Probabilistic Properties of a Curve Number:A Case Study for Small Polish and Slovak Carpathian Basins

The proper determination of the curve number （CN） in the SCS-CN method reduces errors in predicting runoff volume. In this paper the variability of CN was studied for 5 Slovak and S Polish Carpathian catchments. Empirical curve numbers were applied to the distribution fitting. Next, theoretical characteristics of CN were estimated. For loo-CN the Generalized Extreme Value （GEV） distribution was identified as the best fit in most of the catchments. An assessment of the differences between the characteristics estimated from theoretical distributions and the tabulated values of CN was performed. The comparison between the antecedent runoff conditions （ARC） of Hawkins and Hjelmfelt was also completed. The analysis was done for various magnitudes of rainfall. Confidence intervals （CI） were helpful in this evaluation. The studies revealed discordances between the tabulated and estimated CNs. The tabulated CNs were usually lower than estimated values; therefore, an application of the median value and the probabilistic ARC of Hjelmfelt for wet runoff conditions is advisable. For dry conditions the ARC of Hjelmfelt usually better estimated CN than ARC of Hawkins did, but in several catchments neither the ARC of Hawkins nor Hjelmfelt sufficiently depicted the variability in CN.

Comparison of Three Delineation Methods Using the Curve Number Method to Model Runoff

Digital Elevation Models (DEMs) are spatial grids which are used to automate watershed boundary determination. Sinks are present within most DEMs. In order to easily process the watershed boundary, the sinks are reassigned to elevation equivalent to an adjacent cell. The derived DEM is called a “filled” DEM. Due to its relative simplicity, the use of the “filled” DEM is one of the most widely used methods to delineate watershed boundaries and works well in about 70 percent of the watersheds in the US. In landscapes with internal drainage, sinks may accurately represent these depressions. In this study, we compare two delineation methods that do not fill in sinks to another method that does fill in sinks. We examined ten gaged watersheds in Wisconsin and Minnesota. We found the spatial extent of the watersheds from the three methods were significantly different. To evaluate the delineation methods, we modeled ten runoff events using the Curve Number (CN) method and compared them to USGS gage discharge for each watershed. For small storms we found that there were no significant differences in the modeled runoff for three delineation methods. For large storms, we found the no-fill methods had a smaller error, but overall the difference was insignificant. This research suggests that capturing internal drainage by the delineation does not have much of an impact on the widely used CN model.

Using modified Soil Conservation Service curve number method to simulate the role of forest in flood control in the upper reach of the Tingjiang River in China

To improve flood control efficiency and increase urban resilience to flooding,the impacts of forest type change on flood control in the upper reach of the Tingjiang River(URTR) were evaluated by a modified model based on the Soil Conservation Service curve number(SCS-CN) method. Parameters of the model were selected and determined according to the comprehensive analysis of model evaluation indexes. The first simulation of forest reconstruction scenario,namely a coniferous forest covering 59.35km^2 is replaced by a broad-leaved forest showed no significant impact on the flood reduction in the URTR. The second simulation was added with 61.75km^2 bamboo forest replaced by broad-leaved forest,the reduction of flood peak discharge and flood volume could be improved significantly. Specifically,flood peak discharge of 10-year return period event was reduced to 7-year event,and the reduction rate of small flood was 21%-28%. Moreover,the flood volume was reduced by 9%-14% and 18%-35% for moderate floods and small floods,respectively. The resultssuggest that the bamboo forest reconstruction is an effective control solution for small to moderate flood in the URTR,the effect of forest conversion on flood volume is increasingly reduced as the rainfall amount increases to more extreme magnitude. Using a hydrological model with scenarios analysis is an effective simulation approach in investigating the relationship between forest type change and flood control. This method would provide reliable support for flood control and disaster mitigation in mountainous cities.

Spatial mapping and testing the applicability of the curve number method for ungauged catchments in Northern Ethiopia

Understanding the spatial variability of land and water resources has significant importance for its planning,management,and utilization.It is also significant in understanding the response behavior of a catchment in order to model the basic physical processes.In this study,a weighted overlay analysis technique using ArcGIS was implemented for developing a geo-database of the standard curve number(SCN)in a catchment around Northern Ethiopia.The spatial data were used to investigate a'standard curve number method'for the simulation of the direct runoff at the outlet of the catchment.Both spot based rainfall and runoff measuring techniques were adopted for deriving an instant observed flow measurement,and to make a comparison with the simulated flow values.The results showed that the model underestimated most of the simulated values with a coefficient of regression of R^(2)=0.52,with a proportion of higher variances between the simulated and observed runoff events.The result suggests that the accuracy of the model leaves room for significant improvement and the method could not be easily adopted in the catchment and other similar catchments in the semi arid regions of Ethiopia.For improving the prediction capacity of the model,further research in adjusting loss factors in the method is recommended.It is also suggested for developing a localized and modified SCN values by considering geologic,climatic and seasonal variation.The results of this study and the maps generated can be used for improving the hydrological understanding of the catchment.The study is useful for further investigation of the SCN methodology in other un-gauged catchments around the world.

Elliptic Curve Point Multiplication by Generalized Mersenne Numbers

Montgomery modular multiplication in the residue number system （RNS） can be applied for elliptic curve cryptography. In this work, unified modular multipliers over generalized Mersenne numbers are proposed for RNS Montgomery modular multiplication, which enables efficient elliptic curve point multiplication （ECPM）. Meanwhile, the elliptic curve arithmetic with ECPM is performed by mixed coordinates and adjusted for hardware implementation. In addition, the conversion between RNS and the binary number system is also discussed. Compared with the results in the literature, our hardware architecture for ECPM demonstrates high performance. A 256-bit ECPM in Xilinx XC2VP100 field programmable gate array device （FPGA） can be performed in 1.44 ms, costing 22147 slices, 45 dedicated multipliers, and 8.25K bits of random access memories （RAMs）.

Recurrent formula of Bernoulli numbers and the relationships among the coefficients of beam,Bernoulli numbers and Euler numbers

Based on the differential equation of the deflection curve for the beam,the equation of the deflection curve for the simple beamis obtained by integral. The equation of the deflection curve for the simple beamcarrying the linear load is generalized,and then it is expanded into the corresponding Fourier series.With the obtained summation results of the infinite series,it is found that they are related to Bernoulli num-bers and π. The recurrent formula of Bernoulli numbers is presented. The relationships among the coefficients of the beam,Bernoulli numbers and Euler numbers are found,and the relative mathematical formulas are presented.

Effects of urbanization on groundwater level in aquifers of Binh Duong Province,Vietnam

The purpose of this paper was to assess the impact of urbanization on the groundwater level(GWL)in aquifers of Binh Duong(BD)Province.The research method is to analyze the trend of GWL,the recharge capacity of surface over time and the relationship between them.The data of the GWL used in the study are the average values in the dry and rainy seasons of 35 observation wells from 2011 to 2018,which are in Pleistocene and Pliocene aquifers.The ability to recharge groundwater from the surface in this study was represented by the curve number(CN),a parameter used in hydrology for calculating direct runoff or infiltration from rainfall.The land use data to identify the CN was analyzed from the Landsat images.The results show that besides over-exploitation,the change of surface characteristic due to the urbanization development process is also the cause of the GWL decline.The analysis of seasonal GWL data shows that the increase in impervious surface area is the cause of GWL decline in the Pleistocene aquifer,which is more evident in the rainy season than in the dry season.The statistical results also show that in the rainy season and in shallow aquifers,a higher CN change can be found with the wells that had a remarkable GWL decline compared to the remaining wells.

Coupling analysis of short-term weather and runoff in an arid lake basin of China

Changes in the weather will cause variations in the hydrological system.Arid areas,with fragile hydrological systems,are very sensitive to changes in the weather,so the coupling analysis of short-term weather and runoff in arid areas is of great significance.The Daihai Lake is a closed inland lake in an arid area of China.In this paper,Weather Research and Forecasting model mode-Hydrological module(WRF-HYDRO)is used to simulate the coupling of weather and hydrology in the Daihai Lake Basin.Regional optimization of WRF-HYDRO is carried out to determine the optimal parameters.The optimal WRF-HYDRO model is applied to couple the short-term weather and runoff in the Daihai Lake Basin to reproduce several rainstorm and flood events.It is found that runoff infiltration parameter(REFKDT)in WRF-HYDRO is the parameter that has the most severe effect on runoff in the Daihai Lake Basin.WRF-HYDRO can capture the rainstorm moment of the rainstorm events in the Daihai Lake Basin,especially the first rainstorm moment,and its simulation accuracy is good.WRF-HYDRO has a strong ability to capture flood peak,but there is a discrepancy between WRF-HYDRO flood peak and Soil Conservation Service Curve Number(SCS-CN)calculation result at the flood peak moment.The northern part of Zuoyun County should guard against the occurrence of flood disaster in wet season.The coupling of weatherand hydrology can not only make up for the lack of runoff data in arid basins,but also provide a basis for water resources management and disaster prevention and mitigation in the basins.

Economic valuation of water storage function of forest ecosystems (case study: Zagros Forests, Iran)

Forest ecosystem services contribute to human welfare, both directly and indirectly. Here the economic value of water conservation by Bazoft basin located in Zagros forests in western Iran was estimated, using simulation models and Geographic Information System （GIS） as a tool for analyzing the effects of ecological factors on ecosystem services. Rainfall-runoff simulation was carried out by using Curve Number （CN） method in HEC-HMS model. The model requires the inputs of land cover, soil and short term rainfall and discharge data. The efficiency of simu-lated model was revised using observed data and doing calibration stages. The role of forest on water retention and surface runoff reduction by devising four hypothetical scenarios and then the effects of land use changes associated with these scenarios on rainfall-runoff behavior of the region were determined. The results show that under the case of scenario one which assumes that the entire of basin area is covered by forests, total outflow would be in the minimum amount and rainfall initial loss will increase. Forest hydrological services related to water retention was economically assessed using Replacement Cost Method. Valuation results show that each hectare of Bazoft forests can store 84.8 m3 water with 0.5 US$/m3 annual value. So the water retention value of each hectare of these forests will be 43US$. This could have positive economic consequences for the region and would help decision-makers in selecting appropriate and economically feasible development strategies.

Sensitivity Analysis of the ALMANAC Model's Input Variables

Crop models often require extensive input data sets to realistically simulate crop growth. Development of such input data sets can be difficult for some model users. The objective of this study was to evaluate the importance of variables in input data sets for crop modeling. Based on published hybrid performance trials in eight Texas counties, we developed standard data sets of 10-year simulations of maize and sorghum for these eight counties with the ALMANAC (Agricultural Land Management Alternatives with Numerical Assessment Criteria) model. The simulation results were close to the measured county yields with relative error only 2.6% for maize, and - 0.6% for sorghum. We then analyzed the sensitivity of grain yield to solar radiation, rainfall, soil depth, soil plant available water, and runoff curve number, comparing simulated yields to those with the original, standard data sets. Runoff curve number changes had the greatest impact on simulated maize and sorghum yields for all the counties. The next most critical input was rainfall, and then solar radiation for both maize and sorghum, especially for the dryland condition. For irrigated sorghum, solar radiation was the second most critical input instead of rainfall. The degree of sensitivity of yield to all variables for maize was larger than for sorghum except for solar radiation. Many models use a USDA curve number approach to represent soil water redistribution, so it will be important to have accurate curve numbers, rainfall, and soil depth to realistically simulate yields.

Evaluating the Effect of Land Cover, Seasonality and Delineation Method on Runoff at the Watershed Scale

The aim of this study was to determine if runoff estimates from the curve number model were affected by seasons for different land covers. Eighteen watersheds with varying land covers were delineated using three methods. The delineation methods differ in how internal drainage is evaluated. Runoff estimates from storms for spring, summer, and fall were compared to observed runoff from USGS gaging station data. Errors (difference between estimate runoff and observed runoff) were found to be highest for fall by 3% for all the two delineation methods which do not consider internal drainage. Watersheds were categorized by their dominant land cover (agriculture, forest, or urban). Seasonal differences were found to be significant for certain land covers. The greatest differences between observed and estimated data were found in agriculture and urban especially spring versus fall for all delineations. Forest land cover was found to have no seasonal difference for all three delineation methods. The research suggests that this work contributes to the growing body of research suggesting that vegetative seasonal differences have a greater impact on runoff than is accounted for in the runoff model.

Influence of Land Use Land Cover Change on Groundwater Recharge in the Continental Terminal Area of Abidjan,Ivory Coast

The process by which rainfall reaches the aquifer in a sedimentary area is infiltration. This process could be affected quantitatively or qualitatively by the changes in the land use land cover (LULC) as a result of anthropogenic activities which could affect groundwater reserves. This study focuses on the influence of LULC change on groundwater recharge in the context of urbanization and population growth. Four weather stations data and satellite image data were used in order to evaluate water infiltration which is the amount of water that reaches the piezometric surface from 1990 to 2016. The spatial-temporal LULC change in relation to urbanization sprawl was assessed based on a series of Landsat images for 1990, 2000 and 2016. The maximum likelihood pixel-based on classification method was used to analyze the spatial-temporal LULC dynamics. The Thiessen polygon method was used for the mean area precipitation computation. The recharge was determined using water balance method after determining the runoff based on the Soil Conservation Service curve number method. The results show an increase in built-up and agricultural land, while the forest and shrub areas declined with water body remaining unchanged over the period 1990-2016. The decline in forest could be imputed to the demographic and socio-economic growth as expressed by the expansion of agriculture and urbanization. Groundwater recharge and runoff results are respectively 34%, 20% in 1999;21%, 46% in 2000 and 26%, 14% in 2016 of rainfall and show their strong dependence on precipitation and LULC change.

Energy potential assessment and techno-economic analysis of micro hydro-photovoltaic hybrid system in Goda Warke village,Ethiopia

Rural Ethiopia has significant untapped potential for hydro and solar energy generation systems.However,challenges arise from seasonal variations and unfavourable topographic positions of flowing rivers,hindering the efficient exploitation of these resources.Despite the country’s abundance in hydro and solar energy resources,>75%of the population still lack access to electricity from the national grid.This work deals with energy resource potential assessment and techno-economic analysis of micro hydro-photovol-taic(PV)hybrid systems,considered in the case study of Goda Warke village,located in the Yaya Gulele district.A novel framework is proposed that utilizes the Natural Resource Soil Conservation Service curve number method to assess the energy potential of micro-hydro energy in ungauged basins,specifically at the exit point of the Girar River basin catchment.The average monthly flow rate in the basin is 0.975 m3/s,while the area exhibits a solar radiation potential of 5.39 kWh/m^(2)/day.Energy policy promotes expanding ac-cess to modern energy sources and utilization of indigenous energy resources.Simulation results indicate that the hydro/PV/diesel generator(DG)/battery and hydro/PV/battery systems are the most optimal choices based on net present cost,with the inclusion of a DG for economic comparison.Micro-hydro energy covers most of the electric load in the area,achieving a capacity factor of 47.5%.The cost of energy and net present cost were found to be sensitive to variables such as the price of diesel fuel,pipe head loss,and the growth of the village load.The optimized system demonstrated a hydro energy potential of 1405.37 MWh/year and a PV energy output of 274.04 MWh/year,resulting in a levelized cost of energy of 0.0057 and 0.049$/kWh for the hydro and PV components,respectively.

Application of the SCS-CN Model to Runoff Estimation in a Small Watershed with High Spatial Heterogeneity

For reasons of simplicity, the most commonly used hydrological models are based on the Soil Conservation Service Curve Number （SCS-CN） model, which is probably a good choice for the estimation of runoff on the Loess Plateau of China; however, the high spatial heterogeneity, mainly caused by a fragmented landform and variations in soil type, may limit its applicability to this region. Therefore, applicability of the SCS-CN model to a small watershed, Liudaogou on the plateau, was evaluated and the most appropriate initial abstraction ratio （I~/S） value in the model was quantified by the inverse method. The results showed that the standard SCS-CN model was applicable to the estimation of runoff in the Liudaogou watershed and the model performance was acceptable according to the values of relative error and Nash-Sutcliffe efficiency. The most appropriate Ia/S value for the watershed was 0.22 because with this modified Ia/S value, the model performance was slightly improved. The model performance was not sensitive to the modification of the Ia/S value when one heavy rainfall event （50.1 mm） was not considered, which implied that the model, using a standard Ia/S value, can be recommended for the Liudaogou watershed because single rainfall events exceeding 50 mm seldom occurred in that region. The runoff amount predicted for the Liudaogou watershed by the SCS-CN model, using the modified Ia/S value, increased gradually with increasing rainfall when rainfall values were lower than 50 mm, whereas the predicted amount increased rapidly when the rainfall exceeded 50 mm. These findings may be helpful in solving the problem of serious soil and water loss on the Loess Plateau of China.

Identification of potential soil water retention using hydric numerical model at arid regions by land-use changes

Assessment of soil water retention in arid region is an input required parameter in precision water management at large scale.Investigations were carried out in Tanta catchment in the middle Nile Delta,Egypt(30145 N,30155 E),where collecting soil samples covered different hydrological soil groups and land-uses.Based on the natural resource conservation service curve number model(NRCS-CN),CN approach was used to investigate the effect of spatio-temporal variations of different land-uses on soil water retention.Potential soil water retention from 1990 to 2015 was reduced by 118.1 m^(3) per hectare with decreasing cropland area.Urbanization encroachment from 1990 to 2015 was increased by 2.13%by decreasing cropland with 15.3%(5300 ha in 2015).This resulted in losing the potential soil water retention by 625,968.42 m^(3) water for the whole catchment area.Impact of land degradation was pronounced,where 2.65%,29.35%,and 1.11%of the initial crop land-use in 1990 were converted to bare soil,fallow,and urban area,respectively in 2015.Implementation of(S)value of the NRCS-CN model with GIS technique provides useful measure to identify land-use changes of potential water storage capacity at catchment scale.

Evaluation of alternative surface runoff accounting procedures using SWAT model

For surface runoff estimation in the Soil and Water Assessment Tool(SWAT)model,the curve number(CN)procedure is commonly adopted to calculate surface runoff by dynamically updating CN values based on antecedent soil moisture condition(SCSI)in field.From SWAT2005 and onward,an alternative approach has become available to apply the CN method by relating the runoff potential to daily evapotranspiration(SCSII).While improved runoff prediction with SCSII has been reported in several case studies,few investigations have been made on its influence to water quality output or on the model uncertainty associated with the SCSII method.The objectives of the research were:(1)to quantify the improvements in hydrologic and water quality predictions obtained through different surface runoff estimation techniques;and(2)to examine how model uncertainty is affected by combining different surface runoff estimation techniques within SWAT using Bayesian model averaging(BMA).Applications of BMA provide an alternative approach to investigate the nature of structural uncertainty associated with both CN methods.Results showed that SCSII and BMA associated approaches exhibit improved performance in both discharge and total NO3 predictions compared to SCSI.In addition,the application of BMA has a positive effect on finding well performed solutions in the multi-dimensional parameter space,but the predictive uncertainty is not evidently reduced or enhanced.Therefore,we recommend additional future SWAT calibration/validation research with an emphasis on the impact of SCSII on the prediction of other pollutants.