The results you obtained for the comparison are quite characteristic; reasonable differences for temperature and large differences for (monthly) rainfall. Differences for daily rainfall will be even larger. The spatial variability of rainfall is much larger that that of temperature making GCMs less suitable for rainfall simulation. Most rainfall generating mechanisms are not explicitly solved by GCMs but rather parameterized and this often results in a poor simulation of temporal and spatial variability of rainfall at monthly scales and even more at smaller temporal (and spatial) scales.This is a smaller problem for the temperature, also because the energy balance in the primary focus in GCMs rather than the water balance.

Downscaling, often in combination with bias correction, is therefore a must for most impact assessments using GCM data as source data. Also because data from one (GCM) grid cell should preferably not be used in an isolated way, but rather patterns from GCMs should be used for impact assessments. If dynamical downscaling using a regional climate model is not feasible, statistical downscaling can be a good alternative.

Hope this helps,

Martijn

@Martijn,

Thanks for a reply.

Let's say GCM output is A and observed climate is B.

At, the first step, for overlapped periods, I compared GCM output and observed climate to get appropriate comparisons.

At the second step I adjust GCM future climate with the comparison I got in the first step.

Are two steps are enough to do prior to use GCM output in projecting the impacts of future climate on crop yield ?

Given the reservations I made in my previous reply, you might use GCM output in this more or less direct way. The adjustments/ bias correction of GCM output can be carried out in many different ways from simple correction of the mean (e.g. for rainfall by multiplication with a factor) to distribution-based corrections (e.g. distribution-based scaling, see for instance the paper below). If the differences between climate statistics relevant for crop yield for observed and GCM simulated data are too large, a downscaling method probably is necessary. For example a statistical downscaling method can be used in which large scale patterns simulated by the GCM are related to local scale variables such as rainfall and temperature.

Best wishes,

Martijn

Article Uncertainty in Future High Flows in Qiantang River Basin, China

Hi again,

I reproduce your previous reply:

"If the differences between climate statistics relevant for crop yield for observed and GCM simulated data are too large, a downscaling method probably is necessary."

How do we conclude that a deviation between climate output and observed climate is too large?

If the difference between observed and simulated climate statistics have the same order of magnitude as the change in these climate statistics due to increases in greenhouse gas concentrations (i.e. noise ≈ signal), the difference is obviously too large. It is very difficult to give strict criteria or rules, however for climate impact studies biases should be relatively small compared to changes.

I agree with the answer given above and only add that as far as temperature is concerned one would need to be careful about complex terrain features that are not well resolved by the GCM coarse grid. Perhaps dynamical downscaling in this case should be considered.

I think there are valid reasons to use GCM outputs directly. Can anyone please tell possible reasons to use GCM outputs directly?

 @Martijn,

Can you please tell me available methods to do bias correction ? I have observed climate (temp, rainfall) and climate outputs from climate models. Please tell methods to do bias correction.

We have good experiences with the distribution-based scaling method (see one of my previous answers and the paper in Journal of Hydrometeorology). Claudia Teutschbein and Jan Seibert give a nice overview of different methods in their paper in Journal of Hydrology (see attachment). Hope this helps.

@Martijn,

Thanks a lot for the attached article. Are there any software to conduct "distribution mapping methods" and "power transformation methods" ?

I am not aware of any ready-to-use software, but it might exist. Alternatively, you can use for instance MatLab (as my colleague did) or Phyton to do the relatively straightforward calculations.

@Martijn,

Are there any reasonable RMSEs for monthly precipitation (monthly temperature) ? and for seasonal/annual precipitation/temperature ?

What do you mean with RMSEs? For which purpose do you want to use RMSEs?

@Martijn,

I want to compare corrected monthly rainfall and corrected monthly temperature with observed monthly rainfall and observed monthly temperature. any appropriate RMSE ?

I would not use the RMSE (Root Mean Squared Error) since errors are squared so high values will have more influence than low values on the results. Instead, I would use a criterion assessing the absolute error in a relative way (i.e. the Relative Mean Absolute Error): [sum(Tc-To)/To]/N where Tc is the corrected temperature, To the observed temperature and N the total number of observations.

@Martijn,

Is that measurement (Relative Mean Absolute Error) only for comparison monthly climate (precipitation, temperature) or for comparison daily climate too ?

Daily variables can also be compared with the RMAE, in fact variables at any time scale can be compared with this criterion.

RMAE is an example of a criterion; other criteria might also be used depending on the purpose of the comparison. For your purpose (comparing corrected, modelled values and observed values) RMAE seems to be a good option.

@ Martijn,

May I conclude your answers as follows:

1). I should you RMAE instead of RMSE as my data is monthly precipitation instead of daily precipitation;

b). My question is:

if  (after bias correction) seasonal/annual rainfall has RMSE is about 200 mm and RMAE is about 11%.  Does this mean good corrected rainfall ?

You rather would like to use RMAE because this criterion more equally weights low, medium and high values instead of RMSE. This applies both for daily and monthly values.

An error of 11% (and 200 mm) is still a considerable error. With bias correction you would expect a negligible error in the mean value for the calibration period (for which you fitted the bias correction method) and a relatively small error for the validation period (less than 10% for the mean). However, it is difficult to assess these specific errors when not knowing the details.

Additionally, you might use the Relative Mean Error: [sum(Tc-To)/sum(To)]/N which could be and ideally should be 0. By the way, the formula mentioned before for RMAE should be [sum|Tc-To|/sum(To)]/N.

@ Martijn,

Can you please tell any gauge of RMSE for monthly rainfall, monthly temperature ? 

Could please tell me any details I should consider when compare RMSE before and after bias correction

What do you mean with 'any gauge'?

As mentioned before, it is difficult to give strict guidelines for magnitudes of RMAE or RMSE. In general, you would expect a significant decrease of these errors after bias correction. If this is not the case, the bias correction method is not the right one (or not working properly) or bias correction is not useful/ necessary.