Definition
Precipitable water (PW) is defined as the integral of the water vapour content of the atmospheric column and is expressed in mm. It is given by the relationship below where q represents the specific humidity of the atmosphere (kg/kg), p the pressure (Pa) and g the gravity. The integral is calculated between the surface and the top of the atmosphere. In short, PW represents the amount of precipitation that would be produced if all the water vapour in a column of air were to condense.
Link between rainfall and precipitable water
The link between PW and rainfall is illustrated in Figure 1 opposite.
It shows observed rainfall as a function of PW values for four different regions (West Africa is in yellow).
An important property is that hourly and daily precipitation increase with the value of PW: the greater the PW, the greater the precipitation. However, this increase is not linear (regular). There is in fact a threshold effect around 40 / 45 mm depending on the region and the temperature of the troposphere. This is illustrated by the three panels opposite, where the PW/rainfall relationship is shown for 3 values of mean tropospheric temperature.
For example, for a rainfall of 0.5 mm/h, the value of PW increases from 55 mm for a temperature of 270 K to a value of 60 mm when the temperature is 272 K. This implies that the threshold value for triggering rainfall or for obtaining a given rate of precipitation decreases with atmospheric temperature. For example, for PW=50 mm, rain will be heavier if the atmosphere is “cold” than if it is warm.
In the Sahel, an empirical value for rainfall onset > 1 mm/d is around PW=40-45 mm. This is illustrated in the figure on the right for Senegal (red dots). You can also consult the documentation on the convective systems object for more details.
Modulation by equatorial waves
Temporal evolution
Modulations are the result of a balance between several mechanisms, or processes described by the equation below:
The local evolution of PW is thus a function of evaporation (E), precipitation (P) and a term of convergence of moisture fluxes integrated over the vertical. Evaporation strengthens PW, while the occurrence of precipitation reduces PW (this is the fuel for deep convection). One of the advantages of working with PW lies in this moisture convergence term. When there is humidity convergence (or advection of more humid air), the value of PW increases.
Local changes in PW are shown in the figure opposite for Dakar (Senegal). During the period from late June to early July, we can see dry phases where PW ~ 35 mm, with PW values too low to trigger rainfall, and wetter phases during which PW reaches 50 or even 58 mm. By analysing changes in PW, it is possible to anticipate rainfall. This type of graph combining observation and forecasting is available in the forecast time series (link here for the deterministic model and here for the ensemble forecast).
Spatial coherence between rainfall and PW
The strengthening of the monsoon flow and the passage of a wave can, for example, transport PW and modify it locally. The figure on the right shows the moment when the PW wet anomaly associated with an AEW crosses 0°E.
The lower figure shows an alternating dry and wet anomaly bounded by a southerly flow (trough) and a northerly flow (ridge). The link with rainfall is shown in the figure above. The precipitation maximum (of the precipitation anomaly) is centred on the PW maximum and corresponds to an OLR minimum. This marked PW structure propagates from east to west with very good temporal coherence. Note the amplitude of the wet PW anomaly, around 5-10 mm, which allows a PW of 40 mm – too low to trigger rain – to rise to a value of PW=45-50 mm, which is sufficient to generate precipitation.
If we look again at the temporal evolution of PW over Dakar (Fig. 2), we can better understand the variations in PW: the low values of PW ~ 30 mm correspond to negative anomalies of PW compared with the climatology (in grey on the figure) and reflect the dry phase of the African Easterly Wave. This was the case from 4 to 6 July, for example, with values of PW ~ 27 mm compared with the climatological value of 37 mm, corresponding to the situation described in Figure 3: a dry anomaly ahead of the wet anomaly, of around -5, -10 mm.
Once the dry phase had passed, the wet anomaly (or phase) arrived from 6 to 9 July, with PW values of around 10 mm above the climatology.
Precipitable water is potentially modulated by all equatorial waves, although in practice it is mainly the AEW and equatorial Rossby waves that have the greatest impact on PW. In order not to miss a wet anomaly associated with a wave, one of MISVA’s flagship products is the PW intraseasonal anomaly map, which aggregates the effect of all the waves on the evolution of PW. This forecast product and its documentation are available here, by activating the parameter PW.
PW interest in rainfall forecasting
Correlation forecasts and observations
The advantage of working with PW is to have a rain predictor whose spatial and temporal evolution is less noisy than rain, and therefore more predictable. The figures illustrate this point, which is central to the MISVA approach.
The figure above shows a comparison of the mean rainfall (top) and PW (bottom) evolutions over two seasons in West Africa. Despite averaging over a large area, the noisy nature of rainfall compared with PW is clearly visible. A succession of rainfall peaks and troughs can be clearly seen during the monsoon with the observations (black) and to a certain extent for the forecasting models, which have a general tendency to underestimate rainfall (especially mean values). The performance of deterministic forecast models is indicated by correlations with TMPA-3B42 satellite observations. These correlations are of the order of 0.6-0.7, bearing in mind that this is an average over a large area, with correlation values at the grid point being of the order of 0.1-0.3. By contrast, PW shows a much smoother time evolution, with correlation values in excess of 0.98 for all models. This is very important information and shows that PW is better predicted by the models than rain. The mean values are also of the same order of magnitude between observations and forecasting models.
Precipitation and PW biases in forecasting models
The figure opposite gives an idea of the precipitation and PW biases of the ECMWF forecasting model. It shows a rainfall deficit north of 10°N over the entire Sahelian strip and a rainfall surplus between the coast and 10°N. This bias in weekly rainfall is repeated on a daily scale and makes it difficult to have confidence in the rainfall forecast by ECMWF, since it is unable to predict the rainfall events that contribute to the weekly average.
The PW forecast has a very low bias, of the order of 2 mm, which means that we can be confident in the PW values given by the forecast. This is an important point given the threshold effect that exists between PW and rainfall. This threshold is a priori well predicted by the ECMWF forecast model.
PW evaluation for the forecast of AEWs
The last point addressed here concerns the forecasting of PW anomalies associated with African Easterly Waves (AEW). The previous figures show that the ECMWF forecast model behaves well overall in terms of correlation and bias.
The figure opposite shows how a wet anomaly observed over Senegal on D0 is predicted by the forecasts initiated a few days earlier. The analysis at D0 (top figure) shows the typical structure of an AEW with a wet pole surrounded by dry anomalies on its eastern and western flanks. The forecast initialised at D-3 reproduces this structure with a good degree of realism, both for the spatial structures and the intensities of the anomalies. For the 6 and 8 day forecasts, we still find the AEW signal over Senegal in terms of structure, but with a weaker signal.
The ECMWF model is therefore able to forecast the evolution of an AEW, at least its occurrence, but not all of its intensity up to 8-10 days ahead. This gives a strong potential for predictability to the PW anomaly, whose precipitation signature can be deduced from Figure 4 described above.
