GENERATION OF DAILY PRECIPITATION OVER AN AREA1

ABSTRACT: A model was developed of the periodic-stochastic structure of daily precipitation over an area. The model is based ona multivariate normal distribution. The square roots of daily precipitation at a point were found to approximate a sample from a univariate normal distribution that had been truncated at zero. The zero daily precipitation amounts were considered negative amounts of unknown quantity. The multivariate normal distribution was used to describe the variation of daily precipitation over an area. The periodic fluctuations of the model parameters were described with Fourier series. The model was tested using data from two areas of different precipitation characteristics. Data generated with the model contained many of the statistical characteristics observed in the historical data.     

DISTRIBUTION AND STOCHASTIC GENERATION OF ANNUAL AND MONTHLY PRECIPITATION ON A MOUNTAINOUS WATERSHED IN SOUTHWEST IDAHO1

ABSTRACT: The 18-year precipitation record from the dense gage network on the Reynolds Creek Experimental Watershed located in southwest Idaho was used to determine the spatial distribution of annual and monthly precipitation on a mountainous watershed. Analyses of these data showed a linear relationship between annual amounts and elevation. This relationship was best when the gages were grouped into downwind and upwind sites. This grouping was appropriate because most of the winter storms moved over the watershed from the west and southwest, and the heaviest precipitation was on the west (downwind) side of the watershed. Gage sites along the western and southern watershed borders were most representative of the upwind gages on the east side, because they measured the precipitation from the air moving upwind onto the watershed. The maximum annual precipitation on the watershed was just leeward of the western watershed boundary. The monthly precipitation and elevation relationship was also best represented by grouping the gage sites into upwind and downwind sites. However, during the summer when there are only small amounts of pre cipitation and thunderstorms are the source of most precipitation, one equation can be used to represent the elevation relationship. This study also showed that the log-normal distribution could be used to generate the annual synthetic series, and the cube-root-normal distribution could be used to generate monthly synthetic series for all locations on the watershed.     

WEST AFRICA: VOLTA DISCHARGE DATA QUALITY ASSESSMENT AND USE1

ABSTRACT: Water resource management in West Africa is often a complicated process due to inadequate resources, climatic extremes, and insufficient hydrological information. Insufficient data hinder sustainable watershed management practices, one of the top priorities in the Volta River Basin. This research properly fills in missing data by modeling the hydrological distribution in the Volta River Basin. On average, discharge gages across the basin are missing 20 percent of their monthly data over 20 years. Two methods were used to supplement missing data: a statistically linear model and a conceptual hydrological model. A linear equation, developed from the regression of precipitation and runoff, was used to evaluate the quality of existing data. The hydrological model separates the system into root and groundwater zones. Measured values were used to calibrate the hydrological model and to validate the statistical model. The quality of existing data was analyzed and organized for usability. Accuracy of the hydrological model was also evaluated for its effectiveness using R² and standard error. It was found that the hydrological model was an improvement from the linear model on a monthly basis; R² values improved by as much as 0.5 and monthly error decreased. Monthly predictions of the hydrological model were used to fill gaps of measured data sets.     

A COMPARISON OF DELTA CHANGE AND DOWNSCALED GCM SCENARIOS FOR THREE MOUNTAINOUS BASINS IN THE UNITED STATES1

ABSTRACT: Simulated daily precipitation, temperature, and runoff time series were compared in three mountainous basins in the United States: (1) the Animas River basin in Colorado, (2) the East Fork of the Carson River basin in Nevada and California, and (3) the Cle Elum River basin in Washington State. Two methods of climate scenario generation were compared: delta change and statistical downscaling. The delta change method uses differences between simulated current and future climate conditions from the Hadley Centre for Climate Prediction and Research (HadCM2) General Circulation Model (GCM) added to observed time series of climate variables. A statistical downscaling (SDS) model was developed for each basin using station data and output from the National Center for Environmental Prediction/National Center for Atmospheric Research (NCEPINCAR) reanalysis regridded to the scale of HadCM2. The SDS model was then used to simulate local climate variables using HadCM2 output for current and future conditions. Surface climate variables from each scenario were used in a precipitation‐runoff model. Results from this study show that, in the basins tested, a precipitation‐runoff model can simulate realistic runoff series for current conditions using statistically down‐scaled NCEP output. But, use of downscaled HadCM2 output for current or future climate assessments are questionable because the GCM does not produce accurate estimates of the surface variables needed for runoff in these regions. Given the uncertainties in the GCMs ability to simulate current conditions based on either the delta change or downscaling approaches, future climate assessments based on either of these approaches must be treated with caution.     

EVALUATION OF PROBABILITY DENSITY FUNCTIONS IN PRECIPITATION MODELS FOR THE PACIFIC NORTHWEST1

ABSTRACT: Recent work has found that a one-parameter Weibull model of wet day precipitation amount based on the Weibull distribution provides a better fit to historical daily precipitation data for eastern U.S. sites than other one-parameter models. The general two-parameter Weibull distribution was compared in this study to other widely used distributions for describing the distribution of daily precipitation event sizes at 99 sites from the U.S. Pacific Northwest. Surprisingly little performance was sacrificed by reducing the two-parameter Weibull to a single-parameter distribution. Advantages of the single-parameter model included requiring only the mean wet day precipitation amount for calibration, invertibility for simulation purposes, and ease of analytical manipulation. The fit of the single-parameter Weibull to the 99 stations included in this study was significantly better than other single-parameter models tested, and performed as well as the widely endorsed, more cumbersome, two-parameter gamma model. Both the one-and two-parameter Weibull distributions are shown to have b-moments that are consistent with historical precipitation data, while the ratio of b-skew and b-variance in the gamma model is inconsistent with the historical recerd by this measure. In addition, it was found that the two-parameter gamma distribution was better fit using the method of moments estimators than maximum likelihood estimates. These findings suggested that the distribution in precipitation among sites in the Pacific Northwest with dramatically different settings are nearly identical if expressed in proportion to the mean site event size.     

GENERATED MONTHLY STREAMFLOWS FOR THE MIDWESTERN AND SOUTHWESTERN UNITED STATES1

ABSTRACT A critical examination of single gage site, monthly streamflow statistical characteristics for two southern Illinois rivers, an Oklahoma river and a Texas river was made using a digital computer at Northwestern University. High flow variability for the rivers was evident in that, for the rivers tested, 8 to 11 months had coefficients of variation in excess of unity. The gamma distribution was not as efficient as the normal distribution for fitting power or logarithmic transforms of the historical monthly flow data (i.e., F^1-0, F^0-5, F^0-25, Fa¹²⁵, F^0.085, and log F). No single transform to a normal distribution was adequate for all twelve monthly flows, since definite seasonal grouping patterns were found for the four rivers examined. The highly variable flow in the low-flow season(s) indicated much more skewness than was typical of the remainder of the year. For the low-flow seasons, the higher-root (smaller exponent) transforms were particularly useful. Flows were generated from a linear regression model of lag one utilizing two or more transforms for the twelve periods. The definite seasonal patterns found historically were reproduced quite well in the generated streamflows. The effect of a change in data transform from one season to the next was insignificant after one month. Thus the use of different transforms within the year did not bias the results from the linear regression model appreciably, but did help in reproducing the seasonal distribution pattern. The technique seems especially well suited for rivers with highly variable flows.     

VARIABILITY CHARACTERISTICS OF MONTHLY PRECIPITATION IN CENTRAL OKLAHOMA1

ABSTRACT: To fully take advantage of regional climate forecast information for agricultural applications, the relationship between divisional and station scale precipitation characteristics must be quantified. The spatial variability of monthly precipitation is assumed to consist of two components: a systematic and a random component. The systematic component is defined by differences in long-term mean precipitation between stations within a climate division, and the random component by differences between station and divisional standardized values. For the Central Climate Division of Oklahoma, the systematic component has a positive precipitation gradient from west to east with a slope ranging between 3 to 16 mm of precipitation per 100 km depending on the month of the year. On the other hand, the random component ranges between 27 to 48 percent of the mean temporal variation of the monthly precipitation. This significant random spatial variability leads to large localized departures from divisional values, and clearly demonstrates the critical influence of the random component in the utilization of divisional climate forecasts for local agricultural applications. The results of this study also provide an uncertainty range for local monthly precipitation projections that are derived from divisional climate information.     

ADEQUACY OF SELECTED EVAPOTRANSPIRATION APPROXIMATIONS FOR HYDROLOGIC SIMULATION1

ABSTRACT: Evapotranspiration (ET) approximations, usually based on computed potential ET (PET) and diverse PET‐to‐ET conceptualizations, are routinely used in hydrologic analyses. This study presents an approach to incorporate measured (actual) ET data, increasingly available using micrometeorological methods, to define the adequacy of ET approximations for hydrologic simulation. The approach is demonstrated at a site where eddy correlation‐measured ET values were available. A baseline hydrologic model incorporating measured ET values was used to evaluate the sensitivity of simulated water levels, subsurface recharge, and surface runoff to error in four ET approximations. An annually invariant pattern of mean monthly vegetation coefficients was shown to be most effective, despite the substantial year‐to‐year variation in measured vegetation coefficients. The temporal variability of available water (precipitation minus ET) at the humid, subtropical site was largely controlled by the relatively high temporal variability of precipitation, benefiting the effectiveness of coarse ET approximations, a result that is likely to prevail at other humid sites.     

MESOSCALE ATMOSPHERIC 2XCO2 CLIMATE CHANGE SIMULATION APPLIED TO AN OREGON WATERSHED1

ABSTRACT: A 2xCO2 climate and runoff in the Upper Deschutes Basin in central Oregon is simulated using a mesoscale atmospheric model and a watershed model that incorporates spatial variability of the runoff process. A nine‐year control climate monthly time series provides a benchmark for assessing changes related to a warmer and wetter 2xCO2 climate. Potential evapotranspiration is increased by 23 percent and snow water equivalent is reduced by 59 percent in the 2xCO2 climate. Annual runoff increases by 23 percent, while November runoff increases by 55 percent. The average maximum monthly runoff is in May for both the control climate and 2xCO2 climate, but in five of the nine years the monthly maximum runoff for the 2xCO2 climate occurs two to five months earlier than for the control climate. The minimum runoff month is one to five months earlier in the 2xCO2 climate in seven of the nine years, and the month of average minimum runoff is March in the control climate and November in the 2xCO2 climate. Since precipitation is greatest in December in both the control climate and 2xCO2 climate, the earlier maximum and minimum runoff for a 2xCO2 climate indicates greater watershed sensitivity to temperature than to precipitation.     

GENERAL-CIRCULATION-MODEL SIMULATIONS OF FUTURE SNOWPACK IN THE WESTERN UNITED STATES1

ABSTRACT: April 1 snowpack accumulations measured at 311 snow courses in the western United States (U.S.) are grouped using a correlation-based cluster analysis. A conceptual snow accumulation and melt model and monthly temperature and precipitation for each cluster are used to estimate cluster-average April 1 snowpack. The conceptual snow model is subsequently used to estimate future snowpack by using changes in monthly temperature and precipitation simulated by the Canadian Centre for Climate Modeling and Analysis (CCC) and the Hadley Centre for Climate Prediction and Research (HADLEY) general circulation models (GCMs). Results for the CCC model indicate that although winter precipitation is estimated to increase in the future, increases in temperatures will result in large decreases in April 1 snowpack for the entire western U.S. Results for the HADLEY model also indicate large decreases in April 1 snowpack for most of the western US, but the decreases are not as severe as those estimated using the CCC simulations. Although snowpack conditions are estimated to decrease for most areas of the western US, both GCMs estimate a general increase in winter precipitation toward the latter half of the next century. Thus, water quantity may be increased in the western US; however, the timing of runoff will be altered because precipitation will more frequently occur as rain rather than as snow.     

Generation of Monthly Precipitation Under Climate Change for the Upper Blue Nile River Basin,Ethiopia1

Abstract: This work develops a methodology to project the future precipitation in large river basins under limited data and climate change while preserving the historical temporal and spatial characteristics. The computationally simple and reliable conditional generation method (CGM) is presented and applied to generate reliable monthly precipitation data in the upper Blue Nile River Basin of Ethiopia where rain‐fed agriculture is prevalent. The results showed that the temporal analysis with the CGM performs better to reproduce the historical long‐term characteristics than other methods, and the spatial analysis with the CGM reproduced the historical spatial structure accurately. A 100‐year time series analysis using the outcomes of the six general circulation models showed that precipitation changes by the 2050s (2040 through 2069) can be ?7 to 28% with a mean increase of about 11%. The seasonal results showed increasing wet conditions in all seasons with changes of mean precipitation of 5, 47, and 6% for wet, dry, and mild seasons, respectively.     

Load Estimation Method Using Distributions with Covariates: A Comparison with Commonly Used Estimation Methods

Load estimates obtained using an approach based on statistical distributions with parameters expressed as a function of covariates (e.g., streamflow) (distribution with covariates hereafter called DC method) were compared to four load estimation methods: (1) flow‐weighted mean concentration; (2) integral regression; (3) segmented regression (the last two with Ferguson's correction factor); and (4) hydrograph separation methods. A total of 25 datasets (from 19 stations) of daily concentrations of total dissolved solids, nutrients, or suspended particulate matter were used. The selected stations represented a wide range of hydrological conditions. Annual flux errors were determined by randomly generating 50 monthly sample series from daily series. Annual and interannual biases and dispersions were evaluated and compared. The impact of sampling frequency was investigated through the generation of bimonthly and weekly surveys. Interannual uncertainty analysis showed that the performance of the DC method was comparable with those of the other methods, except for stations showing high hydrological variability. In this case, the DC method performed better, with annual biases lower than those characterizing the other methods. Results show that the DC method generated the smallest pollutant load errors when considering a monthly sampling frequency for rivers showing high variability in hydrological conditions and contaminant concentrations.     

A SENSITIVITY ANALYSIS OF THE PALMER HYDROLOGIC DROUGHT INDEX1

ABSTRACT: The sensitivity of the Palmer Hydrologic Drought Index to departures from average temperature and precipitation conditions is examined. A time series of zero index values was calculated and then one monthly temperature or precipitation value was perturbed. The resulting time series shows the effects on the index of one anomalous value. Independent series were calculated for temperature anomalies of plus and minus 1, 3, 5, and 10F and for precipitation anomalies of 25, 50, 75, 125, 150, and 200 percent of normal for each calendar month for Colorado, Indiana, Nevada, New York, Oklahoma, South Carolina, South Dakota, Washington, and Wisconsin. Analysis of the time series showed that the period of time required for the index to reflect actual rather than artificial initial conditions could be more than four years. It was also found that the effects of temperature anomalies are insignificant compared to the effects of precipitation anomalies. In some cases, one anomalous precipitation value could result in established wet or dry spells that last for up to two years. Although not examined in detail, the time series suggest that distributions of index values may be asymmetrical and possibly bimodal.     

GEOGRAPHIC VARIATION OF THE STATISTICAL PARAMETERS OF HYDROMETEOROLOGICAL DATA OF THE UNITED STATES1

ABSTRACT: Having determined various statistical parameters for five mean monthly hydrometeorological time series of the United States, directional variation of the autocorrelation numbers, their spatial distribution over the United States and statistical significances are presented in this paper. Two conceptually different approaches (one using directional strips of large combined watersheds and the other with analysis of variances) are employed to explore the geographic variation of the statistical parameters (autocorrelations and explained variances) in question. Results adequately indicate the correspondence between these variations and the observed topographic, climatologic and hydrologic characteristics over the United States.     

Comparison of the Performance of Statistical Models in Forecasting Monthly Total Dissolved Solids in the Rio Grande1

Abudu, S., J.P. King, Z. Sheng, 2011. Comparison of the Performance of Statistical Models in Forecasting Monthly Total Dissolved Solids in the Rio Grande. Journal of the American Water Resources Association (JAWRA) 48(1): 10‐23. DOI: 10.1111/j.1752‐1688.2011.00587.x Abstract: This paper presents the application of autoregressive integrated moving average (ARIMA), transfer function‐noise (TFN), and artificial neural networks (ANNs) modeling approaches in forecasting monthly total dissolved solids (TDS) of water in the Rio Grande at El Paso, Texas. Predictability analysis was performed between the precipitation, temperature, streamflow rates at the site, releases from upstream reservoirs, and monthly TDS using cross‐correlation statistical tests. The chi‐square test results indicated that the average monthly temperature and precipitation did not show significant predictability on monthly TDS series. The performances of one‐ to three‐month‐ahead model forecasts for the testing period of 1984‐1994 showed that the TFN model that incorporated the streamflow rates at the site and Caballo Reservoir release improved monthly TDS forecasts slightly better than the ARIMA models. Except for one‐month‐ahead forecasts, the ANN models using the streamflow rates at the site as inputs resulted in no significant improvements over the TFN models at two‐month‐ahead and three‐month‐ahead forecasts. For three‐month‐ahead forecasts, the simple ARIMA showed similar performance compared to all other models. The results of this study suggested that simple deseasonalized ARIMA models could be used in one‐ to three‐month‐ahead TDS forecasting at the study site with a simple, explicit model structure and similar model performance as the TFN and ANN models for better water management in the Basin.     

LONG TERM TRENDS OF ANNUAL AND MONTHLY PRECIPITATION IN JAPAN1

ABSTRACT: Long term trends in Japan's annual and monthly precipitation are investigated in this study. The statistical significance of a trend at a study site is assessed by the Mann‐Kendall (MK) test, and field significance of trends in climatic Regions II, III, and IV is evaluated using the bootstrap test preserving cross correlation. The practical significance of a trend is judged by a percentage change of the sample mean over an observation period. The field significance assessment demonstrates that annual precipitation in Region II did not show any significant change, but regional precipitation shifts occurred in different months. Precipitation significantly increased by 12.2 percent in May, while it significantly decreased by 12.0, 10.5, 15.6, and 19.7 percent, respectively, in April, September, October, and December. In Region III, annual precipitation declined by 11.8 percent, and monthly precipitation significantly decreased from September through January and in April, with the greatest decrease (38.2 percent) in December. In Region IV, significant reductions occurred in both annual precipitation (by 15.6 percent) and monthly precipitation from September through February and in June and July, with the worst reduction (44.7 percent) in December.     

FLOW PERSISTENCE AS A MODIFIER OF SEASONAL RUNOFF PATTERNS1

ABSTRACT: The effect of flow persistence on seasonal patterns of watershed runoff was modeled by using runoff of the immediate antecedent month as an index. Monthly runoff was expressed as a function of monthly rainfall, season of the year, and runoff of the antecedent month. The three independent variables were expressed functionally as sliding polynomials, thus producing a piece-wise, form-free, three-dimensional causative structure. A model form allowing complete interactivity of the three independent variables could not be optimized because of insufficient data with high values of both antecedent runoff and monthly rainfall. A model with reduced interactivity was successfully optimized. Data sets from five watersheds ranging from 0.14 to 398 square miles were analyzed. Results were presented as a series of contour maps that showed contours of monthly runoff in the data space of season and monthly rain. In the series of maps, the patterns of the runoff contours changed with changing values of antecedent runoff. During the wet season of the year the contours changed significantly with antecedent runoff, but changes in the dry season were minimal. The quantitative change of runoff was more readily portrayed with cross-sections through the contoured surfaces.     

STOCHASTIC ANALYSIS OF TIME-AGGREGATED HYDROLOGIC DATA1

Stochastic models fitted to hydrologic data of different time scales are interrelated because the higher time scale data (aggregated data) are derived from those of lower time scale. Relationships between the statistical properties and parameters of models of aggregated data and of original data are examined in this paper. It is also shown that the aggregated data can be more accurately predicted by using a valid model of the original data than by using a valid model of the aggregated data. This property is particularly important in forecasting annual values because only a few annual values are usually available and the resulting forecasts are relatively inaccurate if models based only on annual data are used. The relationships and forecasting equations are developed for general aggregation time and can be used for hourly and daily, daily and monthly or monthly and yearly data. The method is illustrated by using monthly and yearly streamflow data. The results indicate that various statistical characteristics and parameters of the model of annual data can be accurately estimated by using the monthly data and forecasts of annual data by using monthly models have smaller one step ahead mean square error than those obtained by using annual data models.     

TESTS OF THE CREAMS MODEL ON AGRICULTURAL FIELDS IN VERMONT1

ABSTRACT: The computer model, CREAMS, has been developed for field-sized agricultural areas to aid in best management practices evaluation and planning. A test of CREAMS was performed by comparing monthly observed and simulated values for runoff, sediment, and phosphorus exports from two agricultural fields in Vermont to determine the applicability of the model in cold climates. Water quality samples were collected from field runoff and analyzed for both total suspended solids and total phosphorus. Generally, exports were overestimated during low flow months and underestimated during high flow months. Significant r²values (p <0.05), ranging from 0.78 to 0.90, between simulated and observed data were found for all comparisons except for sediment export from one field. Comparisons of the slopes of the regressions between observed and simulated values and the ideal slope of one using t-tests revealed significant differences between simulated and observed monthly runoff, sediment, and phosphorus exports. It is postulated that this lack of adequate prediction could be attributed to the use of average monthly, instead of daily, temperature and solar radiation in calculations of evapotranspiration and snowmelt, and the use of static parameter values for parameters that vary seasonally.     

PRECIPITATION DISTRIBUTION IN COASTAL BRITISH COLUMBIA1

ABSTRACT: The spatial distribution and the temporal and spatial variation of the annual, seasonal, and monthly precipitation in two mountainous watersheds in southwestern British Columbia, Canada, have been analyzed using a detailed database for 1971–1990 in the Capilano and Seymour watersheds. The analysis showed that the precipitation increases up to the mid-position of the watersheds, and then either levels off or decreases. Precipitation on mountain slopes and in the valley at the same distance from the beginning of the slope is similar, and the barrier height is identified as the dominant parameter which influences the precipitation distribution. The temporal variation of the precipitation is the smallest at the mid-position of the watersheds. This variability is the least in the fall and winter and largest in the summer. Correlation between the precipitation accumulations at various stations is large, ranging from 0.80 for the wet period of October-March to 0.65 for the dry period of April-September for distances less than 32 km. Comparison with other studies and the analyses of precipitation and runoff data from coastal British Columbia showed that the results of this study are perhaps general and thus transferable to similar areas in the coastal Pacific Northwest.