Dear Naveed,

Typically, a 95% significance level is seen as convincing evidence of a trend identified using Mann Kendall and Sen Slope statistics. Having said this, I am curious as to why you are using daily data for your study. It is relatively easy to identify significant trends in daily data collected from any region with a high degree of seasonality. A daily temperature time series that starts in the winter and ends in the summer would have a statistically significant increaisng trend, but it would not be terribly meaningful. This is perhaps wher eexpert judgement comes in. If you have 30+ years of daily data that you use to extract monthly statistics (e.g. mean, maximum and minimum daily temperatures observed during that month) and then subject these data to a seasonal Mann Kendall analysis, you should generate a robust estimate of long term trends, and their associated significance.

Sincerely,

Martyn

Dear Naveed,

There is no unique answer to your question, because it all depends how you are going to use that information. The climate community does not recommend specific levels of statistical significance in absolute terms, outside of any particular application.

In general, the answer to that type of question is determined by conducting a cost-benefit analysis or some similar investigation, where the pros and cons of different levels of significance are taken into account.

For instance, let's say, for the purpose of the argument, that a positive trend in temperature "in high altitude mountainous region" results in melting glaciers, which can cause floods (when the melt occurs too fast) or droughts (once the ice has disappeared). Hence, the Government may be interested in building dams to keep some of the water in place and regulate the flow. Dams are expensive to build, especially in remote or high-altitude locations, so there is a risk of financial loss if the dam is built but actually not required (or built in the wrong place), while there is also a risk of financial loss if the dam is not built and exceptional melting created floods and landslides.

If dams are built everywhere, there will be very large investments, and not all of them may be useful. If no dams are built, potentially large populations may be at risk, and rescue and recovery activities can also be quite expensive. In such a situation, there is often (though not necessarily always) an optimum solution where some dams are built and some resources are set aside for emergencies, which is cheaper than either of the extreme options mentioned above. Economists would evaluate the risks of different scenarios, based on their probability of occurrence, and therefore require information on the degree of certainty associated with a given rate of warming. Hence, the determination of that economic optimum may be based on the degree of reliability (or statistical significance) one can assign to the trend, as derived from the underlying climate data. And by the same token, a different user may want to use a different level of significance for another application.

Of course, these comments are not intended to mean that financial costs are the only, or even the main criterion that should be used in this case: this is just an example to show that a quantitative approach to the solution of a complex issue may require climate information with a known level of significance, because of the costs of making a wrong or sub-optimal decisions.

Please remember also that, again in general, the more you insist on being very sure about the validity (statistical significance) of a result, the more limited the applicability of the method. Again, returning to the previous example, if you have data for multiple stations within the mountainous region, some will exhibit trends with a higher level of significance than others.

Lastly, you can also try to answer a similar but slightly different question: in the latter case (multiple stations), you can calculate at which level of significance each station exhibits a positive trend, and then use that information instead.

I hope this may help you. Best regards, Michel.

Dear Dr. Martyn,

Sir, first of all many thanks for your detailed answer. My research area has one of the most threat to Climate change and this trend of temperature during winter and autumn is meaningfully significant.

I have more that 50 years of daily data and I have done my analysis on Regional Scal, Annual, Seasonal and also on individually stations for each month using mean monthly Tmax, Tmin Tmean. For all these analysis I do analysis for 95% significance level.

Now, I am working on climate extreme indices defined by WMO and my analysis results are about 10% significant at 95% level while 35% results are significant 99% and rest of them at 99.99%. That's why I was asking for expert opinion.

Regards

Naveed

Dear Naveed,

It sounds like your data support a hypothesis of non-stationarity in climate extreme indices in your region. However, I would urge caution in the interpretation of p-values. For the case of spatially correlated data (e.g. climate indices), the estimated p-values may be biased as the input data do not satisfy the most rigorous assumptions of the trend test.

Douglas et al. (2000) present an informative review of this problem and its consequences for assessing trends in floods and low flows in the US. I think the ideas they present may be relevant for your study.

Sincerely,

Martyn

Douglas, E.M., Vogel, R.M. and Kroll, C.N., 2000. Trends in floods and low flows in the United States: impact of spatial correlation. Journal of hydrology, 240(1-2), pp.90-105.

Deer Dr.Martyn and Dr.Michel,

Sir, many many thanks for your detailed guidance.

Regards

NaveedAhmed.