IRMA - Integrated Relative Modelling Approach

What does the model do?

IRMA is a semi–empirical statistical model. The core version was introduced in Wechsung et al. (2008). It relates inter–annual yield changes of agricultural crops to inter–annual changes of predefined timely aggregated climate variables as the photo–thermal quotient, potential evapotranspiration, precipitation. The energy dependence of assimilation on the incoming photosynthetic radiation, the losses of assimilates by the temperature driven respiration, the request of water for evapotranspiration and the supply of water by precipitation are reflected by the terms of the model. The term definition follows basic plant physiological reasoning about plant growth. It is not derived from correlation analysis. Therefore, we use the term semi–empirical to distinguish it from fully empirical models.

IRMA is mainly aimed at regional application, but can also be applied at experimental test sites. For regional application the model is formulated, parametrized and simulated at the sub–unit scale (county, sub–basin), and then aggregated for the unit scale of interest (state, country, basin). The model can be used to project the yield changes for an upcoming single year and a projected sequence of years, respectively. The yield changes are related to the last observed year and can be rescaled to the mean or another sub–set of observed years. Spatial correlation maps of the model terms can be used to substantiate the model outcome (Gornott &  Wechsung, 2016).

There are three parametrization schemes available. The model can be estimated per sub–unit as separate time series model (STSM), across all sub–unit with one slope and one intercept (due to the usage of first differences) as panel data model (PDM) and as random coefficient model (RCM) with slopes and intercepts that randomly normal distributed diverge from the mean values. Usually the STSM is best performing in out–of–sample validations for comprehensive data sets (Gornott &  Wechsung, 2016). However, PDM’s and RCM’s have advantages when data are missing at the sub-unit scales.

The model scheme is particularly suitable for annual weather and climate impact assessment.  The usage of annual yield changes eliminates trends that can be approximated by an exponential formulation. The remaining variability at the sub–unit scale is therefore mainly due to climate factors. The usage of normalized independent variables allows a direct combination of the model with weather and climate models without bias correction.

The model was applied at the regional scale for Eastern Germany (Lüttger et al., 2011, Wechsung et al., 2008), at the national scale for Germany (Conradt et al., 2016, Gornott &  Wechsung, 2016) and at the global scale (Schauberger et al., 2017). Recently the model was used to access the consequences of the drought in 2018 and 2019 on German wheat yields (Conradt, 2018, Conradt, 2019)

What are the next steps in the development of the model architecture?

The IRMA core model is flexible for expansions in formulation and parametrization. The original model formulation was expanded by climatic (Lüttger et al., 2011, Schauberger et al., 2017) and economic terms (Gornott &  Wechsung, 2016) already. However, the extension ideally allows the integration in a pre–defined scheme as the number of heat and frost days that were suggested in Schauberger et al. (2017). Otherwise, the model terms lose ground for regional substantiation and become more empirical. Upcoming specification of the model will particularly address the Temperature response of the model. The impact of an increased atmospheric CO2 concentration on projected crop yields under climate change can be taken into account by external correction of the yield outcome as suggested in (Wechsung et al., 2008). A modification of this approach might follow.

The model parametrization was expanded already from STSM to PDM and RCM for a given structure of scales. Conradt et al. (2016) has combined the STSM concept with a cluster approach for defining a most promising direction of aggregation.

The model application does not request a specific software shell. It is implemented in SAS and R. Other software might be suitable as well. Support for application can be given on request.

Who maintains it?

Frank Wechsung (SAS), Christoph Gornott & Tobias Conradt (R.)

Key publications

Conradt T, Gornott C, Wechsung F (2016) Extending and improving regionalized winter wheat and silage maize yield regression models for Germany: Enhancing the predictive skill by panel definition through cluster analysis. Agricultural and Forest Meteorology, 216, 68-81.

Gornott C, Wechsung F (2016) Statistical regression models for assessing climate impacts on crop yields: A validation study for winter wheat and silage maize in Germany. Agricultural and Forest Meteorology, 217, 89-100.

Lüttger A, Gerstengarbe FW, Gutsch M et al. (2011) Klimawandel in der region Havelland-Fläming. In: PIK Report. pp Page.

Schauberger B, Gornott C, Wechsung F (2017) Global evaluation of a semiempirical model for yield anomalies and application to within-season yield forecasting. Global Change Biology, 23, 4750-4764.

Wechsung F, Lüttger A, Hattermann F (2008) Projektionen zur klimabedingten Änderung der Erträge von einjährigen Sommer- und Winterkulturen des Ackerlandes am Beispiel von Silomais und Winterweizen. In: Die Ertragsfähigkeit ostdeutscher Ackerflächen unter Klimawandel. (eds Wechsung F, Gerstengarbe F, Lasch P, Lüttger A) pp Page, Potsdam, PIK.

Wechsung, F., Gerstengarbe, F.-W., Lasch, P. and Lüttger, A. (2008): Die Ertragsfähigkeit ostdeutscher Ackerflächen unter Klimawandel, PIK Report N°112, Potsdam, S. 98.