Hi Summera,

It's virtually impossible to help you without any further information because your question is very vague.

Please indicate first what data you have access to (nature, amount, geographical and temporal coverage, accuracy, etc.), how you got hold of them (where you obtained the data, who collected those in the first place, how they were measured, etc.), and why you think those data are inhomogeneous.

Specifically, what do you mean by inhomogeneous data? Are there missing data points? Do you suspect the presence of outliers? Do you think those data were acquired with uncalibrated or poorly calibrated instruments? Are the values internally inconsistent? Or do you have evidence of incompatibility with independent evidence? What is your criterion for establishing inhomogeneity? In other words, why do you think there is a problem, and what exactly is its nature? When that is clearer, it may be possible to provide you with some advice.

Michel M. Verstraete I am using gauge data for temperature and precipitation.

For few stations, data ranges from 1961 to 2019 and for the other it ranges from 1995-2019.

It is daily data.

I have applied homogeneity test using XLStat. (Petit, SNHT, Von-Neumann, Buishand test) at daily, monthly, seasonal and annual scale.

Most of the time series are found to be inhomogeneous at different temporal resolutions.

However, I am more interested in daily data.

I want to further use these time series to predict trend and then want to use it to know there effect on water resources.

@Summera,

I am still somewhat confused about your data and objectives. In your first message, you talked about "water resources", "watershed" and "gauges" so I thought you were trying to analyze river flow data. In your second message you mention measurements of "temperature and precipitation", which would be weather data instead. Please clarify as there are important differences between those variables, especially in terms of continuity.

I was not familiar with XLStat, so I explored the features of this package on Internet. Could you please confirm that you have applied those tests (Pettit, SNHT, Von-Neumann, Buishand) to each individual time series? If so, are you getting the same results for temperature and precipitation at each location? In that case, those results suggest that the mean values of the corresponding distributions change in time. This would not be very surprising if your watershed of interest experienced droughts or floods during the periods for which you have the data. Remember also that temperature may be more continuous than precipitations, which are intrinsically discrete events.

In any case, many time series are inhomogeneous in that sense (variable mean value at different times and over different periods), but that does not mean one cannot do anything with those data. You just need to use appropriate tools, depending on your objectives. In general, non parametric statistics may be more suitable than standard approaches. You may also want to model your data using Markov chains, for instance.

There may also be usable complementary sources of data for your problem: Where is your watershed? How large is it? What exactly do you mean by "sparsely located"? Large weather and climate research institutions such as the European Centre for Medium-Range Weather Forecasts (ECMWF) run atmospheric general circulation models in "reanalysis mode" to generate detailed descriptions of the past states of the atmosphere that are compatible with the limited amount of historical data available: Search the web for "ERA-40" to get more information on this approach. These reanalyses might provide either an alternative or a supplementary source of data for your problem, depending on the size of your area of interest and your expectations in terms of spatial resolution.

Good luck with your investigations. Michel.

Michel M. Verstraete

Thank you very much for your response.

I am working on Upper Indus Basin, which has few gauging stations.

I am attaching XLSTAT results for one gauging station (homogeneity analysis of daily precipitation time series).

12 change points in the series have also been detected using RH_dailyprcp test.

Since I have no metadata available.

So it cannot be confirmed that whether this inhomogeneity is due to natural climate change or due to some human/instrumental error.

So what should I do now as inhomogeneous series may give false increasing/decreasing trends.

I am new to climate studies.

Any help will be much appreciated.

Dear Summera,

I guess your question may regard to rough error removal of precipitation measurements that you called inhomogeneous. Rough error can come from different sources such as from human, animals, failed trees... I think if this measurements change a lot the your trend, you just avoid them (delete) or replace them by long-term mean annual data of the same day.

Hopefully it helps.

Best,

Quang