Two methods of linear trend estimation: the ordinary least squares (OLS, parametric) and Theil-Kendall (TK, nonparametric) are compared in the paper. The comparison was made using 65 time series of annual totals, Pa, and annual daily maximum, Pmax, of precipitation, 30-year long each, recorded in the south-eastern part of Poland (the Upper Vistula catchment). The OLS and TK slope coefficients of trends revealed high similarity for both Pa and Pmax series. The signs of slopes are the same for 64 sites for Pa and 63 sites for Pmax with positive signs prevailing: the numbers of decreasing trends for Pa OLS and TK slopes were 3 and 4, respectively, and, for Pmax, 13 for both OLS and TK slopes. In trend significance testing, both methods produced similar results for Pa time series: out of 16 significant trends, 13 were determined with both OLS and TK at the same sites. For Pmax series such agreement was found for 4 trends out of 10. Spatial distribution of significant trends showed a kind of clustering in certain parts of the investigated area. ...
In Polish hydrology and water management the term characteristic flow exists denoting a specific value of flow at the given cross-section of a river calculated as the long-term minimum, mean, median or maximum calculated using the annual minimum, mean, median or maximum flow taken for each year from a series of (usually) daily flows. Some of these characteristic flows are used to define the low-flow (o drought) periods while the another criterion: a percentage flow Qp taken from the long-term flow duration curve is also widely used. In the paper the study on the frequency structure the empirical exceedance probability of a given characteristic flow made for some low and average characteristic flows (SNQ, WNQ, NSQ and SSQ) is presented. The results show that the exceedance probability of a given characteristic flow is variable, and the amount of this variability may be large, as is the case of WNQ and NSQ. So assigning a characteristic flow to a single FDC quantile value Qp (as can be find in the literature) cannot be justified.Correlation analysis made for the pairs ( , characteristic flow), ( , catchment area) and ( , gauging station elevation) revealed some significant correlations. Only ...
For adopted 12 drought definitions and basing on 49-year time series of daily flows at four cross-sections in the Mała Wisła catchment, it was found that the probability distributions of drought duration T and drought deficit V may be described by the two-dimensional lognormal distribution with parameters estimated by the maximum likelihood method. The goodness-of-fit quality was tested by the Anderson-Darling and Cramér-von Mises tests. Both test did not reject the tested distributions neither for any definition nor any cross-section: all of the p-values were greater than 20%. ...
For adopted 12 drought definitions and basing on 49-year time series of daily flows at four cross-sections in the Mała Wisła catchment, it was found that the probability distributions of drought duration T and drought deficit V may be described by the lognormal distribution with parameters estimated by the maximum likelihood method. The goodness-of-fit quality was tested by the Anderson-Darling and Cramér-von Mises tests. Both test did not reject the tested distribution neither for any definition nor any cross-section, as the p-values were greater than 15% for the former test and greater than 20% for the latter. ...
Basing on four 49-year time series of daily flows in the Mała Wisła catchment, the influence of the adopted POT-type drought definition on the stationarity of four drought characteristics: drought starting time, inter-drought time , duration T and deficit V, as well as their mean characteristics were investigated. The drought definition depended on three parameters: p, Tmin and min, i.e., the mean percent exceedance time of the given threshold flow Qp (p = 60, 70, 80 i 90%), minimum drought duration T¬min and minimum inter-drought time min; (Tmin, min) = (7;7), (14;7) and (14;14) days. The mean characteristics exhibited regular (in some cases very regular) dependence on p. It was shown that the monthly average number of drought starting times has clear minimum in March, and the null hypothesis on the zero slope value of the time regression for the remaining three characteristics, , T and V may be accepted in most cases.
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Basing on four 49-year time series of daily flows in the Mała Wisła catchment, two methods of creating flow duration curves (FDCs) were analysed: a traditional method where one FDC is produced (period-of-record FDC) using all flow from N-year period, and mean annual FDC created as the average of N annual FDCs. The latter FDC differs from the former especially in the area of minim flows. In this area, for assumed exceedance durations p = 60, 70, 80 i 90%, a Qp taken from a mean annual FDC is higher from about 10% for p = 60% to even more than 20% for p = 90%. This increase and its amount are of value for selecting threshold flow when defining drought and for water supply design.The application of the second method implies that instead of a single value of exceedance time, p% or 365p days, and a single value of flow Qp, an N-element set of exceedance times of a fixed flow value, and an N-element set of flows Qp for fixed p are given. These set exhibit the variability of both the exceedance time and the flows Qp for fixed p. Both variabilities were studied and were shown to ...
The Chomicz model of 1953 for DDF curves, used in Poland mainly as a comparative model, is based on not quite adequate data and the approach presented by Chomicz was not substantiated enough, which raises serious doubts on the correctness of the method. Of course, the scarcity and relevance of the then data bases should be taken into account. However, independently of that problem, there are substantial reservations about the correctness of the design rainfalls developed by Chomicz for exceedance probabilities 10%, 20%, 50% and 100%. The most significant reservation concerns the correctness of the method of extending measured rainfall depth over its measured duration. The method can hardly be accepted, because it assumes that that the greatest rainfall interval intensity occurs in the end of the rainfall event, which is not supported by observations. Moreover, the number of extended rainfall depths, i.e., the number of semi-empirical values, used to develop the model of design rainfall, increases strongly with rainfall duration doubling the number of original data in the extreme case of the longest duration of 180 minutes. Also, no rationale is given for adopted criterion for the time limit of rainfall extension over the measured duration. ...
Commonly applied in Poland, the Błaszczyk equation of 1954 for design rainfall is based on not quite reliable data and the approach presented therein raises serious doubts concerning the correctness of the method. Of course, not only the scarcity of the then data bases should be taken into account, but also computational difficulties existing in those years. However, independently of these problems, there was no rationale for accepting 67 years as the length of the observation series when the actual number of observation years was 37. As a consequence, the resulting design rainfall intensities for given exceedance probabilities were lower than the values that would be obtained if the correct length of the observation series had been adopted. There is also second critical point of the discussed method: the estimation procedure of the model parameter is incompatible with that presented in the paper and, moreover, is clearly erroneous. ...
Four methods of forecasting: „no-change", LOESS, local linear regression and Holt-Winters were applied to annual minimum water levels observed at ten cross-sections of two tributaries of the Vistula river. The 1-, 2-, ..., 5-year forecasts were made for each year after some initial year, and four quality measures: bias, root mean square error, mean absolute error and maximum absolute error were calculated for each time series and lead time. The naïve model turned out to be always the worst in it bias and almost always very good, sometimes the best regarding the other measures.
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The analysis of time variability of riverbed elevation recorded at four cross-sections of two rivers: Raba and Dunajec was made. The causes of very intense erosion were pointed out, namely: intensive sediment extraction, inadequately carried out river training works including shortcuts and narrowings of riverbeds, and constructions of hydro-technical facilities, disrupting the continuity of sediment transport along the river length. Forecasting was carried out using a local weighted regression method, LOESS. In order to examine how far the length of the historical series influences the quality of forecasts, a comparison was made between the 5-year forecasts based on the 5-year history and the 5-year forecasts based on the 10-year history. The results suggest the need for preliminary data analysis before using a particular version of the model in or-der to take into account the type of variation exhibited by the historical series. ...
All uninterrupted time series of annual maximum flows of size at least 30 recorded in the period 1951-2016 in the Upper Vistula River catchment, were taken into trend analysis. Each of the 138 time series ended not earlier than in 2012. To estimate the trend, the nonparametric Theil-Kendall linear regression method was used. After removing the trend, lag-1 Kendall rank autocorrelation coefficient was calculated and, if the coefficient was significant at 5% level, was used to correct the variance of the Kendall S statistic which otherwise remained unchanged. Finally, the variance-corrected Mann-Kendall trend test was used, detecting 22 significant (at 5% level) linear trends of which only two were the effect of autocorrelation. All 138 significant and non-significant trends showed certain areal clustering clearly visible on the map of the catchment, which suggested dividing the area into three parts according the direction of trend and/or the number of statistically significant trends. Generally, the trends in the southern of the Upper Vistula River catchment are increasing, the opposite is true for the northern part. This finding does not concern the north-west part of the catchment where both kinds of trends are observed, which may be explained by strong anthropogenic influence. ...
