I don't think there is a best model for this type of analysis. It depends heavily on the characteristics of the data and on the the statistics you are concerned with. In general, if you are looking at annual mean flows, for instance, where serial correlation is seldom an issue, Mann-Kendall e Spearmen-rho tests are very often used for monotonic trend. They have basically the same performance. Sen's slope and Mann-Kendall-Sen procedure can also be used. If you are sure your data is independent and normally distributed, a linear regression (least square square estimation of the trend) procedure is certainly the best option, although it is hard to be sure about this assumption. If the data has seasonal components, one needs to take that into account. You can use the Seasonal Kendall test (Hirsch and Slack (1984)) or you can apply an appropriate technique to remove the seasonality. If the data is serially correlated, things get more complicated. There are many different techniques to be used in this situation.

There is also the possibility of applying a regional analysis, often called field significance. But I am not sure if it is what you are looking for.

I suggest you take a look at the following papers to have a better understanding of these issues:

Gocic, M., & Trajkovic, S. (2013). Analysis of changes in meteorological variables using Mann-Kendall and Sen's slope estimator statistical tests in Serbia. Global and Planetary Change, 100(C), 172–182. doi:10.1016/j.gloplacha.2012.10.014

Hamed, K. H. (2008). Trend detection in hydrologic data: The Mann–Kendall trend test under the scaling hypothesis. Journal of Hydrology, 349(3-4), 350–363. doi:10.1016/j.jhydrol.2007.11.009

Hirsch, R. M., & Slack, J. R. (1984). A nonparametric trend test for seasonal data with serial dependence. Water Resources Research, 20(6), 727–732.

Hirsch, R. M., Slack, J. R., & Smith, R. A. (1982). Techniques of trend analysis for monthly water quality data. Water Resources Research, 18(1), 107–121.

Khaliq, M. N., Ouarda, T. B. M. J., & Gachon, P. (2009a). Identification of temporal trends in annual and seasonal low flows occurring in Canadian rivers: The effect of short- and long-term persistence. Journal of Hydrology, 369(1-2), 183–197. doi:10.1016/j.jhydrol.2009.02.045

Khaliq, M. N., Ouarda, T. B. M. J., Gachon, P., Sushama, L., & St-Hilaire, A. (2009b). Identification of hydrological trends in the presence of serial and cross correlations: A review of selected methods and their application to annual flow regimes of Canadian rivers. Journal of Hydrology, 368(1-4), 117–130. doi:10.1016/j.jhydrol.2009.01.035

Yue, S., Pilon, P., & Cavadias, G. (2002). Power of the Mann–Kendall and Spearman's rho tests for detecting monotonic trends in hydrological series. Journal of Hydrology, 259(1), 254–271.

Kulkarni, A., & Storch, Von, H. (1995). Monte Carlo experiments on the effect of serial correlation on the Mann-Kendall test of trend. Meteorologische Zeitschrift, 4(2), 82–85.

Zwiers, F. W., & Storch, Von, H. (1995). Taking serial correlation into account in tests of the mean. Journal of Climate, 8(2), 336–351.

Some good references listed by Dirceu above! We used a similar approach in our trend analysis of river flows in western Britain published in:

Harry Dixon, Damian M. Lawler and Asaad Y. Shamseldin 2006.

"Streamflow trends in western Britain"

GEOPHYSICAL RESEARCH LETTERS, VOL. 33, L19406, doi:10.1029/2006GL027325, 2006

The full paper is attached.

For the period 1962–2001, we analysed 11 quantiles of the Daily Mean Flow distribution from 56 river flow gauging stations, from low flow across the full flow spectrum up to high flows. Our method statement reads:

"Monotonic trends were analysed using the nonparametric

‘‘distribution free’’ Mann-Kendall test for the given

quantiles of the cumulative streamflow distribution [see

Lins and Slack, 1999]. A detailed explanation of the rank-based

Mann-Kendall hydrological trend test used here is

given by Kundzewicz and Robson [2000, 2004]: this is

often employed for flow trends [e.g., Bırsan et al., 2005;

Lettenmaier et al., 1994; Zhang et al., 2001]. Being

distribution free and robust with regard to outliers, it is

well suited to the analysis of streamflow time series which

tend to be non-normally distributed. An assumption made in this test is that the data are

not serially correlated."

Hope this paper, and others we and Dirceu cited, are helpful!

Damian Lawler

We wrote a second paper, which might also be of interest, on the effects of data record length on the flow trends which emerge from analyses. Record length is often crucial to the trend slopes and significance levels which are actually obtained through statistical analysis, and so careful decisions need to be made on the start and end points of the data period

Reference is (pdf copy is attached below, and other papers are on my profile):

Harry Dixon, Damian M. Lawler, Asaad Y. Shamseldin & Paul Webster. 2006.

The effect of record length on the analysis of river flow trends in Wales and central England. In: Climate Variability and Change—Hydrological Impacts (Proceedings of the Fifth FRIEND World Conference held at Havana, Cuba, November 2006), IAHS Publ. 308, 2006.

Abstract:

The detection of trends in hydrological variables is directly affected by the length of time series available for analysis and is of key importance to the global FRIEND community. Long-term (≤50 years) seasonal gauging station records from Wales and the English Midlands are analysed for different time spans up to 2001 to demonstrate the effect of record length on linear trend analysis. Non-parametric Mann-Kendall trend methods are applied to time series of different flow quantiles, and for different seasons, thereby assessing trends across the streamflow spectrum. Key differences are quantified between trends of varying record lengths, but the dominant trend is for streamflow increases at high and low flows over time periods greater than 30 years. The implications for the FRIEND community are widespread and support the need to maintain gauging station networks and maximise instrumental records.