MATHEMATICAL GENERALIZATION OF STREAM TEMPERATURE IN CENTRAL NEW ENGLAND1

ABSTRACT: The empirical fit of an annual harmonic function to stream temperature measurements in central New England can be improved by considering a harmonic period of less than 365 days instead of 365 or 366 days. Generalized equations, developed using periodic temperature data from 27 streamflow stations, allow predictions of stream temperature at any site given (1) the mean basin altitude (E), in meters above mean sea level, and (2) station latitude (LAT), in degrees. Stream temperature t, in degrees Celsius, on day number d, in days starting with January 1, is estimated as: in which, M = 31.48 – 0.0025 (E) ? 0.4635 (LAT) with standard error of estimate of 0.62°C, and τ= 1228.88 – 21.01 (LAT) with standard error of estimate of 14.1 days.     

ESTIMATING THE PROBABILITY OF EXCEEDING GROUNDWATER QUALITY STANDARDS1

ABSTRACT: A model for estimating the probability of exceeding groundwater quality standards at environmental receptors based on a simple contaminant transport model is described. The model is intended for locations where knowledge about site-specific hydrogeologic conditions is limited. An efficient implementation methodology using numerical Monte Carlo simulation is presented. The uncertainty in the contaminant transport system due to uncertainty in the hydraulic conductivity is directly calculated in the Monte Carlo simulations. Numerous variations of the deterministic parameters of the model provide an indication of the change in exceedance probability with change in parameter value. The results of these variations for a generic example are presented in a concise graphical form which provides insight into the topology of the exceedance probability surface. This surface can be used to assess the impact of the various parameters on exceedance probability.     

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.     

COMPARING THE PALMER DROUGHT INDEX AND THE STANDARDIZED PRECIPITATION INDEX1

ABSTRACT: The Palmer Drought Index (PDI) is used as an indicator of drought severity, and a particular index value is often the signal to begin or discontinue elements of a drought contingency plan. The Standardized Precipitation Index (SPI) was recently developed to quantify a precipitation deficit for different time scales. It was designed to be an indicator of drought that recognizes the importance of time scales in the analysis of water availability and water use. This study compares historical time series of the PDI with time series of the corresponding SPI through spectral analysis. Results show that the spectral characteristics of the PDI vary from site to site throughout the U.S., while those of the SPI do not vary from site to site. They also show that the PDI has a complex structure with an exceptionally long memory, while the SPI is an easily interpreted, simple moving average process.     

AN EARLY WARNING SYSTEM FOR DROUGHT MANAGEMENT USING THE PALMER DROUGHT INDEX1

ABSTRACT: The Palmer Drought Severity Index (PDSI) is used in a non-homogeneous Markov chain model to characterize the stochastic behavior of drought. Based on this characterization an early warning system in the form of a decision tree enumerating all possible sequences of drought progression is proposed for drought management. Besides yielding probabilities of occurrence of different drought severity classes, the method associates a secondary measure in terms of likely cumulative precipitation deficit to provide timely guidance in deciding drought mitigation actions. The proposed method is particularly useful for water availability task forces in various states for issuing drought warnings in advance. The applicability of the technique is illustrated for the Tidewater climatic division of Virginia.     

PLANNING FOR DROUGHT: THE ROLE OF STATE GOVERNMENT1

ABSTRACT: Although droughts are a frequent occurrence over much of the United States, response by state and federal government has been ineffective and poorly coordinated. Recently, several states have recognized the value of drought emergency planning and have developed plans to assist them in responding more effectively to prolonged periods of water shortage. These states have created an organizational structure to coordinate the assessment and response activities of state and federal agencies. Each state's drought response plan is unique since each state's water supply and management problems, and their consequent impacts, are unique. The drought response plans developed by Colorado, South Dakota and New York are reviewed here in detail. We recommend that other states affected by frequent and severe water shortages also develop drought emergency plans. These plans will enhance state government's ability to implement effective measures in a timely manner and, ultimately, may provide added incentive for the federal government to develop the national drought response plan called for by the General Accounting Office in 1979.     

A SCALE‐INVARIANT GAUSS‐MARKOV MODEL FOR DESIGN STORM HYETOGRAPHS1

Abstract. Hyetographs are essential to many hydrological designs. Many studies have shown that hyetographs are specific to storm types and durations. Recent work presented evidence that dimensionless hyetographs are scale invariant. We show that the simple scaling property of rainfall guarantees that the normalized rainfall rates of different storm durations are identically distributed and propose a nonstationary Gauss‐Markov model based on the annual maximum events that arise from the dominant storm type. We derive the unique estimators for the parameters of the Gauss‐Markov model under two constraints that: (a) the typical peak rainfall rate is preserved, and (b) the most likely hyetograph is obtained. One attractive feature of this model is that it allows translating hyetographs between storms of different durations. Two examples illustrate our model.     

THE PALMER DROUGHT SEVERITY INDEX AS A MEASURE OF HYDROLOGIC DROUGHT1

ABSTRACT: The Palmer Drought Severity Index (PDSI) is perhaps the most widely used regional drought index. However, there is considerable ambiguity about its value as a measure of hydrologic drought. In this paper the PDSI for climatic divisions in New Jersey is compared to the occurrence within each climatic division of streamflows in their lower quartile for the month (streamflow index), and ground-water levels in their lower quartile for the month (ground-water index). These indices are found to have distinct properties. It is not uncommon for PDSI values to indicate “severe” or “extreme” drought at times when the streamflow or groundwater index is above its lower quartile at many stations within the climatic division. The PDSI values and groundwater index indicate more persistent subnormal conditions than the streamflow index for truncation levels yielding the same total duration of drought over a period. The ground-water index tends to indicate a later beginning to droughts and of the three indices is the most conservative indicator of a drought's end. Drought timing and duration properties for the ground-water index are found to be highly influenced by the average depth to water in the well. Overall, the three indices of drought can provide three very different characterizations of drought. In particular, the results indicate that considerable caution should be exercised in drawing conclusions about hydrologic drought from the PDSI.     

A UNIFYING SET OF PROBABILITY TRANSFORMS FOR STOCHASTIC HYDROLOGY1

Abstract: An ordered set of probability sensity functions was derived form transforms of the normal distribution. Variate transforms are based on orders of exponentiation. The set of distributions includes the log-normal. a partial basis for use of these functins in hydrology is demonstrated by establishing some required properties. A concept of mixed samples of zero and nonzero elements forming nonseparable sets of virtual and real elements is introduced to establish a physical lower limit of sampled diata independent of functional bounds.     

SPATIAL COMPARABILITY OF THE PALMER DROUGHT SEVERITY INDEX1

ABSTRACT: The Palmer Drought Severity Index, which is intended to be of reasonable comparable local significance both in space and time, has been extensively used as a measure of drought for both agricultural and water resource management. This study examines the spatial comparability of Palmer's (1965) definition of severe and extreme drought. Index values have been computed for 1035 sites with at least 60 years of record that are scattered across the contiguous United States, and quantile values corresponding to a specified index value were calculated for given months and then mapped. The analyses show that severe or extreme droughts, as defined by Palmer (1965), are not spatially comparable in terms of identifying rare events. The wide variation across the country in the frequency of occurrence of Palmer's (1965) extreme droughts reflects the differences in the variability of precipitation, as well as the average amount of precipitation. It is recommended first, that a drought index be developed which considers both variability and averages; and second, that water resource managers and planners define a drought in terms of an index value that corresponds to the expected quantile (return period) of the event.     

POLICY DROUGIT: THE CASE OF SOUTH FLORIDA1

ABSTRACT: In this paper, we review recent experience with drought in south Florida, and report some results of a study of the likely agricultural economic impacts of drought. Our conclusions can be summarized as follows. (1) Whether a period of low rainfall becomes a “drought” in south Florida is determined largely by institutional factors. (2) The impacts of a drought event are dependent on the rules the Water Management District uses to manage the event. If the rules involve effective reductions in irrigation supply, the financial impacts may be large, but are sensitive to the way in which cutbacks are imposed. (3) Current drought management regulations do not appear to minimize the short-run cost of drought. (4) Current policies which seek to minimize the short-run cost of drought are inconsistent with dynamically-optimal policies.     

APPLICATION OF A MULTIPURPOSE UNEQUAL PROBABILITY STREAM SURVEY IN THE MID‐ATLANTIC COASTAL PLAIN1

ABSTRACT: A stratified, spatially balanced sample with unequal probability selection was used to design a multipurpose survey of headwater streams in the Mid‐Atlantic Coastal Plain. Objectives for the survey include unbiased estimates of regional stream conditions, and adequate coverage of unusual but significant environmental settings to support empirical modeling of the factors affecting those conditions. The design and field application of the survey are discussed in light of these multiple objectives. A probability (random) sample of 175 first‐order nontidal streams was selected for synoptic sampling of water chemistry and benthic and riparian ecology during late winter and spring 2000. Twenty‐five streams were selected within each of seven hydrogeologic subre‐gions (strata) that were delineated on the basis of physiography and surficial geology. In each subregion, unequal inclusion probabilities were used to provide an approximately even distribution of streams along a gradient of forested to developed (agricultural or urban) land in the contributing watershed. Alternate streams were also selected. Alternates were included in groups of five in each subregion when field reconnaissance demonstrated that primary streams were inaccessible or otherwise unusable. Despite the rejection and replacement of a considerable number of primary streams during reconnaissance (up to 40 percent in one subregion), the desired land use distribution was maintained within each hydrogeologic subregion without sacrificing the probabilistic design.     

MANAGING THE COLORADO RIVER IN A SEVERE SUSTAINED DROUGHT AN EVALUATION OF INSTITUTIONAL OPTIONS1

ABSTRACT: This paper presents a summary of the findings and recommendations of the studies of severe, sustained drought reported in this special issue. The management facilities and institutions were found to be effective in protecting consumptive water users against drought, but much less effective in protecting nonconsumptive uses. Changes in intrastate water management were found to be effective in reducing the monetary value of damages, through reallocating shortages to low-valued uses, while only water banking and water marketing, among the possible interstate rule changes, were similarly effective. Players representing the basin states and the federal government in three gaming experiments were unable to agree upon and effect major changes in operating rules. The conclusions are (1) that nonconsumptive water uses are highly vulnerable to drought, (2) that consumptive uses are well-protected, (3) that drought risk is greatest in the Upper Basin, (4) that the Lower Basin suffers from chronic water shortage but bears little drought risk, (5) that opportunities exist for win-win rule changes, (6) that such rule changes are extremely difficult to make, and (7) that intrastate drought management is very effective ^m in reducing potential damages.     

THE TREE-RING RECORD OF SEVERE SUSTAINED DROUGHT1

ABSTRACT: Frequent and persistent droughts exacerbate the problems caused by the inherent scarcity of water in the semiarid to arid parts of the southwestern United States. The occurrence of drought is driven by climatic variability, which for years before about the beginning of the 20th century in the Southwest must be inferred from proxy records. As part of a multidisciplinary study of the potential hydrologic impact of severe sustained drought on the Colorado River, the physical basis and limitations of tree rings as indicators of severe sustained drought are reviewed, and tree-ring data are analyzed to delineate a “worst-case” drought scenario for the Upper Colorado River Basin (UCRB). Runs analysis of a 121-site tree-ring network, 1600–1962, identifies a four-year drought in the 1660s as the longest-duration large-scale drought in the Southwest in the recent tree-ring record. Longer tree-ring records suggest a much longer and more severe drought in 1579–1598. The regression estimate of the mean annual Colorado River flow for this period is 10.95 million acre-feet, or 81 percent of the long-term mean. The estimated flows for the 1500s should be used with caution in impact studies because sample size is small and some reconstructed values are extrapolations.     

HYDROLOGICAL ASPECTS OF THE 1988 DROUGHT IN ILLINOIS1

ABSTRACT: Drought is evaluated in terms of the magnitude and duration of the 1988 spring and summer precipitation shortfall, and according to various components of the hydrologic budget, both surface and sub-surface. The response time of some of these components is investigated, relative to the time of precipitation. Individual water users perceived a beginning and ending of the drought at different times relative to their activities. Some statistics better describe some components of a drought to some users, and better answer some questions, than do others.     

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.     

AIR-WATER TEMPERATURE RELATIONSHIP IN ILLINOIS RIVER1

Application of harmonic analysis to daily mean air, water temperature records for a location indicates that the first harmonic accounts for a major portion of the total variance in the records. Water temperature residuals are well correlated with air temperature residuals. Parametric values of the mathematical model for predicting water temperatures from air temperature records are stable from year to year. The air-water temperature relationship appears to be a stationary linear process. Consequently, it is possible to predict water temperatures at a location from the ambient temperature records provided both air and water temperature records are available for another similarly situated water body.     

COMPARATIVE STUDY OF DROUGHT PREDICTION TECHNIQUES FOR RESERVOIR OPERATION1

ABSTRACT: Predicting the likelihood of a drought markedly enhances the efficiency of reservoir operations. This study applies the kriging method and time series analysis to predict inflows to Shihmen Reservoir in northern Taiwan. A subsequent reservoir operation simulation is employed to determine the drought lead time (DLT), the time before the onset of a drought. A more efficient reservoir operational strategy can be established with the aid of DLT and the probability of successful drought prediction (P s). Simulation results of reservoir operation over a period of three decades demonstrate that, at one month DLT, the kriging approach achieves 0.86 of P s for moderate droughts and 0.94 of P s for severe droughts. The kriging approach generally outperformed the time series approach in terms of DLT, P s of drought prediction, and the number of correctly predicted drought events.     

THE ARMA MODELS APPLIED TO THE FLOW OF KARSTIC SPRINGS1

ABSTRACT: Autoregressive moving average (ABMA) models have been applied to study the flow series of the karstic springs of La Villa, Fuente Mayor (Spain), and Aliou (France). The theoretical meaning of the parameters involved in the model upon applying it to a simplified scheme of the emptying of a karstic aquifer is first analyzed. The types of transformations necessary to apply these models to the flow series that lack normality and have strong periodic components are also indicated, as are the advantages of this type of model and the physical significance of the parameters obtained, with respect to the standpoint of hydraulics, ranging from rather homogeneous aquifers (La Villa) to extremely karstic (Aliou), including aquifers with intermediate characteristics (Fuente Mayor).     

MERITS OF STATISTICAL CRITERIA FOR THE PERFORMANCE OF HYDROLOGICAL MODELS1

ABSTRACT: The performance of a hydrological model is usually assessed first by visual inspection of the measured and computed hydrographs. Numerous statistical criteria are available for numerical evaluations of model accuracy in each single year, in a particular season of the year, or in a sequence of years or seasons. In the last case, the problem of computing the overall result has to be considered. If too many criteria are used and the criteria are switched frequently, an assessment of a model's performance becomes difficult for a potential user. Therefore, this paper concentrates on just three criteria and their combined evaluation: The Nash-Sutcliffe coefficient, which compares the model computed discharge with the average measured discharge; the “coefficient of gain from daily means” in which a uniform average discharge is replaced by daily average discharges; and the volumetric difference between the total measured and computed runoff. The three criteria are combined in a three dimensional representation that allows intercomparisons of model performance in a single diagram.