for a Precipitation Product over the Upper Heihe River Basin, China

Precipitation monitoring is important for earth system modeling and environmental management. Low spatial representativeness limits gauge measurements of rainfall and low spatial resolution limits satellite-derived rainfall. SM2RAIN-based products, which exploit the inversion of the water balance equation to derive rainfall from soil moisture (SM) observations, can be an alternative. However, the quality of SM data limits the accuracy of rainfall. The goal of this work was to improve the accuracy of rainfall estimation through merging multiple soil moisture (SM) datasets. This study proposed an integration framework, which consists of multiple machine learning methods, to use satellite and ground-based soil moisture observations to derive a precipitation product. First, three machine learning (ML) methods (random forest (RF), long short-term memory (LSTM), and convolutional neural network (CNN)) were used, respectively to generate three SM datasets (RF-SM, LSTM-SM, and CNN-SM) by merging satellite (SMOS, SMAP, and ASCAT) and ground-based SM observations. Then, these SM datasets were merged using the Bayesian model averaging method and validated by wireless sensor network (WSN) observations. Finally, the merged SM data were used to produce a rainfall dataset (SM2R) using SM2RAIN. The SM2R dataset was validated using automatic meteorological station (AMS) rainfall observations recorded throughout the Upper Heihe River Basin (China) during 2014–2015 and compared with other rainfall datasets. Our results revealed that the quality of the SM2R data outperforms that of GPM-SM2RAIN, Climate Hazards Group InfraRed Precipitation with Station data (CHIRPS), ERA5-Land (ERA5) and multi-source weighted-ensemble Precipitation (MSWEP). Triple-collocation analysis revealed that SM2R outperformed China Meteorological Data and the China Meteorological Forcing Dataset. Ultimately, the SM2R rainfall product was considered successful with acceptably low spatiotemporal errors (RMSE = 3.5 mm, R = 0.59, and bias = −1.6 mm).

A storm-centered multivariate modeling of extreme precipitation frequency based on atmospheric water balance

Abstract. Conventional rainfall frequency analysis faces several limitations. These include difficulty incorporating relevant atmospheric variables beyond precipitation and limited ability to depict the frequency of rainfall over large areas that is relevant for flooding. This study proposes a storm-based model of extreme precipitation frequency based on the atmospheric water balance equation. We developed a storm tracking and regional characterization (STARCH) method to identify precipitation systems in space and time from hourly ERA5 precipitation fields over the contiguous United States from 1951 to 2020. Extreme “storm catalogs” were created by selecting annual maximum storms with specific areas and durations over a chosen region. The annual maximum storm precipitation was then modeled via multivariate distributions of atmospheric water balance components using vine copula models. We applied this approach to estimate precipitation average recurrence intervals for storm areas from 5000 to 100 000 km2 and durations from 2 to 72 h in the Mississippi Basin and its five major subbasins. The estimated precipitation distributions show a good fit to the reference data from the original storm catalogs and are close to the estimates from conventional univariate GEV distributions. Our approach explicitly represents the contributions of water balance components in extreme precipitation. Of these, water vapor flux convergence is the main contributor, while precipitable water and a mass residual term can also be important, particularly for short durations and small storm footprints. We also found that ERA5 shows relatively good water balance closure for extreme storms, with a mass residual on average 10 % of precipitation. The approach can incorporate nonstationarities in water balance components and their dependence structures and can benefit from further advancements in reanalysis products and storm tracking techniques.