TRENDS IN RIVER RUNOFF IN LATVIA FOR THE PERIOD 1951–

A time series of monthly, seasonal and annual mean specific runoff of rivers in Latvia are analysed in order to detect trends for the period 1951–2020. Trend analysis is performed by applying the Mann-Kendall test and the trend slope is calculated using Sen’s method. There were significant seasonal changes in the time series of specific runoff measured at 32 stations during the study period. In all hydrological regions, the trend values obtained for the winter season are statistically significant, but they are relatively weaker in the Eastern region. At the same time, river runoff in April and May has notably decreased, indicating a shift of the runoff maximum to an earlier time. Long-term changes in specific runoff are statistically significant in April in all hydrological regions, and only in May for the Eastern region. Generally, statistically insignificant trends in specific runoff are observed for the summer and autumn months. Annual mean specific runoff has not revealed any strong trends in spite of the increased precipitation and temperature. Clear seasonal changes have been found in several earlier studies in the Baltic countries, and they are confirmed by the current one.


Introduction
The Baltic Sea basin is among the most sensitive regions in the world to global warming, which was stated in the first BACC (2008) assessment and is still valid in the current situation (Meier et al., 2022).This has encouraged the development of many studies of the warming climate and its impact upon hydrological processes at various spatial and temporal scales.The highest number of studies are summarised in the assessment of BACC Team (2008;2015) and by Meier et al. (2022), which also includes the Baltic countries.The authors of these studies found that increasing trends in river runoff were characteristic of the winter season during the 20 th century (Jaagus et al., 2017) and the beginning of 21 th century.By contrast, the spring season is characterised by a decrease in runoff.By applying different hydrological models, changes in river runoff in this region were modelled for the case of continuous climate warming.The results indicated continuous increase in runoff in winter and decrease in spring, which could lead to drought and flood conditions in different seasons at the end of this century.
Long-term fluctuations in climatic parameters are reflected in the dynamics of river runoff that has a relatively short residence time (Jaagus et al., 2017).River runoff in Latvia is characterised by significant seasonal and interannual variability.It is mostly caused by precipitation variations and snow conditions during winter and the period of melting in spring.The runoff regime is also affected by physiographical conditions, including hydrographical and hydrogeological ones, where relatively large differences can be found among different rivers' catchment areas in Latvia.Long-term changes and variability in river discharge in Latvia has been analysed by many authors within the context of the Baltic countries (Reihan et al., 2007;Kļavinš et al., 2009;Reihan et al., 2012;Kriaučiūniene et al., 2012;Sarauskiene et al., 2015) and within the context of a single country (e.g.Kļaviņš & Rodinovs, 2008).One recent study was conducted by Apsīte et al. (2013), during which two periods of study (1951-2009 and 1881-2009) were analysed.The study revealed that a long-term trend analysis of two periods of study for the same river and hydrological station mostly indicated the same significant changes in the monthly, seasonal and annual discharge regime.
This study represents a new contribution, and is motivated by a scientific interest to find out if the last ten years have changed the nature of the trends.In order to answer this question, the objective of our study is an analysis of long-term seasonal changes, i.e. trends, in specific runoff of rivers in Latvia within four hydrological regions, using the updated time series for the period 1951-2020.

Data and methods
A data series of daily discharge registered by 32 river hydrological station was used in this study (Figure 1).The data were obtained from the Latvian Environment, Geology and Meteorology Centre (LEGMC).Missing data were taken from CD (Zīverts & Strūbergs, 2000) or calculated from adjacent monitored river basin, using linear regression analysis where the coefficient of determination is r 2 ≥ 0.7.Specific runoff of rivers was used because it allows observed data from river basins of different size to be compared and results of statistical analysis to be assessed.Specific runoff was calculated as follows: discharge value distributed with catchment area and multiplied by 1,000.Monthly, seasonal and annual specific runoff values for the period of 1951-2020 were used.Seasons were defined as three months, as is usual in hydro-climatological studies: spring (MAM), summer (JJA), autumn (SON) and winter (DJF).
As a rule, hydrological data are not normally distributed and are characterised by positive skewness.Therefore, the non-parametric Mann-Kendall test is applied to detect trends in time series.The test is distribution-free and robust to missing data and outliers (Libiseller & Grimvall, 2002).In Europe, the Mann-Kendall test is the most widely used test of discharge trend analyses (Madsen et al., 2014).The trend magnitude was calculated by applying the non-parametric linear Sen's slope estimator.
The Theil-Sen estimator is more robust than the least-squares estimator because it is much less sensitive to outliers.Trend values are presented by changes per decade.The p<0.05 level was used for critical significance.Trends are considered statistically significant at p<0.05, p<0.01 and p<0.001 levels were presented in the results.The computer software program MAKESENS was used for calculating trends (Salmi et al., 2002).
The classification of hydrological regions by Glazacheva (1980) was used, according to which the country is divided into four regions: Western, Central, Northern and Eastern.

Results and discussion
Results of the trend analysis by applying the Mann-Kendall test are presented in Table 1 in a generalised form within the four hydrological regions and in Latvia as a whole.If the mean trend value was positive, then all trends at the stations would also be positive and vice versa.
In the middle latitudes snow accumulation and melting presently dominate in the hydrological regime.Warmer winters are naturally related to higher runoff in winter and early maximum in spring after the snowmelt that is typical for the Baltic countries.Also in this study during 1951-2020, a major significant changes in specific runoff of rivers have observed in the winter and spring seasons in all hydrological regions and total in Latvia (Figure 2).In winter season the runoff of rivers increase (trend values varies from 0.55 to 1.22 L s -1 km -2 per decade -1 ) and the trends are upward due to milder winters and early snowmelt.All changes are statistically significant at p < 0.001, but in the Eastern region at p < 0.01.At the same time, the trends obtained for the spring season are statistically insignificant, as the spring months (March, April and May) do not reveal the same pattern of change.In the Western hydrological region, specific runoff of rivers increased more significantly in January and February.Moreover, in the Central, Northern and Eastern regions, more significantly runoff increase in January, February and March.All changes are at p < 0.001 and p < 0.01 levels of significance.The highest increase was detected in the Western district: trend values vary from 1.11 to 1.49 Ls -1 km -2 per decade -1 .The lowest increase was obtained in the Eastern region where trend values vary from 0.59 to 1.01 L s -1 km -2 per decade -1 .Downward trend in streamflow was detected in April and May in all hydrological regions.Long-term changes are statistically significant at p < 0.01 in April and at p < 0.05 in May for the Eastern region.In April the highest decrease in specific runoff was detected for the Central region, where the trend value is -1.72 L s -1 km -2 per decade -1 .The lowest decrease in runoff was observed for the Western region, where the trend value is -1.13 L s -1 km -2 per decade -1 .
In the Western part of Latvia, greater impact of meteorological processes occurring over the North Atlantic and the Baltic Sea on the river hydrological regime is observed than for other parts in Latvia.This influence decreases from west to east with the eastward increase of continentality.Furthermore, in western and central hydrological regions comparatively shorter ice-cover and thinner snow cover was also observed, resulting in earlier onset of spring flooding.The Eastern region is characterised by more continental climate conditions than the others, i.e. warmer summers and colder winters with thick snow cover.Spring floods of rivers begin later and their duration is longer (Apsite et al., 2013).
Generally, statistically insignificant trends in specific runoff are observed for summer and autumn months.However, mean specific runoff has significantly increased in some rivers (e.g. in the rivers Venta, Imula, Lielupe, Mūsa, Salaca and Aiviekste) in June and July.This could be due to an increase in precipitation in June for the Western, Central and Eastern regions for the period 1950-2020.Another specific feature emerges: the river runoff decreased in September and October.The highest decrease in trend values was detected in the Eastern region while the lowest decrease was seen in the Western region.According to Jaagus et al. (2016) this could be explained by warmer autumns, and increased evapotranspiration and decreased precipitation in September.
Similar to the findings in a study conducted in Estonia (Jaagus et al., 2017), our results indicate that, despite the increase in precipitation and temperature, the annual mean specific runoff did not show any significant trends.A statistically significant change in runoff was found in some rivers (the rivers Lielā Jugla, Salaca and Vaidava) and in Western region (the rivers Irbe, Užava and Rīva).
The results of this study are in line with previous studies in the Baltic countries (e.g.Kļavinš et al., 2009;Reihan et al., 2012;Kriaučiūniene et al., 2012;Apsīte et al., 2013;Jaagus et al., 2017), indicating major significant long-term changes in river runoff during the last few decades between the winter and spring seasons.

Conclusion
Changes in streamflow during the 20 th century and the beginning of the 21 th century revealed a redistribution of runoff over the year, with a significant increase in winter in all hydrological regions and a tendency for decreasing spring floods particularly in the Central and Eastern hydrological regions.In this study, by using the updated time series of 1951-2020, the trends in river runoff duration in Latvia has not changed very much in comparison with the results of the previous study for the period 1951-2009.The obtained results of trend analysis could be considered as logical consequences of the climate warming that is projected in Latvia.

Figure 1 .
Figure 1.Location of river hydrological stations and hydrological regions of Latvia.Hydrological regions: I-Western; II-Central; II-Northern and IV-Eastern (I.Vinogradov's figure based on data from the LEGMC and Glazacheva, 1980)

Figure 2 .
Figure 2. Trends of mean specific runoff of rivers in Latvia (seeTable 1) (authors' figure based on data from the LEGMC and Zīverts & Strūbergs 2000)

Table 1 . Trend values of spatially averaged monthly, annual and seasonal mean specific runoff of rivers (L s -1 km -2 per decade -1 ) within each hydrological region and in Latvia as a whole in the period 1951-2020. Total number of stations for each hydrological region and Latvia as a whole is indicated in brackets
(authors' calculations based on data from the LEGMC and Zīverts & Strūbergs 2000)