Concept¶

The objective of this module is the adjustment of radar-based rainfall estimates by rain gage observations. However, this module could also be applied to adjust satellite rainfall by rain gage observations, remotely sensed soil moisture patterns by ground truthing moisture sensors, or any dense spatial point pattern which could be adjusted by sparse point measurements (ground truth).

Basically, we only need two data sources:

• point observations (e.g. rain gage observations)
• set of (potentially irregular) unadjusted point values (e.g. remotely sensed rainfall)

[Goudenhoofdt2009] provide an excellent overview of adjustment procedures. The general idea is that we quantify the error of the remotely sensed rainfall at the rain gage locations, assuming the rain gage observation to be accurate.

The error can be assumed to be purely additive (AdjustAdd), purely multiplicative (AdjustMultiply, AdjustMFB) or a mixture of both (AdjustMixed). If the error is assumed to be heterogeneous in space (AdjustAdd, AdjustMultiply, AdjustMixed), the error at the rain gage locations is interpolated to the radar bin locations and then used to adjust (correct) the raw radar rainfall estimates. In case of the AdjustMFB approach, though, the multiplicative error is assumed to be homogeneous in space.

Quick start¶

The basic procedure consists of creating an adjustment object from the class you want to use for adjustment. After that, you can call the object with the actual data that is to be adjusted. The following example is using the additive error model with default settings. obs_coords and raw_coords represent arrays with coordinate pairs for the gage observations and the radar bins, respectively. obs and raw are arrays containing the actual data:

adjuster = AdjustAdd(obs_coords, raw_coords)


Both obs and raw need to be flat (1-dimensional) arrays of shape (n,) that have the same length as the the obs_coords and raw_coords arrays, respectively.

The user can specify the approach that should be used to interpolate the error in space, as well as the keyword arguments which control the behaviour of the interpolation approach. For this purpose, all interpolation classes from the wradlib.ipol module are available and can be passed by using the ipclass argument. The default interpolation class is Inverse Distance Weighting (Idw). If you want to use e.g. linear barycentric interpolation:

import wradlib.ipol as ipol


Warning

Be aware that there are a lot of control parameters that can dramatically influence the behaviour of the adjustment (which gauges are considered, how is an error interpolation carried out, …). Read the docs carefully and try to experiment with the effects of the different control parameters. There might be situations in which the algorithms decides - based on the control parameter - not to do an adjustment and just return the unadjusted values.

Cross validation¶

Another helpful feature is an easy-to-use method for leave-one-out cross-validation [Cross-validation]. Cross validation is a standard procedure for verifying rain gage adjustment or interpolation procedures. You can start the cross validation in the same way as you start the actual adjustment, however, you call the xvalidate method instead. The result of the cross validation are pairs of observation and the corresponding adjustment result at the observation location. Using the wradlib.verify module, you can compute error metrics for the cross validation results:

adjuster = AdjustAdd(obs_coords, raw_coords)

 AdjustBase The basic adjustment class that inherits to all other classes. AdjustMFB Multiplicative gage adjustment using one correction factor for the entire domain. AdjustMultiply Gage adjustment using a multiplicative error model AdjustAdd Gage adjustment using an additive error model. AdjustMixed Gage adjustment using a mixed error model (additive and multiplicative). RawAtObs Get the raw values in the neighbourhood of the observation points GageOnly Same behaviour as the other adjustment classes, but returns an interpolation of rain gage observations AdjustNone Same behaviour as the other adjustment classes, but simply returns the unadjusted data.