Function Of Rainfall Research Articles

Impact of Infiltrability on Flooding in Thiaroye, Dakar, Senegal

For a long time, the drinking water supply to the Dakar region was provided by the Thiaroye boreholes. But the advance of the salt wedge has led the state authorities to order a halt to these drillings. This disconnection has not only led to a decrease in drinking water production in the area, but it has also encouraged the recurrence of flooding due to the rise of the water table. The objective of this work is to study the impact of infiltability on floods in Thiaroye. For the determination of infiltration capacity, the Horton model was used. The evolution of infiltration as a function of rainfall according to the wetness of sandy clay soils shows that the wetter the soil, the lower the infiltration, the greater the return time, the lower the infiltration for the same duration. The submersion time, which corresponds to the beginning of the runoff, arrives instantaneously after the onset of the downpour and after calculation, the value of the runoff is 14.16 mm on 30 mm rain; a runoff coefficient of 47.2%. The calculated runoff coefficients are around 0.50 and depend on the intensity and duration of the rainfall. Keywords: Infiltrability, Thiaroye, flow, humidity

The development of laterite weathering profiles as a function of rainfall and time: A geophysical approach

AbstractLaterite weathering profile (LWP) thicknesses are functions of precipitation rate and time, but their exact dependence on them is uncertain. We investigate LWP development on ground surfaces in Hawai'i that are neither aggrading nor eroding across substrates from 0.01 to 4 Ma and rainfall rates of <250 to >3000 mm/a. The Hawaiian Islands provide an excellent opportunity for LWP studies across climates and over millions of years on a single rock type, basalt. LWP weathering rates are usually determined by geochemical approaches. We present a geophysical method once bedrock ages and precipitation rates are known. We employed multichannel analysis of surface waves and horizontal‐to‐vertical spectral ratio methods. Results indicate that >70% of the variability in LWP thickness is due to precipitation and bedrock age. The remainder is attributed to measurement uncertainty and heterogeneity in the permeability of basalt. LWPs develop by two paths. Dry (<1000 mm/a) areas have a negative water balance with evapotranspiration exceeding rainfall. LWPs thicken until they reach a steady state where the storage capacity of the saprolite precludes the percolation of water into subjacent lava. In wetter areas, downslope interflow produces thick laterite wedges near coastlines that migrate upslope over ~1 Ma. Subsequently, they thicken and reach a steady state where precipitation cannot deliver water through the vadose zone. LWPs' thickness (T) increases as a function of time (t) and precipitation (P) according to the expression (95% confidence): . The first partial derivative, or weathering rate, is . Weathering rates decrease with time and are strong functions of t and P. These expressions add considerable insight into the rates and processes driving weathering at large scales and can also be solved for t, giving a rough estimate of the time of landscape formation of eroded surfaces.

Groundwater Level Trend Analysis and Prediction in the Upper Crocodile Sub-Basin, South Africa

Disasters related to climate change regarding water resources are on the rise in terms of scale and severity. Therefore, predicting groundwater levels (GWLs) is a crucial means to aid adaptive capacity towards disasters related to climate change in water resources. In this study, a Gradient Boosting (GB) regression modelling approach for GWL prediction as a function of rainfall and antecedent GWL is used. A correlation analysis carried out from 2011 to 2020 demonstrated that monthly GWLs can be predicted by antecedent GWLs and rainfall. The study also sought to understand the long-term effects of climate events on groundwater levels over the study area through a Mann–Kendall (MK) trend analysis. A total of 50% of the groundwater stations revealed declining trends, while 25% had no trends and the other 25% showed an increasing trend. Again, the correlation analysis results were used in justifying the trends. The GB predictive model performed satisfactorily for all groundwater stations, with the MSE values ranging from 0.03 to 0.304 and the MAE varying from 0.12 to 0.496 in the validation period. The R2 ranged from 0.795 to 0.902 for the overall period. Therefore, based on projected rainfall and antecedent groundwater levels, future GWLs can be predicted using the GB model derived in this study.

Time-resolved triggering and runout analysis of rainfall-induced shallow landslides

AbstractRainfall-induced shallow landslides often turn into flows. These phenomena occur worldwide and pose severe hazard to infrastructure and human lives on mountainous areas. Risk assessment, and the design of mitigation measures, can both be informed by back-analysis of previous events. However, shallow instabilities are frequently spread over a large area, with the generated flows occurring in sequences, or surges. Conventionally, back-analysis exercises tackle the problem by simulating runout as a single event, with all surges happening simultaneously. This simplification has repercussions that have not been explored in the literature so far, and whose impact in hazard assessment practice is unclear. Therefore, a novel time-resolving procedure is proposed in this paper, which can for the first time be applied to resolve instability sequences of arbitrary duration. The methodology discretizes the event, detecting instabilities at equally spaced time intervals as a function of rainfall. Thanks to this, the post-failure behaviour of each surge can be tracked by a runout model, with a separate simulation performed every time a new instability is detected. The methodology robustness is tested on two documented case studies. The results reveal that, under some conditions, the time-resolving procedure can lead to significantly different results in terms of runout path, flooded area, and flow heights. This leads to criticism on how back-analysis is conventionally applied, prompting for a review of historical cases.

Climate Change and Food Security in the Northern and Eastern African Regions: A Panel Data Analysis

The problem of food insecurity is growing across the world, in particular in developing countries. Due to their economic structure, climate change represents one of the major threats for food security levels in African countries. The object of this work was to assess the impact of climate change on the level of food security in the North and East African countries, using a panel data analysis for the period 2000–2012. Average protein supply and average dietary energy supply adequacy were the two different indicators of food security we identified as most appropriate. Indeed, both indicators can provide information concerning the amount and the nutritional value of food supply. The determinants of food security are expressed as a function of rainfall, temperature, land area under cereal production, size of population and GDP. Findings showed that food security in the Northern and Eastern African countries is adversely affected by climate change. Policy makers need to promote those actions capable of mitigating global warming and reducing its economic impact.

Climate change and local anthropogenic activities have altered river flow regimes across Canterbury, New Zealand

River flow regimes influence ecologic, cultural, social, aesthetic, and economic values. Detecting changes in river flows and attributing their causes is important but challenging due to the combined influence of climate and relevant local activities, and the lack of data on water abstraction, drainage modification or land use management. This study assessed the degree to which trends in river flows could be attributed to changes in climate versus local anthropogenic activities across Canterbury, Aotearoa New Zealand. Trends were assessed for a period that started immediately after a change in regulatory regime in 1991 and ended in 2020, that coincided with increases in water abstraction and changes in water management practices. Trends in observed summer conditions indicated that rainfall was stable, temperature increased, and flows decreased for many sites during the assessed period. Models representing flow as a function of rainfall and temperature were trained and tested using cross-validation for an earlier baseline period. Predictions for the 1991–2020 period made with the models were used to account for the effect of change in climate. The difference between predicted and observed flows were attributed to changes in local activities. Decreases in summer flows were partially associated with changes in climate, but changes in summer flows in several catchments were also associated with local activities. The findings indicate changes to both climate and local activities have combined to alter flow regimes, suggesting that hydrological impacts of local activities should be considered alongside climate change when making river flow management decisions.

Comparative Analysis of the Sensitivity of SAR Data in C and L Bands for the Detection of Irrigation Events

Comprehensive knowledge about irrigation timing is crucial for water resource management. This paper presents a comparative analysis between C- and L-band Synthetic Aperture Radar (SAR) data for the detection of irrigation events. The analysis was performed using C-band time series data derived from the Sentinel-1 (S1) satellite and two L-band images from the PALSAR-2 (ALOS-2) sensor acquired over irrigated grassland plots in the Crau plain of southeast France. The S1 C-band time series was first analyzed as a function of rainfall and irrigation events. The backscattering coefficients in both the L and C bands were then compared to the time difference between the date of the acquired SAR image and the date of the last irrigation event occurring before the SAR acquisition (Δt). Sensitivity analysis was performed for 2 classes of the Normalized Difference Vegetation Index (NDVI ≤0.7 and NDVI >0.7). The main results showed that when the vegetation is moderately developed (NDVI ≤0.7), the C-band temporal variation remains sensitive to the soil moisture dynamics and the irrigation events could be detected. The C-VV signal decreases due to the drying out of the soil when the time difference between the S1 image and irrigation event increases. For well-developed vegetation cover (NDVI >0.7), the C-band sensitivity to irrigation events becomes dependent on the crop type. For well-developed Gramineae grass with longs stalks and seedheads, the C band shows no correlation with Δt due to the absence of the soil contribution in the backscattered signal, contrary to the legume grass type, where the C band shows a good correspondence between C-VV and Δt for NDVI > 0.7. In contrast, analysis of the L-band backscattering coefficient shows that the L band remains sensitive to the soil moisture regardless of the vegetation cover development and the vegetation characteristics, thus being more suitable for irrigation detection than the C band. The L-HH signal over Gramineae grass or legume grass types shows the same decreasing pattern with the increase in Δt, regardless of the NDVI-values, presenting a decrease in soil moisture with time and thus high sensitivity of the radar signal to soil parameters. Finally, the co-polarizations for both the C and L bands (L-HH and C-VV) tend to be more adequate for irrigation detection than the HV cross-polarization, as they show higher sensitivity to soil moisture values.

Flow Rate Determination as a Function of Rainfall for the Ungauged Suhareka River

Flow Rate Determination as a Function of Rainfall for the Ungauged Suhareka River

A Hawaiian Tropical Dry Forest Regenerates: Natural Regeneration of Endangered Species under Biocultural Restoration

Tropical dry forests (TDFs) are among the most at-risk ecosystems globally. In Hawai‘i, more than 45% of TDF species are threatened or endangered. Despite decades of active TDF restoration, there remains limited information on the potential for long-term success, since there are few studies of natural regeneration. We assess natural regeneration of endangered plants at Ka‘ūpūlehu dryland forest, a Hawaiian biocultural restoration initiative. Drawing on 6 annual censuses we (1) assess rates and patterns of natural regeneration across species and as a function of rainfall and (2) identify bottlenecks. Our surveys document natural recruits of 11 of the 12 endangered species first outplanted 15–20 years ago. Higher annual rainfall increased the number of new recruits per year and growth, but decreased survival of larger recruits. The total number of natural recruits increased three-fold over the study period and varied across species. For nearly half of the species, we documented a second generation of recruits. Successes appear to be a function of time, including a changing microclimate and adaptive management practices. Remaining bottlenecks include lack of seed dispersal, and seed predation and herbivory by introduced species. The success at Ka‘ūpūlehu highlights the potential for TDF restoration and the value of a biocultural approach.

Water table response to rainfall and groundwater simulation using physics-based numerical model: WASH123D

Study regionFour districts (Meinong, Qishan, Dashu, and Daliao) of Kaohsiung city, Southern Taiwan Study focusThe understanding of aquifer recharge in terms of water table response to rainfall is of critical importance to groundwater systems management and various endeavors have been made to estimate the amount of recharge using rainfall data. The purpose of this study is to evaluate the groundwater level response to rainfall and determine the recharge potential for shallow aquifers. We showed a simple approach to estimate specific yield (Sy) and hydraulic conductivity (k) as functions of rainfall and water level data. New hydrological insights for the regionCorrelation method is applied to investigate groundwater level response to associated rainfall and it was found that the rise in water table linearly depends on the rainfall amount per event. Results show the annual recharge rates of 244–1472 mm year─1, which represent 12–43% of rainfall in the study area. The estimated k (order of 10─4 to 10─5 m s─1) and Sy (0.20–0.51) were used as prior values to setup groundwater numerical modeling using WASH123D. The real-time case scenario simulation using pumping and rainfall data indicated the reasonable hydrological response of groundwater levels to rainfall. The long-term simulations should be performed with WASH123D to deal with the subjectivity of sustained groundwater pumping and sustainability of aquifers for better groundwater resource planning and management.

Estimation of seasonal and annual river flow volume based on temperature and rainfall by multiple linear and Bayesian quantile regressions

Investigation of river flow volume in different conditions as a function of temperature and rainfall variables can be quite effective in understanding the hydrological and hydro-climatic conditions of the watershed. Multiple linear regression models were applied in estimating river flow in several studies due to their straightforwardness and appropriate interpretation of results. In this study, to overcome the limitations of the multiple linear regression model, the Bayesian quantile regression model was used to estimate the river flow volume as a function of rainfall and temperature, and the results were compared. The data and information used for the Qareh-Sou basin in northern Iran are of substantial environmental and socio-economic importance. Five data series, including spring, summer, autumn, winter, and annual series, were created and used for this study. It was found that the Bayesian quantile regression model has considerable flexibility to model the volume of flow for different quantiles, predominantly upper and lower quantiles, and can be used to model high and low flows. With increasing the values of quantiles, a limited decreasing pattern in the effect of rainfall on the volume of flow was identified, which can be due to increasing the effect of other factors in the formation of extreme flows of the river. For summer data in high quantiles, the effect of rainfall on river flow volume shows an increasing pattern. This pattern is different from the other studied series, which may be due to the low base flow in summer. The results confirm that the application of Bayesian quantile regression compared to multiple linear regression leads to much more valuable information on the impact of rainfall and temperature on river flow volume.

Electronic sensors to monitor functionality and usage trends of rural water infrastructure in Plateau State, Nigeria

Internet-connected sensor technologies have recently been used to monitor water service infrastructure in remote settings. In this study, 397 groundwater pumps were observed in Plateau State, Nigeria over 12 months in 2021. Two hundred of these sites were instrumented with remotely reporting electronic sensors, including 100 hand-pump sensors, 50 electrical pump sensors, and 50 cistern water-level sensors. Every two months, phone calls and site visits were used to collect a ground-truth of pump functionality: whether the pump was capable of delivering water, regardless of actual use. Our study examined: (1) What are the operating characteristics and trends of these different kinds of water pumps?; (2) Can water-point functionality be predicted with electronic sensors?; and (3) Does the instrumented water-point sample accurately represent average water-system functionality across the region? An automated classifier generated functional/non-functional diagnostics for instrumented pumps on a weekly basis. Classifier diagnostics were compared to ground-truth data, showing an overall accuracy of 91.7% (96.1% for hand-pumps, 63.9% for cisterns, and 93.2% for electrical boreholes), with high fleet-wide sensitivity in correctly identifying a functional pump (94.4%), but poor overall specificity in correctly identifying a non-functional, broken pump (25.0%). This discrepancy is attributable to the sensors’ difficulty in distinguishing between a broken pump and an unused pump. Varied patterns were seen in pump usage as a function of rainfall, with hand-pump use decreasing significantly, electrical pump usage decreasing to a lesser degree, and cistern use increasing in response to local rainfall. A comparison of the 200 instrumented to 197 non-instrumented sites showed statistically similar repair and failure rates. The high overall accuracy of the sensor–diagnostic system—and the demonstration that sensor-instrumented sample sites can represent population-level breakdown and repair frequencies—suggests this technology’s utility in supporting sample-based monitoring of overall water pump functionality and water volume delivery. However, the poor performance of the system in distinguishing between broken and unused pumps will limit its ability to trigger repair activities at individual pumps.

Potential impacts of stratospheric aerosol injection on drought risk managements over major river basins in Africa

Most socio-economic activities in Africa depend on the continent’s river basins, but effectively managing drought risks over the basins in response to climate change remains a big challenge. While studies have shown that the stratospheric aerosol injection (SAI) intervention could mitigate temperature-related climate change impacts over Africa, there is a dearth of information on how the SAI intervention could influence drought characteristics and drought risk managements over the river basins. The present study thus examines the potential impacts of climate change and the SAI intervention on droughts and drought management over the major river basins in Africa. Multi-ensemble climate simulation datasets from the Stratospheric Aerosol Geoengineering Large Ensemble (GLENS) Project were analysed for the study. The Standardized Precipitation Evapotranspiration Index (SPEI) and the Standardized Precipitation Index (SPI) were used to characterize the upper and lower limits of future drought severity, respectively, over the basins. The SPEI is a function of rainfall and potential evapotranspiration, whereas the SPI is only a function of rainfall, so the difference between the two indices is influenced by atmospheric evaporative demand. The results of the study show that, while the SAI intervention, as simulated in GLENS, may offset the impacts of climate change on temperature and atmospheric evaporative demand, the level of SAI that compensates for temperature change would overcompensate for the impacts on precipitation and therefore impose a climate water balance deficit in the tropics. SAI would narrow the gaps between SPEI and SPI projections over the basins by reducing SPEI drought frequency through reduced temperature and atmospheric evaporative demand while increasing SPI drought frequency through reduced rainfall. The narrowing of this gap lowers the level of uncertainty regarding future changes in drought frequency, but nonetheless has implications for future drought management in the basins, because while SAI lowers the upper limit of the future drought stress, it also raises the lower limit of the drought stress.

Radioecological modeling of the 131I activity dynamics in different types of grass vegetation in the Chernobyl accident year

The dynamics of 137Cs and 131I radioactivity in the crude biomass of the grass fodder and food vegetation in Mazovia, Poland, in 1986, the year of the Chernobyl accident, has been estimated. Density of 137Cs and 131I in the soil and vegetation have been measured as a function of rainfall and biomass density as of the time most of the fallout took place. A method is described to convert the instrumental data for the radionuclide activity dynamics in vegetation of one type to vegetation of other types. The results of such data conversion from lawn grass to other types of food and fodder grass vegetation are presented. A method is described for adjusting the dynamics of the radionuclide transport through the food chain components (pasture grass, green meat – milk – human body) by normalizing successively the estimated data in each next component for the average value of the instrumental data ratio to the estimated data in the preceding component. The proposed methods are intended to generate a mutually consistent base of estimated and reconstructed instrumental data: 137Cs and 131I activity in the atmosphere – rainfall – 137Cs fallout density on terrain – specific activity of 131I in vegetation. Such radioecological database will provide for a longer reliability of the estimated 131I specific activity dynamics in milk and in human body and, in the long run, when estimating the thyroid internal exposure doses.

Quantitative Analysis of Geomorphologic Characteristics for Surface Runoff Determination in Amala River Catchment in Kenya

Hydrological response of a catchment is a function of rainfall as influenced by catchment characteristics comprising geomorphology, land cover, and management practices. In this study, the analysis mainly focused on how geomorphological characteristics influence the catchment hydrological response. Geomorphological analyses of catchment geometry, stream patterns, relief, and slope can be used to characterize the catchment features that affect the drainage network. These characteristics are catchment specific and therefore unique to provide an insight into its hydrologic response. The objective of this research was to quantitatively analyze geomorphologic characteristics; linear, areal, drainage pattern, and relief aspect, of Amala River catchment, using ArcGIS tools and infer its hydrological behavior. The morphometry of the catchment was derived from the DEM within the ArcMap environment. These parameters as well as mathematical map equations were used to derive geomorphological characteristics such as bifurcation ratio, rho coefficient, drainage density, infiltration number, form factor among others. The results show that the Amala River catchment is elongated with uniform lithology and a higher probability of delayed peak hydrographs due to longer lag time and time of concentration. The catchment exhibits a dendritic drainage pattern with an average bifurcation ratio of 4.26 which is closer to the upper bound value of 5. This indicates a reduction in peak flows and a delayed time to peak. The surface runoff yield efficiency was low and non-uniform with an average drainage density of 1.073 km/km2. The catchment was characterized by higher infiltration characteristics as compared to surface flows, this varied spatially, with sub-basins far North of the outlet having high infiltration than those near the outlet. The catchment relief was characterized as steep and therefore high stream velocity was inferred. The investigation and findings of this study on catchment geomorphology and inferred hydrologic behavior will be of great importance in catchment management, water resource planning within the catchment, and water harvesting at a spatial scale. Thus, the outcomes provide a baseline for informed water pan and water harvesting structures site.

The convexity of carbonate hilltops: 36Cl constraints on denudation and chemical weathering rates and implications for hillslope curvature

Abstract Carbonate hillslopes are often soil mantled and display a classic convex morphology. In this study we examine controls on carbonate hillslope denudation and morphology using a modified regolith mass balance equation to account for chemical weathering and dust input—two fluxes that are commonly neglected in settings with silicate-dominated bedrock. We utilize seven study sites in the Eastern Mediterranean across a significant gradient in the mean annual rainfall and dust deposition flux. Combining cosmogenic 36Cl-derived hilltop denudation rates with an estimate of the regolith chemical depletion and the quantified fraction of dust in the regolith we predict hilltop curvature and compare our predictions with observations based on high-resolution airborne LiDAR (light detection and ranging). Denudation rates vary from 5 to 210 mm/k.y. and increase with mean annual rainfall. Less resistant carbonates (chalk) experience faster denudation rates relative to more resistant dolo-limestone and are less prone to chemical weathering. Soil production exhibits a humped dependency on soil thickness. The observed hilltop curvature varies as a function of rainfall and dust flux with a minimum at sub-humid sites. While trends in hilltop convexity are often solely attributed to variations in erosion rate, our results illustrate the additional effects of dust production and chemical depletion. Our mass balance model implies that drier sites in the south probably experienced a more intricate history of regolith production due to dust flux fluctuations. Thus, by incorporating dust flux and chemical weathering to the classic hillslope evolution model we are able to identify a complex relation between hilltop curvature, soil production, and climate.

Modern Strategies for Time Series Regression

SummaryThis paper discusses several modern approaches to regression analysis involving time series data where some of the predictor variables are also indexed by time. We discuss classical statistical approaches as well as methods that have been proposed recently in the machine learning literature. The approaches are compared and contrasted, and it will be seen that there are advantages and disadvantages to most currently available approaches. There is ample room for methodological developments in this area. The work is motivated by an application involving the prediction of water levels as a function of rainfall and other climate variables in an aquifer in eastern Australia.

Evaluation of physicochemical water parameters in watersheds of southern Brazil

Water-quality monitoring is one of the main instruments for water-resource management. This work therefore evaluated the water quality of the contribution basin of the Sinnott water treatment plant as well as the relationship between physicochemical water parameters, and analyzed the seasonal variation of water quality parameters as a function of rainfall. The study area encompassed the contribution basin of the Sinnott water treatment plant, formed mainly by the drainage areas of the Pelotas stream and its tributary, the Quilombo Stream, located in the city of Pelotas - Rio Grande do Sul, Brazil. A set of 118,368 data points for each stream was analyzed between 2007 and 2012. The following water quality parameters were evaluated: turbidity, temperature, color, pH, hardness, dissolved oxygen, organic matter, and alkalinity. Results showed that dissolved oxygen and water pH values conformed with Brazilian legislation in the 6 years evaluated. However, water color was the parameter that remained the greatest number of days above the set limits, mainly in the Pelotas Stream. Result indicates the need for conservation actions in the catchment, especially considering the importance of color for the assessment of water quality for public supply, in terms of both treatment costs and of public health. Highest values for water color, turbidity, and organic matter coincided with the occurrence of the highest rainfall values. Agricultural activities may potentiate sedimentation in the contribution basin of the Sinnott water treatment plant.

Comparison of rainfall-runoff models for climate change projection – case study of Citarum River Basin, Indonesia

Climate change affects temperature, rainfall and hydrological properties in the river basins. Projected rainfalls for several climate change models are widely available nowadays. However, in water resources planning and management, river discharges data is unfortunately more important. The information on climate change impact on river discharges is very limited. Conversion from the projected rainfall to the runoff in the rivers is needed. This study analyzes the performance of rainfall-runoff models: 1) Empirical Model that defines the discharge as a function of rainfall, evaporation, and temperature, widely applied by climate scientist; and 2) simple lump conceptual model of NRECA. These two rainfall-runoff models are applied during the control period in the year of 2006 to 2015 of the rainfall projections from the seven CMIP5 Global Circulation Models with the worst scenario, RCP 8.5. The ground station river discharge data selected is Nanjung river gauging station at Citarum River, situated just upstream of Saguling Reservoir, the uppermost of the cascade of three reservoirs Saguling-Cirata-Jatiluhur, with the catchment area of 1, 675 square kilometers. The results show that the simple conceptual model NRECA significantly gives better fitted to the observation data than the Empirical Model, especially during the dry season.

Agricultural productivity of cassava under the rainfall of Pajeú river basin

The crop, joined with livestock, are the most important activities in semiarid of Pernambuco and the rural activities developed in semiarid, in majority, are made by dry crops, so this kind of activity is highly dependent of rainfall that occur in the region. The main aim of this research was assess cassava productivity in function of rainfall in Pajeu river basin. Were used to this research, statistical methods applied to fill gaps of rainfall data and to model yearly cassava agricultural productivity. In general, at least 4 of 7 stations obtained good statistical relationship between the variables recording r between 0.505 and 0.723. Cassava productivity has better relationship with rainfall in center of basin between january and march and north center of basin between april and june. Figured out spatial variabilities in the rainfall influence over cassava productivity. The rainfall and productivity presented patterns with different levels of definitions over time and figured out that the potential of predictability of the agricultural productivity using rainfall to the adopted standards in the researches was satisfied, however, with some errors that can be relevant to the quality of the forecasting until 13 years.